TY - JOUR
AU - Lavoie,, Marc
AB - Abstract This article studies coordination between firms in a multi-sectoral macroeconomic model with endogenous business cycles. Firms are both in competition and interdependent, and set their prices with a markup over unit costs. Markups are heterogeneous and evolve under market pressure. We observe a systematic coordination between firms of each sector, and between each sector. The resulting pattern of relative prices is fairly consistent with the labor theory of value. These emerging features are robust to technology shocks. The most important subjects which economics seeks to investigate are ones which concern systems of many firms, or of all firms, which require consideration not only of how all firms, individually, behave, but also of how their individual activities interact and constrain each other, in markets, broad sectors and the whole economy. (Wood, 1971: 38) 1. Introduction Markup, or cost-plus pricing, is a convenient pricing heuristic in making what would otherwise be complex and difficult decisions in a world of uncertainty (Lavoie, 1992: 134). It is widely used in the industrial organization and macroeconomic literature, both in Dynamic stochastic general equilibrium models (hereafter DSGE) and agent-based models (hereafter ABMs), and it finds strong empirical support (see Fabiani et al. (2006) for a survey in the Euro area for instance). Indeed, there is a whole tradition associated with cost-plus pricing that starts with the well-known studies on administered pricing of Means (1936) and the Oxford pricing study of Hall and Hitch (1939). This tradition, as recalled by Lee (1998) in his book devoted to industrial pricing behavior, claims that most firms set prices by computing some kind of standard unit cost and adding to it a costing margin based on a percentage markup. Thus firms set the markup and prices. It is an ex ante decision. Based on sales and fixed costs, the firm may or may not achieve a profit margin as measured ex post. This is the pricing procedure which is at the heart of our article. In most macroeconomic models, markups are an exogenous constant set over the marginal cost of firms under monopolistic competition, where market power stems from the preferences of consumers over differentiated goods—see Dixit and Stiglitz (1977) and Rotemberg and Woodford (1999) who provide an extensive discussion of these models. In line with the industrial organization literature, several ABMs have modeled price setting through markups on unit costs that evolve with the firms’ market shares. However, the problem of the determination of the level of the markup is usually not really solved, as the distribution law remains partly exogenous (see e.g. Dosi et al., 2010). One rare example of genuine endogenous markup procedure can be found in Caiani et al. (2016a), but it is not a true administered price, in the sense that the markup is increased or decreased when inventories are above or below target, in an effort to adjust demand to supply (see p. 384). Moreover, this contribution leaves out the analysis of the emerging markups, and their consequence for sectoral relative prices. Even when prices are set in a decentralized fashion as a simple function of inventories (Assenza et al., 2015; Riccetti et al., 2015) or following more sophisticated estimation techniques (Dawid et al., 2011), the ex post markups, while endogenous, are not subject to further study. As Blanchard (2008: 18) notes, “How markups move, in response to what, and why, is however nearly terra incognita for macro… we are a long way from having either a clear picture or convincing theories, and this is clearly an area where research is urgently needed.” Here we take up the view that the pricing problem faced by firms is nontrivial: increasing its markup allows the firm to increase its profit margins, but at the expense of its market share. Firms have to solve this trade-off in a situation of strategic uncertainty, especially once firms’ heterogeneity is brought into the picture. Indeed, in a market economy, firms are both competitors and interdependent. Finally, firms’ pricing decisions as a whole feed back into the macroeconomic dynamics, as they affect the distribution of income between the different sectors and agents, and therefore the level of aggregate demand. We do not hypothesize that there exists a simple solution to this complex coordination problem. Fully in tune with the best ABM approach, we therefore decide not to guide the firms that populate our model. Instead we let them explore as widely as possible the range of pricing strategies, and we observe whether market processes allow for a coordination and, if so, characterize which collective solution emerges. In this article, we seek to answer the following questions: In a market economy, which levels of markup can firms achieve? Do they differ between sectors and can we identify forces that drive their evolution? These questions lie within a broader perspective. The coordination problem faced by firms is a central question ever since Adam Smith’s metaphor of the “invisible hand.” On the one hand, the division of labor reinforces the interdependence between all sectors; on the other hand, private ownership and individual initiative induce the fragmentation of production between competing units: Indeed we must not forget that if the division of labour joins interests solidly together, it does not mix them together: it leaves them distinct, and in competition with one another. (Durkheim, 1984: 160) Given such a contradiction, are markets able to coordinate the activity of a large number of interdependent and competing actors? Walrasian economics answers this question with an auctioneer. Neoclassical macroeconomics envisions the question through a fixed point reasoning, by computing optimal reaction functions and solving for equilibrium relative prices. In this article, we contribute to this question without these strong assumptions, making use instead of a framework that is suited for tackling this problem in its full complexity, namely, an ABM. ABMs are conceived to analyze out-of-equilibrium dynamics and adaptation processes from heterogeneous and interacting entities [see, e.g., Tesfatsion (2006) and Caiani et al. (2016b) for an introduction to the agent-based (hereafter AB) approach approach]. On a more specific note, we use a stock-flow consistent (hereafter, SFC) framework. Following up on the works of Cincotti et al. (2010); Kinsella et al. (2011) and Seppecher (2012), there has been a number of macroeconomic models that combine two important features: the principle of decentralization/disaggregation which is found in ABM and the principle of stock-flow consistency formalized by Godley and Lavoie (2007) (see Caverzasi and Godin, 2015 for a historical and theoretical account of the rapprochement between those two strands of the macroeconomic literature). In an ABM, macroeconomic variables are the result of a simple process of aggregation of individual data, as in the real word (Cohen, 1960), so that the accounting accuracy provided by the SFC approach ensures the relevance of the aggregation process (Bruun, 1999), as well as the interconnected nature of the balance sheets of all agents. Symmetrically, AB principles could provide micro-foundations to SFC macroeconomics, that is, a way to logically articulate and rigorously organize the interactions between the micro and the macro levels. A SFC-ABM appears as the ideal tool for the study of our research question. Disaggregation and heterogeneity are required to study coordination issues. Micro interactions are necessary to model market mechanisms and the endogenous emergence of aggregate patterns. We model decentralization of both the goods and labor markets, on both the supply and the demand sides, which allows us to present a precise formalization of market competition and selection. For instance, firms set individually their prices and wages, so that the resulting wage rate and income distribution in the economy are endogenous. We further introduce evolutionary mechanisms that go hand in hand with heterogeneity and emerging behaviors under selection pressure. On this aspect, we rely on the evolutionary procedure developed by Alchian (1950), as it is best suited for modeling the emergence of norms and customs under market competition. In our model, besides the standard decisions that firms need to take with regard to production and the management of their inventories, evolutionary mechanisms determine markup levels and target leverage ratios.1 The selection of strategies operates through market competition, so that strategies that lead to bankruptcy tend to be abandoned by firms, while strategies that are successful tend to get generalized. Idiosyncratic shocks also constantly introduce innovations into firms’ strategies, and provide them with adaptability when facing changes in market conditions. We wish to stress that we do not rely on any ad hoc selection operators, such as replicator dynamics, to emulate a selection pressure (see e.g. Dosi et al., 2016): in our model, the market mechanisms directly and “naturally” eliminate unfit behavior. Furthermore, there is a macro closure which, besides modeling the financial and banking sectors, takes into account the aggregate demand arising from the behavior of households and resulting, at least partly, from the decisions taken by firms. More precisely, we elaborate on the model of Seppecher et al. (2018) and its “leverage engine,” which generates endogenous business cycles. We extend this model to a multi-sector economy, in which production and consumption involve three types of goods, to model an economy structured by strong interdependence relationships between competing firms, at both at the real and monetary levels. While monetary interdependence, as explained above, is inspired by the works of Godley and Lavoie (2007), real interdependence is inspired by Leontief (1936, 1937); Sraffa (1960); Lowe (1976); Pasinetti (1977), and more recently by Lee (2011) who present models with several interdependent industrial sectors. Although there are a few ABMs that exhibit both radical decentralization and stock-flow consistency,2 we are not aware of any other ABM that also encompasses several interdependent production sectors.3 Some macroeconomic ABMs include only two sectors, a capital good sector and a consumption good sector, see e.g. Cincotti et al. (2010); Dosi et al. (2010); Dawid et al. (2014); Assenza et al. (2015), or Caiani et al. (2016a). However, in these models, the capital good sector is oversimplified: it only employs labor, and thus, the production of capital goods is never limited by capacities. Furthermore, the question of relative prices and that of the emergence of an endogenous structure of sectoral markups are not studied. Our reasons for using such a complex representation of the production process go beyond the simple fact that the analysis of three sectors is likely to be more fancy than one based on two sectors. First it should be pointed out that authors who have shown concern for multi-sector analysis and the dynamics of relative prices have insisted that such questions require at least three sectors. For instance, Shaikh (2016: 442), at the end of a chapter devoted to these issues, concludes that “the smallest representative model would be a three-sector model with three functionally distinct commodities: one material input (basic good) that entered into all production, one consumption good, and one capital good (machine).” Similarly, Lee (2014: 26), after a long discussion of the various combinations of production sectors that could be used to study capitalism, also opts for a production scheme “representing, in elementary form, the economy as a whole in which corn is an intermediate input for the production of all the output, machine is a tool that transforms the intermediate input into each of the outputs, and the output consists of three different goods—corn (basic good), machine (basic good), and food (non-basic good),” exactly as was the case with Shaikh. This, as we shall see, corresponds closely to the structure that we have adopted in our article. The only difference is that our intermediate good will not be a basic good, as it will only be needed for the production of the consumption good.4 Second, it should be obvious that a three-sector model involves problems of coordination that are much more complex. There is a rigid relationship between the consumption good and its intermediate good, since the consumption good cannot be produced without the intermediate good, while there is a flexible relationship between these two goods and the capital good, since the capital stock can be used with different degrees of utilization. As we shall see, since capacity utilization is endogenous in each of the three sectors, in a decentralized economy bottlenecks are likely to occur in one sector, while another sector may quite likely turn out to have large excess capacities. In addition, costs will enter in a different way in each of the three sectors because of the asymmetry in the production process. Thus, in our view, our model helps to respond to the qualms of Steedman (1992) against the use of vertically integrated sectors in much of the heterodox macro literature, by providing the smallest representative structure that can handle the complexities associated with the interdependence of multi-sector analysis. The exercise that we conduct brings three main results. First, the overall economic system endogenously converges around a stationary state, where average markups and gross profits do not fall to zero, but systematically stabilize at a strictly positive level. Second, we observe intra-sectoral coordination between firms. The mechanism of market selection gives rise to the formation and the evolution of social norms such that firms are eventually constrained to use costing markups consistent with the literature on normal-cost pricing (Hall and Hitch, 1939; Coutts et al., 1978; Lee and Irving-Lessmann, 1992; Coutts and Norman, 2013). According to this literature, prices are not set so as to insure the equality between supply and demand; instead they are perceived as reproduction prices, that is, prices that insure the reproduction of the system: … custom and competition are predominant among the determinants of the mark-up for profit… whatever competitive factors affect the determination of the mark-up, the role of custom and convention is significant enough to place the motivation of the price administrators outside the simple description of maximizing profits…. (Lee, 1994: 325–326) This post-Keynesian view is compatible with Simon’s (1979) satisficing hypothesis, which denies that firms set prices in an attempt to maximize profits, presuming instead that they follow simple rules of thumb or routines (see also Nelson and Winter, 1982 and the discussion in Mazzoleni and Nelson, 2013). Still, prices should cover unit labor and material costs, and generate a profit rate on the value of the financial capital required by firms. Our model shows that once market competition and selection processes do their work, this is precisely what happens. However, short-run fluctuations in prices and markups persist, as a result of the constant tension between seeking higher market shares and increasing profitability—a trade-off made ever complicated by ever-changing market conditions. Third, we observe inter-sectoral coordination: markup levels differ between sectors in a systematic way. This hierarchy of markups is driven by the production technology assumed in the model, insofar as the technology determines the real interdependence between firms in each of the three sectors. Most importantly, we found that the markups evolve so as to get relative prices in each sector to gravitate near their labor values, “natural prices,” as hypothesized by the Classical school of thought. Finally, our contribution in this article shows that the AB approach provides more than just useful tools to simulate macroeconomic dynamics with a high level of realism; it can also provide decisive contributions to highly debated theoretical issues, such as the question of relative prices/pricing behaviors in market economies. The rest of the article is organized as follows: Section 2 describes the model, Section 3 provides the simulation protocol and our main hypotheses, Section 4 presents our results along with our hypotheses, and Section 5 concludes. 2. The model We now provide a general description of the model, focusing on the firms. Tables in the Supplementary Appendix C report the stock-flow consistency of the model. Supplementary Appendix D provides a detailed account of the timing of events within one period, including the exact behavioral rules followed by each category of agents for every decision (see Supplementary Appendix D.3), as well as the initialization of all micro and macro variables (see Supplementary Appendix Table D.1). 2.1 Structure The model is populated by a collection of heterogeneous firms, indexed by j and heterogeneous households, indexed by i, as well as a bank. Figure 1 illustrates the structure of the model. At the beginning of any simulation, the firms are distributed between three industrial sectors: the intermediate goods sector (denoted as “Sector 1” or S1), the consumption goods sector (denoted as “Sector 2” or S2), and the investment goods sector (denoted as “Sector 3” or S3). Figure 1. View largeDownload slide Structure of real interactions. Figure 1. View largeDownload slide Structure of real interactions. There are two types of households: the “workers” who supply labor to the firms, and the “shareholders” who hold shares of the firms and receive dividends. Households, both workers when supplying labor or shareholders when buying shares, are indifferent between industrial sectors. The distribution of firms between the three sectors and of households between the two types remains unchanged for the whole simulation. All sectors need to combine machines with labor under constant returns to scale to produce goods. In every period and in every sector, one unit of labor has to be combined with one machine to result in production. All machines within a sector have the same, exogenously fixed, productivity. A fixed amount of investment goods (produced by S3) is required to be transformed into a machine. This amount of investment goods varies across the different sectors (see Supplementary Appendix Table D.2) so as to allow for differentiated capital/workforce ratios across sectors. Thus, despite each machine being operated by one worker, by construction, the technical coefficients of each sector are different. Additionally, production in the consumption goods sector requires intermediate goods (see Table 1). Production in the model then consists of machines with labor producing investment goods (S3); machines with labor producing intermediate goods (S1); and machines with labor and intermediate goods producing consumption goods (S2). Table 1. Real interdependence links Type of goods Supply Demand Intermediate goods S1 S2 Consumption goods S2 Workers, shareholders Capital goods S3 S1, S2, S3 Type of goods Supply Demand Intermediate goods S1 S2 Consumption goods S2 Workers, shareholders Capital goods S3 S1, S2, S3 Table 1. Real interdependence links Type of goods Supply Demand Intermediate goods S1 S2 Consumption goods S2 Workers, shareholders Capital goods S3 S1, S2, S3 Type of goods Supply Demand Intermediate goods S1 S2 Consumption goods S2 Workers, shareholders Capital goods S3 S1, S2, S3 One single bank stands for the whole banking and financial sector. This “super-bank” provides loans to the firms to finance wages and investment, over an exogenously given number of periods, at a risk-free interest rate set by a Taylor rule that targets consumer price inflation.5 It also hosts households’ and firms’ deposits (at a zero interest rate), allocates shareholders’ excess cash to firms with excess leverage, and implements the foreclosure procedure for bankrupted firms (see below). 2.2 The firms Unless otherwise stated, all firms in all sectors have the same behavioral rules. 2.2.1 Production plan Firms set both prices and quantities. We assume that firms set prices according to a markup over the unit cost of their goods. Unit costs include only the direct production costs, i.e., the wages and the costs of the intermediate goods that have been necessary to their production (it does not include the indirect costs such as interest payments or depreciation costs). Since firms carry inventories of produced but yet unsold products at each moment of time, one has to decide which unit cost will be the basis of the pricing procedure. We use the average unit direct cost, that is, the overall direct production cost of all the goods still in stock divided by the number of goods in the stock of inventories.6 The quantities to produce, and conversely the demand for labor, are set by gradual adjustments as a function of the firm’s past sales, its production capacities, and the level of its inventories. Furthermore, we assume that firms in S2 keep a buffer stock of intermediate goods. Additionally, firms set their wage offer. The wage-setting procedure is designed to account for both an adjustment component to labor market tightness and an “institutional” component which is an essential determinant of wage levels in developed countries. In the model, large firms tend to be wage makers. They adjust their wage offer according to their observed level of vacancies and their past wage levels, while small firms tend to be wage takers, and simply use the wage levels prevailing in larger firms of their sector. 2.2.2 Investment decisions Investment goods depreciate at an exogenous, fixed rate. In each period, firms may consider to invest in new machines, both to renew their depreciated capital and to expand their production capacities. Investment is financed with retained earnings and bank loans. In this respect, we assume that firms have a leverage target ratio.7 Only if their actual leverage lies below this target will the firms consider to invest. If they do so, their investment goods demand will correspond to the number of investment goods that gives the highest net present value of the investment project. This net present value is computed on the basis of the prices supplied by the producers of investment goods and on the basis of expectations regarding other prices, wage rates, and interest rate levels, as assessed from present and past average values. 2.2.3 Finance through bank loans Firms borrow from the bank to finance their production and their real investments. Their anticipated wage bill and intermediate goods purchases are financed by non-amortized short-term loans. Those loans are automatically granted for an exogenously fixed period of time at the risk-free interest rate. Investment is financed by amortized loans, granted for a longer period of time (corresponding to the expected lifetime of a machine). In every period, firms repay part of the capital and the due interests on their loans. If a firm is unable to make its due payment, it is downgraded to “doubtful.” It will then be given access to an overdraft facility, but at a higher interest rate that includes a fixed risk premium. 2.2.4 Finance through emission of new shares We introduce a stock market in a very rudimentary way by allowing firms with excess indebtedness (compared to their targeted level) to get funds from shareholder-households by issuing new shares. Those potential shareholders are all shareholder-households with excess cash, i.e., whose money balances exceed some fraction of their portfolio value. The firms issue as many shares as needed to meet their financial needs. These shares are randomly allocated to potential shareholders, within the limits of their available excess cash. The price of the firms’ shares is simply set with a Tobin’s q ratio equal to unity (i.e., the stock value of the firm is equal to its book value). This pricing assumption is a reasonable assumption in a stylized environment where shares are blindly attributed to randomly selected shareholder-households who, therefore, do not display any return-seeking behavior. We further assume that Ponzi firms (i.e., those whose gross profits are lower than their interest repayments) are excluded from the financial market, so that nonprofitable firms remain open to the risk of bankruptcy. Indeed, if a firm becomes insolvent (i.e., its liabilities exceed its assets), it goes bankrupt and the bank launches the foreclosure procedure. It is important to note that a failed firm does not disappear per se.8 When bankruptcy occurs, part of the liabilities of the firm are erased and absorbed by the bank’s capital,9 its book value drops to zero, its current shareholders lose their shares, and the bank recapitalizes the firm with the excess cash-on-hand of randomly drawn shareholders, who then become the new owners of the firms. The second change concerns the pricing and debt strategies, which are described in the next subsection. The rest of the characteristics of the failed firm (e.g., work contracts, inventories, machines, etc.) remain unchanged. Shareholders receive dividends from the firms (and the bank). In each period, the firms retain a constant fraction of their average past net profits, and distribute the rest as dividends. The bank has an exogenously fixed target of net worth, and simply distributes as dividends all its net worth beyond that target. The bank’s shareholders are households randomly drawn at the beginning of each simulation. 2.2.5 Market adaptation and production of norms The firms update their markup levels and leverage targets using an evolutionary algorithm along the lines of Alchian (1950). In the simplest version of this evolutionary learning process, two operators are essential: an exploration process that constantly introduces new, potentially more profitable strategies into the population of existing strategies, and an exploitation process that propagates the profitable strategies among the population of firms. Selection stands for the exploitation process of the evolutionary algorithm. In our setting, selection simply goes hand in hand with the market selection pressure, as the market determines what a profitable strategy is. Strategies of bankrupted firms are considered to be nonprofitable, and are therefore replaced by more profitable ones. We assume that when a firm goes bankrupt, it does not disappear, but its set of strategies (pricing and leverage) is replaced and copied from the strategies of another operating firm. This firm is randomly selected among the non-bankrupted firms of the same sector. A scenario for this process could be the following: an insolvent firm is always purchased by a group of shareholders that put in place a new management team that has been trained in one of the existing firms operating in the same sector, and the new managers bring with them the strategies of their former employment. A natural way to model the exploration process is through idiosyncratic shocks. We assume that, in every period, the firms are subject to small individual shocks that slightly modify their markup and their leverage target. Focusing on the markup determination, in each period t, the markup of any firm j, denoted by θj,t ⁠, is given by: θj,t=θj,t−1+εj,t, εj,t,→N(0,σ), (1) where σ is small. Therefore, at the level of the population, the arithmetic average markup is not modified by the individual shocks ε. Possible economic interpretations of those shocks include small-step innovations by a “trial-and-error” process, or control errors in the implementation of the strategies. We note that this specification does not rule out the possibility of negative markups. Yet, as negative markups do not allow firms to make profits, they should be eliminated by the bankruptcy of those firms, and replaced by another (most likely positive) markup from the population of firms. The same way, there may be an upper bound to the markups, but there is not clear prior or guideline about such a ceiling. For those reasons, we prefer not to restrict ex ante the values of the markups that can emerge in the ecology of firms to assess the effects of market pressure. As our results below show (see for instance Figure 5), negative markups remain rare and of small amplitude, which confirms the validity of our selection process. Exploration and exploitation operate separately in each sector, so that different norms between sectors may emerge from the market selection pressure. 2.3 The households Both workers and shareholders consume the consumption goods. Workers’ income comes from labor income (if employed) and shareholder’s income arises from dividends (if any). To smooth their consumption when facing unanticipated income variations, both types of households follow a buffer-stock rule and build precautionary savings. Households cannot borrow, and consumption is budget-constrained in every period. We assume that the saving rate out of income from equity ownership is higher than that out of labor income. This assumption has been common when studying income distribution, and it is supported by a vast amount of empirical work (Marglin, 1984: 404; Lavoie and Stockhammer, 2013). It has found some support in behavioral theories of consumption (see the so-called “mental accounting” theory, Thaler, 1990). In the labor market, workers have a reservation wage that they adjust downward if unemployed. 2.4 Matching on markets In the labor market, firms with vacancies send job offers to a randomly selected pool of unemployed workers. An unemployed worker only accepts an offer if the offered wage is higher than his or her reservation wage. The length of the contract is then randomly drawn from a uniform distribution. All goods markets operate on a principle of “loyalty to reliable suppliers” (Kirman and Vriend, 2000). Buyers keep in memory a list of suppliers from which they fulfill their demand schedule, buying first from the cheapest one. In every period, the most expensive supplier as well as those who have rationed the buyer in the previous period are removed from the list of potential suppliers, and are replaced by randomly drawn suppliers. The selection of suppliers is primarily based on the capacity to provide goods, which facilitates the creation of supplier–customer networks despite the heterogeneity in firms’ sizes. The only difference between the three goods markets is the demand schedule: households’ spending decisions are in nominal terms and are budget-constrained, while firms schedule their intermediate and investment goods demand in real terms, and borrow from the bank if their cash reserves are insufficient. Aggregate variables are simply the result of the sum of individual ones across all agents. 3. Simulation protocol 3.1 Calibration We devoted some efforts to the calibration of the model. The purpose of this exercise is to reach values for the main variables that are familiar to macroeconomists. In a weak sense, this helps to provide validity to the model, since we can find parameters such that those variables reach reasonable values. The successful calibration does not prove that the model structure is right, in the sense that it would faithfully reproduce the true structure of real economies. However, one could argue that if it had been impossible to calibrate the model so as to reach any realistic value, this would have implied a rejection of the model. This calibration exercise is not essential for the simulations that will be performed and analyzed hereafter. We now discuss the main variables in which we are interested. By construction, in each period, the model respects the two following accounting equations (subscripts t have been dropped for clarity): r=muv, (2) ι=sfm+sp(1−sf)m+sw(1−m)⇔m=ι−swsf+sp(1−sf)−sw, (3) where r is the gross profit rate, m the profit share, u the rate of capacity utilization, v the capital to capacity output ratio, ι the investment to income ratio, sf the retention rate of corporations (both firms and bank), sp the propensity to save of the shareholders, and sw the propensity to save of the workers. The propensities to save sf, sp and sw can be derived from the different parameters determining the behavior of the two types of agents (see Supplementary Appendix Table D.2). In the same way, we can approximately control the (long run) investment to income ratio ι by modifying the technical coefficients relevant to the production function of the machines in each sector. The capital to capacity output ratio is similarly determined by those technical coefficients. As a consequence, we can fix, at least approximately, the (long run) share of profits in our model. However, the utilization rate u and the profit rate r seem to be essentially endogenous. Nonetheless, following a trial-and-error process involving both the saving behaviors and the production technical coefficients, we succeeded in defining a scenario that exhibits plausible ex post values for each of these variables, as shown in Table 2. Note that the model is quite stable across stochastic simulations, as reflected in the small values of the standard deviations. Table 2. Observed values of main endogenous variables (on average from t = 500 to t = 2000) in 100 Monte Carlo (MC) simulations of the baseline scenario. See Franke (2017) for a discussion of the empirical values of these variables Variables 100 MC simulations Mean σ Retention rate of corporations sf 0.4088 0.0261 Propensity to save of shareholders sp 0.4382 0.0615 Propensity to save of workers sw 0.0727 0.0112 Investment to income ratio ι 0.2532 0.0169 Profit share m 0.3040 0.0087 Utilization rate u 0.8214 0.0099 Capital to capacity output ratio v 1.1460 0.0243 Profit rate r 0.2179 0.0027 Variables 100 MC simulations Mean σ Retention rate of corporations sf 0.4088 0.0261 Propensity to save of shareholders sp 0.4382 0.0615 Propensity to save of workers sw 0.0727 0.0112 Investment to income ratio ι 0.2532 0.0169 Profit share m 0.3040 0.0087 Utilization rate u 0.8214 0.0099 Capital to capacity output ratio v 1.1460 0.0243 Profit rate r 0.2179 0.0027 Table 2. Observed values of main endogenous variables (on average from t = 500 to t = 2000) in 100 Monte Carlo (MC) simulations of the baseline scenario. See Franke (2017) for a discussion of the empirical values of these variables Variables 100 MC simulations Mean σ Retention rate of corporations sf 0.4088 0.0261 Propensity to save of shareholders sp 0.4382 0.0615 Propensity to save of workers sw 0.0727 0.0112 Investment to income ratio ι 0.2532 0.0169 Profit share m 0.3040 0.0087 Utilization rate u 0.8214 0.0099 Capital to capacity output ratio v 1.1460 0.0243 Profit rate r 0.2179 0.0027 Variables 100 MC simulations Mean σ Retention rate of corporations sf 0.4088 0.0261 Propensity to save of shareholders sp 0.4382 0.0615 Propensity to save of workers sw 0.0727 0.0112 Investment to income ratio ι 0.2532 0.0169 Profit share m 0.3040 0.0087 Utilization rate u 0.8214 0.0099 Capital to capacity output ratio v 1.1460 0.0243 Profit rate r 0.2179 0.0027 3.2 Hypotheses In the case at hand, we are interested in testing a number of hypotheses. First of all, we want to assess whether our model is viable, and provides a reasonable approximation of a simple economic system. In this respect, ABMs allow us to separately and simultaneously establish the characteristics of the emerging micro and macro behaviors. Simulation outcomes can then be compared to macro stylized facts—such as co-movement, persistence and cross-correlation patterns in output, debt, etc.—and to micro stylized facts—such as the distribution of the firms’ sizes. We refer the reader here to Dosi et al. (2010, 2015) for a state-of-the-art demonstration of empirical validation of an ABM, which we will partly follow here, and Stock and Watson (1999) for an account of major macroeconomic stylized facts. Therefore, our first hypothesis is the following: Hypothesis 1 (Validity).The model is able to reproduce itself from period to period in a way that generates patterns that are in line, at least qualitatively, with empirical regularities both at the microeconomic and the macroeconomic levels. If Hypothesis 1 cannot be rejected by the simulations, then we are interested more specifically in the pricing behaviors that emerge from the interaction between the evolutionary mechanism and market competition: Hypothesis 2 (Intra-sectoral coordination).Firms coordinate their markup around steady, sector-specific, values in a systematic way. Hypothesis 2 implies that the average level of the markup across firms of each sector systematically reaches the same order of magnitude in all the stochastic simulations, while idiosyncratic shocks will maintain heterogeneity in firms’ strategies in every period. If Hypothesis 2 cannot be rejected by the simulation data, we are then interested in the determinants of the values reached by the markups. Given the multi-sector structure of the model, an immediate research question relates to the determinants of the relative levels of the markups, and therefore the relative prices between sectors. Our next hypothesis is guided by a reading of Classical authors and Pasinetti (1977, 1988): the determination of the relative prices has something to do with the amount of labor directly and indirectly required to produce the different goods. Appendix A derives these corresponding “natural prices.”10 Our next hypothesis is then: Hypothesis 3 (Inter-sectoral hierarchy of markups).Firms set their markups, so that the relative prices between sectors “gravitate” close to the “natural prices” implied by the technical coefficients of the production functions and the quantities of labor required for the production of the goods. If we cannot reject Hypothesis 3, an immediate corollary is the question of the adaptability of pricing behaviors when facing exogenous technological shocks that modify permanently the production function in one sector. We therefore come up with the following hypothesis: Hypothesis 4 (Adaptability).In case of a permanent technological change, the natural prices are modified, and firms adjust their markup, so that relative prices gravitate close to these new values. We now discuss the simulation results in Section 4 in light of those four hypotheses. 4. Simulation results 4.1 Overview To test Hypothesis 1, we discuss the outcomes of our baseline scenario along three groups of stylized facts: business cycles, industrial dynamics, and financial facts (see, for instance, Delli Gatti et al., 2007). To start on the aggregate level of our simulations, Table 3 displays several statistics over 100 replications of the baseline scenario. As was the case in Table 2, the reported values of our four variables look plausible. The particularly small standard deviations further ensure that the model outcomes are stable across stochastic replications of the baseline scenario. Table 3. Average values (standard deviations in brackets) over 100 replications of the baseline scenario, t∈[500,2000] ⁠, annualized values Sectors Gross profit rate Net profit rate Bankruptcy rate Debt ratio All industries 0.1875 0.1173 0.1137 0.5605 (0.0189) (0.0119) (0.0129) (0.0567) S1 0.2133 0.059 0.1 0.5512 (0.0215) (0.0064) (0.0125) (0.0565) S2 0.1711 −0.0003 0.1422 0.5948 (0.0174) (0.0068) (0.0177) (0.0613) S3 0.1987 0.0515 0.0927 0.493 (0.0201) (0.0061) (0.011) (0.0508) Sectors Gross profit rate Net profit rate Bankruptcy rate Debt ratio All industries 0.1875 0.1173 0.1137 0.5605 (0.0189) (0.0119) (0.0129) (0.0567) S1 0.2133 0.059 0.1 0.5512 (0.0215) (0.0064) (0.0125) (0.0565) S2 0.1711 −0.0003 0.1422 0.5948 (0.0174) (0.0068) (0.0177) (0.0613) S3 0.1987 0.0515 0.0927 0.493 (0.0201) (0.0061) (0.011) (0.0508) Note: profit rate figures for all industries include the bank. Table 3. Average values (standard deviations in brackets) over 100 replications of the baseline scenario, t∈[500,2000] ⁠, annualized values Sectors Gross profit rate Net profit rate Bankruptcy rate Debt ratio All industries 0.1875 0.1173 0.1137 0.5605 (0.0189) (0.0119) (0.0129) (0.0567) S1 0.2133 0.059 0.1 0.5512 (0.0215) (0.0064) (0.0125) (0.0565) S2 0.1711 −0.0003 0.1422 0.5948 (0.0174) (0.0068) (0.0177) (0.0613) S3 0.1987 0.0515 0.0927 0.493 (0.0201) (0.0061) (0.011) (0.0508) Sectors Gross profit rate Net profit rate Bankruptcy rate Debt ratio All industries 0.1875 0.1173 0.1137 0.5605 (0.0189) (0.0119) (0.0129) (0.0567) S1 0.2133 0.059 0.1 0.5512 (0.0215) (0.0064) (0.0125) (0.0565) S2 0.1711 −0.0003 0.1422 0.5948 (0.0174) (0.0068) (0.0177) (0.0613) S3 0.1987 0.0515 0.0927 0.493 (0.0201) (0.0061) (0.011) (0.0508) Note: profit rate figures for all industries include the bank. The panel of Figures 2 and 3 provides an illustration of a typical baseline simulation. As our model abstracts from demographic or technological growth, it is a long-run stationary model, as clear from Figure 2b. The correlation patterns between the main macroeconomic variables across 100 replications of the baseline scenario are reported in Supplementary Appendix B.1, to which we refer the reader for the figures that we now discuss.11 We then observe that the model is able to create endogenous business cycles, i.e., fluctuations that are irregular and common across sectors. Those fluctuations are persistent as illustrated by the autocorrelation pattern of gross domestic product (GDP) (Supplementary Appendix Figure 11a) or unemployment (Supplementary Appendix Figure 11b) in the baseline simulation.12 The observed business cycles display the characteristics of credit cycles as illustrated by Supplementary Appendix Figure 11g: firms’ indebtedness leads GDP growth by a couple of periods. This emerging feature, detailed in [Seppecher et al. (2018)], is robust to the present multi-sectoral model. As credit finances investment in our model, we observe that S3 is also slightly leading (see Supplementary Appendix Figure 11e), which is in line with an investment multiplier effect. From Supplementary Appendix Figure 11d, S2 (aggregate consumption) is also pro-cyclical. Moreover, S2 leads S1, which is easily explained by the mechanical interdependence between the two: the intermediate goods produced in S1 are dependent of the planned production in S2. Moreover, investment (S3) is more volatile than GDP, and aggregate consumption (S2) is less volatile than GDP.13 Figure 2. View largeDownload slide Baseline scenario—real indicators. (a) Output. (b) Potential Output Growth. (c) Labor market. (d) Unemployment. (e) Beveridge curve. (f) Phillips curve. Figure 2. View largeDownload slide Baseline scenario—real indicators. (a) Output. (b) Potential Output Growth. (c) Labor market. (d) Unemployment. (e) Beveridge curve. (f) Phillips curve. Figure 3. View largeDownload slide Baseline scenario—financial indicators. (a) Returns on assets. (b) Interest and inflation rates. (c) Ponzi firms. (d) Default rate of the firms (all sectors). Figure 3. View largeDownload slide Baseline scenario—financial indicators. (a) Returns on assets. (b) Interest and inflation rates. (c) Ponzi firms. (d) Default rate of the firms (all sectors). These cycles impact the labor market (Figures 2c and 2d), and produce an alternating pattern of periods of unemployment and periods of full employment. Figure 2e displays a downward-slopping Beveridge curve, linking unemployment and vacancies, and Figure 2f shows a downward-sloping Phillips curve, inversely relating consumer price inflation (S2) and unemployment. In line with those observations, Supplementary Appendix Figure 11c displays a strong negative relationship between GDP and unemployment, featuring the Okun relation, and Supplementary Appendix Figure 11k reports a lagging and pro-cyclical inflation. Supplementary Appendix Figure 11p–11r are consistent with recent evidence on the cyclicality of markups, at least for S1 and S2, even though the literature seems to hold divergent views on this issue (see e.g. Nekarda and Ramey, 2013, Figure 2, and the discussion herein). Entering the detail of that debate and uncovering the causes of the sector-specific cyclicality lies beyond the scope of our article, especially given that this is not key for our results and the objectives of our present study. Even if not essential to our research question, it is interesting to note that our model also replicates a countercyclical and leading consumption price level (Supplementary Appendix Figure 11j), pro-cyclical changes in inventories (Supplementary Appendix Figure 11h), and capacity utilization (Supplementary Appendix Figure 11i), as well as countercyclical real interest rates (Supplementary Appendix Figure 11l). We can also shed some light on the cross-correlation patterns between the real and financial variables along those business cycles. Figure 3c displays the proportion of firms in each sector that become Ponzi firms, as defined by Minsky (1982): business cycles seem to be closely connected to the fluctuations in the proportion of Ponzi firms. This is indeed the case, as firms’ bankruptcies are strongly countercyclical (Supplementary Appendix Figure 11m), which clearly shows the tight interplay between the financial cycle and the cycle associated with real production (Minsky, 1975). We refer here the reader to [Seppecher et al. (2018)] for an extensive discussion of the firms’ investment and debt behaviors in a closely related model. In a nutshell, when individual firms try to increase their debt level to invest, they collectively create overcapacities and increase their financial fragility, which eventually leads to a sudden downturn. Figure 3a reports the returns on assets in each sector, as well as for the bank, and provides a similar interpretation. Profits in the banking sector are dictated by the interest rates (see Supplementary Appendix Figure 11n), which are set by the Taylor rule (Figure 3b). Hence, the bank’s profits are inversely related to the profits of the firms, for which higher (real) interest rates represent costs that weight on their profits (Supplementary Appendix Figure 11o). Interestingly, the returns on assets in each of the three industrial sectors seem closely interconnected, which attests to the co-movement between all the sectors along the business cycles. ABMs also allow us to characterize the distribution of individual characteristics. We then take a look at the microeconomic level of the simulation outcomes. Learning by individual firms combined with market selection has been identified as a major driver of the dynamics within the firms’ population (Dosi et al., 2016). In our model, despite all characteristics of the firms being perfectly homogenously initialized, a strong underlying heterogeneity emerges within the firm population, which is a core mechanism of the evolutionary adaptation processes in our model. To illustrate and characterize this emerging heterogeneity, Supplementary Appendix Figure 12, also found in Supplementary Appendix B.1, reports the cross-sectional distribution of firms’ sizes (measured by the number of machines) and firms’ investments. These distributions are measured across all sectors and the indicators are averaged over the periods 989–1000 (i.e., equivalent to 12 months) of the baseline simulation, while firms are initialized with the same size in period 0. Supplementary Appendix Figure 12a and the associated reported normality tests suggest that the cross-sectional distributions of the firms’ sizes are not normal and right-skewed (i.e., with fat tails). Additionally, Supplementary Appendix Figure 12b reports the so-called “lumpiness in investment,” i.e., within the same time period, some firms invest a lot, while most (i.e., roughly 75%) do not.14 Those results indicate that, even though our exercise is not designed to reproduce quantitatively any stylized fact, the economy that we have modeled is broadly in tune with empirical regularities. We cannot therefore reject our first hypothesis about the viability of our model. 4.2 Endogenous markups Figure 4 displays the evolution of the weighted average markups (by market shares). We first see that the markups systematically stabilize at strictly positive and sector-specific values.15 This phenomenon of collective adaptation does not require any individual adaptation, but only the heterogeneity of the population of firms (the economic equivalent of biodiversity). The evolution of weighted average markups is driven by the increase in sale volumes and the sizes of successful firms, i.e., of firms whose pricing and debt strategies allow them to gain market shares. We first take a look at what a “successful” strategy looks like, and we defer to the next section the explanation of the emerging sector-specific markup structure. Figure 4. View largeDownload slide Evolution of markups (average weighted by market shares) per sector in a typical baseline simulation (left panel) and over 100 MC simulations (right panel, average ± 1 standard deviation). (a) Weighted average markups, typical run. (b) Weighted average markups, 100 replications. Figure 4. View largeDownload slide Evolution of markups (average weighted by market shares) per sector in a typical baseline simulation (left panel) and over 100 MC simulations (right panel, average ± 1 standard deviation). (a) Weighted average markups, typical run. (b) Weighted average markups, 100 replications. Figure 5 plots the firms’ markups against their return on assets in a typical baseline simulation. This figure illustrates the trade-off that the firms face when deciding upon a pricing strategy. This trade-off is materialized by the emergence of two boundaries: a lower bound (squeeze of profit margins) and an upper bound (loss of market shares). The lower bound (zero) is clearly common to the three sectors, and shows that higher markups provide higher profitability. Figure 5. View largeDownload slide Markups and profitability: distribution of individual markups of the firms against their return on assets, as recorded in every 12 periods from t = 1008 to t = 1200 of a typical baseline simulation. The vertical line represents the weighted average markup (by market shares) in the sector over that time span. (a) Sector 1. (b) Sector 2. (c) Sector 3. Figure 5. View largeDownload slide Markups and profitability: distribution of individual markups of the firms against their return on assets, as recorded in every 12 periods from t = 1008 to t = 1200 of a typical baseline simulation. The vertical line represents the weighted average markup (by market shares) in the sector over that time span. (a) Sector 1. (b) Sector 2. (c) Sector 3. However, this relationship is non-monotonic, and the upper bound indicates that, above a certain threshold, increasing the markup comes at the expense of market shares. This upper bound seems lower in S2, and the scatter plot of markups is more “condensed” toward the bottom than in S1 and S3. This observation tends to indicate that firms in S2 have less space to increase their markups when demand increases. In other words, price competition seems stronger in S2 than in the other sectors. Figure 6 confirms that intuition. It displays the level of the markups in each sector as a function of market concentration, measured by the normalized Herfindhal–Hirschman index (the higher the index, the higher the degree of concentration). The level of competition is higher in S2, as proven by lower values of the index, while it is comparable in S1 and S3 (despite the same number of firms in S1 and in S2 and fewer firms in S3, see Supplementary Appendix D.2 for the calibration). As a result, the volatility of the markups is lower in S2 than in S1 and S3, and the scatterplot looks more “compressed.”16 Figure 6. View largeDownload slide Markups and concentration: weighted average markup against the Herfindhal–Hirschmann concentration index in each sector between t = 1000 and t = 2000 of a typical baseline simulation. (a) Sector 1. (b) Sector 2. (c) Sector 3. Figure 6. View largeDownload slide Markups and concentration: weighted average markup against the Herfindhal–Hirschmann concentration index in each sector between t = 1000 and t = 2000 of a typical baseline simulation. (a) Sector 1. (b) Sector 2. (c) Sector 3. Figure 7 provides further insight into the market dynamics and the markup selection process by displaying the distribution of firms per markup levels. In line with this trade-off between profitability and market share, we observe that most firms use a markup that is close to the average markup in their sector, as their profitability suffers from an overly high or low markup. Interestingly, firms with average markups not only tend to realize higher profits but also gain market shares (see the top panel). Figure 7. View largeDownload slide Markups and demand: market shares (top panel) and inventories (bottom panel) per markup range; individual data, as recorded in every 12 periods from t = 1008 to t = 1200 of a typical baseline simulation. The vertical line represents the weighted average markup (by market shares) in the sector over that time span. (a) Sector 1. (b) Sector 2. (c) Sector 3. (d) Sector 1. (e) Sector 2. (f) Sector 3. Figure 7. View largeDownload slide Markups and demand: market shares (top panel) and inventories (bottom panel) per markup range; individual data, as recorded in every 12 periods from t = 1008 to t = 1200 of a typical baseline simulation. The vertical line represents the weighted average markup (by market shares) in the sector over that time span. (a) Sector 1. (b) Sector 2. (c) Sector 3. (d) Sector 1. (e) Sector 2. (f) Sector 3. This suggests that “following the crowd” by sticking close to the average pricing strategy is the best profit-maximizing strategy in our environment. The bottom panel of Figure 7 sheds some light on the reasons for this success. When looking at the level of inventories of firms as a function of their markup, the average markup in each sector represents a clear-cut threshold. The level of inventories serves as a good proxy for the level of demand that each firm faces. The panel of figures clearly shows that firms with below-average markups operate without any inventories, which indicates that they face an excess demand for their products, and could increase their markup to seek higher profits. Things are not so clear however in the case of S3. The reason is that investment goods sector is more responsive to the business cycle, so that an adequate markup may quickly become improper, that is, too low or too high. From the above observations, we conclude that Hypothesis 2 cannot be rejected: firms coordinate their markup around steady, sector-specific values in a systematic way. Let us emphasize that this outcome is quite remarkable. Indeed, in our model, firms set their price independently from each other, while they are competing for customers. This competition is based both on their prices (as goods are homogeneous across sectors) and on their ability to supply the goods (the quantity side), as described in Section 2.4. Hence, firms are in a situation of quantity and price competition, without knowing each other’s prices. While we assume away an explicit coordination through market forces, we end up observing both intra- and inter-sectoral coordination. Market competition is able to solve the nontrivial pricing decision. Individual adaptation by selection and imitation forces the firms that have less profitable strategies to adopt observed, more profitable, behaviors. The most profitable markup strategy is to comply with the average markup in the sector. Let us point out that, even though the markups are determined in a quasi-unintentional way in the short-run and at the individual level, meaning that prices are not set by firms to match supply and demand, their emergent structure appears to be driven by market conditions. There is therefore a slow and “noisy” reconciliation between the post-Keynesian theory of administered pricing, tied to the supply side, and the forces arising from the demand side. Finally, as mentioned above, Figure 4a and b reveals a quick evolution toward a hierarchy of sectoral markups that we have not discussed yet. S1 and S3 seem to have comparable levels of markup, while the consumption goods sector (S2) uses significantly lower markups. This structure is a robust feature of the baseline simulation, and is stable despite the business cycle variations. This observation reveals the existence of underlying forces driving the respective levels of the sectoral markups. We can now discuss this emerging hierarchy. 4.3 Structure of relative prices While short-term variations in the markups can be related to the tension between profit seeking and market-share chasing in ever-changing market conditions, we are still left without an explanation of the long-run average level reached by the markups in all replications of the baseline scenario. We therefore test Hypothesis 3, and report the average distances over 100 replications of the actual relative prices P1P2 and P2P3 from their relative natural prices implied by the production technology (see Supplementary Appendix Figure 13). Despite the volatility observed at short frequencies, the long-run stability of these distances is remarkable, and strikingly they gravitate around zero. This result is illustrated in a typical baseline simulation in Figure 8. Figure 8. View largeDownload slide Relative prices compared to the natural prices derived in Appendix A in a typical baseline simulation (results over 100 replications are in Figure A3), and relationship between the direct costs of production in each sector in a typical baseline simulation. (a) S1 to S2. (b) S2 to S3. (c) S3 to S1. Figure 8. View largeDownload slide Relative prices compared to the natural prices derived in Appendix A in a typical baseline simulation (results over 100 replications are in Figure A3), and relationship between the direct costs of production in each sector in a typical baseline simulation. (a) S1 to S2. (b) S2 to S3. (c) S3 to S1. We observe that the relative prices “gravitate” near the “natural prices,” defined as the ratio of the quantities of direct, indirect, and hyper-indirect labor required for the production of these goods. We conclude that Hypothesis 3 cannot be rejected. As an illustration, Figure 8a–c displays the evolution of the three relative prices in the baseline simulation along with the three respective natural prices. It should be noted that the higher volatility observed in P2P3 and P3P1 compared to P1P2 can be attributed to the higher volatility displayed in S3, the investment goods sector. Our simulation results are in line with the results of the empirical and analytical investigations pursued by Petrovic (1987) and Shaikh (2016: ch. 9). These authors show that as long as profit rates are within a reasonable range, that is, as long as they are close to the growth rate of the economy, relative prices should be nearly proportional to relative labor values (defined as the direct, indirect and hyper indirect labor)—our natural prices. It is the case here where profit rates are between 0 and 6 per cent on average and where the economy is stationary. The deviation of relative prices from their theoretical natural prices in our simulations remains below 10 per cent, as was famously claimed by David Ricardo with his so-called “93% labor theory of value,” and as was also verified empirically by Petrovic and Shaikh. At this stage, one could argue that prices do not only depend on the markups, but that unit costs of production represent a fundamental component of the prices that we have not uncovered yet. As direct costs in our model are essentially labor costs, they are of course related to the labor values of each type of goods; one should not forget however that the direct costs of S2 also include the cost of intermediate products, and hence they also incorporate the profits of S1, since the price of the intermediate S1 good includes both the unit wage cost and the profit per unit of the S1 good. And of course direct costs do not include the cost of using fixed capital. To address this point, Figure 8a–c also reports the relation between the direct unit costs of production in each sector in a typical baseline simulation. We can easily see that the relative costs in S1 with respect to S2 lie below the natural price between these two sectors (Figure 8a). Intuitively, this implies that for the gravitation to operate, the markup levels in S1 must be higher than in S2. The exact opposite holds between S2 and S3 (Figure 8b). Finally, from Figure 8c, the relative costs in S3 with respect to S1 are visually equivalent to their natural price level, and so should be the markups in those two sectors. This hierarchy in the markups—in which the markup levels in S3 and S1 are roughly similar, while those in S2 are lower—corresponds exactly to the emerging structure that we discuss in Section 4.2. This hierarchy of markups seems then necessary to the emergence of the gravitation phenomenon, given the cost constraints specified in the three sectors. We eventually conduct an experiment in which the markups of all firms in S2 are suddenly increased and set to an exogenous value of 0.6. The shock therefore increases and homogenizes the markups within this sector (while they are on average equal to 0.3 before the shock). This experiment aims to uncover the markup dynamics along the convergence path back to the pre-shock situation, and shed light on the causal mechanism that determines the evolution of the markups and their long-run values. Figure 9 describes the successive steps along this dynamics. The brutal increase in markup in S2 distorts the markup structure between the three sectors, and first leads to an increase in profits of this sector. This higher profitability in turn implies a higher investment in S2 (Figure 9a), which creates overcapacities in this sector with respect to S3 and particularly S1 (Figure 9b and c). However, this state of affairs is only transitory: the idiosyncratic shocks gradually differentiate the firms’ markups, so that firms with lower-than-average markups gain market shares at the expense of firms with higher markups. This can be clearly assessed from the movement of the average markup weighted by market shares which evolves downward in the aftermath of the shock (Figure 9d). Adaptation through market shares is a rather fast process. In contrast, a look at the arithmetic average of the markups (Figure 9e) reveals a much slower evolution, along with a lower volatility, as this indicator depicts a long-run trend that is dictated by bankruptcies and the abandonment of nonprofitable markup strategies. This simple exercise shows that heterogeneity is a strong vector of collective adaptation of the pricing strategies among firms. Figure 9. View largeDownload slide Adaptation of the system in the aftermath of a shock on the markups in S2 in a typical baseline simulation. The red dots represent the transition periods following the shock (100 periods measured yearly in (a), and 400 periods measured yearly in (b) and (c)). (a) Net profits and investment in S2 (measured yearly). (b) (Excess) capacities of S2 w.r.t. S3. (c) (Excess) capacities of S2 w.r.t. S1. (d) Average markup weighted by market shares. (e) Arithmetic markup average. Figure 9. View largeDownload slide Adaptation of the system in the aftermath of a shock on the markups in S2 in a typical baseline simulation. The red dots represent the transition periods following the shock (100 periods measured yearly in (a), and 400 periods measured yearly in (b) and (c)). (a) Net profits and investment in S2 (measured yearly). (b) (Excess) capacities of S2 w.r.t. S3. (c) (Excess) capacities of S2 w.r.t. S1. (d) Average markup weighted by market shares. (e) Arithmetic markup average. 4.4 Introducing an exogenous technological shock Finally, we are interested in the reaction and the ability of the ecology of firms to adapt to technological shocks. Starting from the baseline scenario, and using our model as a virtual laboratory, we dramatically change one technical coefficient during the simulation to produce an exogenous technological shock. Figure 10 reports the effects of such a shock in S2, while we defer the treatments of the shocks on S1 and S3 to Supplementary Appendix B.3, as the observed dynamics obey the same logic (see Supplementary Appendix Figures 14 and 16). Figure 10. View largeDownload slide Effects of a technological shock in S2: (results over 100 replications on Supplementary Appendix Figure 15). (a) Productivities. (b) Workforce distribution. (c) Markups, weighted by sales. (d) Relative prices: S1 to S2. (e) Relative prices: S2 to S3. (f) Relative prices: S3 to S1. Figure 10. View largeDownload slide Effects of a technological shock in S2: (results over 100 replications on Supplementary Appendix Figure 15). (a) Productivities. (b) Workforce distribution. (c) Markups, weighted by sales. (d) Relative prices: S1 to S2. (e) Relative prices: S2 to S3. (f) Relative prices: S3 to S1. The coefficient of the productivity of the machines in the consumption goods sector— pr2—is doubled, from pr2=100 to pr2′=200 in period 1000 (as shown in Figure 10a). As this new technology is incorporated only in the new machines produced from period 1000 on, the diffusion of the productivity shock displays some inertia. The new, more productive, machines gradually replace the old machines as the latter progressively depreciate and disappear. As S2 becomes more productive, we observe a reallocation of the workforce from S2 to S1 and, to a lesser extent, toward S3 (Figure 10b). If we are correct in our interpretation of the emergence of the structure of relative prices, this shock should affect the relative prices of S1 to S2 and of S2 to S3, but not that of S3 to S1. An examination of Figure 10d–f demonstrates that this is indeed the case. After the shock, relative prices are modified and converge toward their new natural values. To uncover why this is the case, recall that, by construction, at the microeconomic level, prices are determined through a markup procedure over production costs. Therefore, the change in relative prices consecutive to the technological shock must be explained by a change in those two components. The productivity shock in S2 does have an immediate effect on the quantity of labor that is necessary to produce consumption goods (see Figure 10b), and hence on the production costs in S2: the unit costs of production in S2 fall sharply, and so do the relative costs and the natural price in S2 with respect to the other sectors (see Figures 10d–f). However, it is important to point out that the movements in the relative costs alone are not enough to allow the prices to gravitate around the new natural prices after the shock. A closer look at Figure 10d for instance shows that the gap between the relative costs and natural prices between S1 and S2 is wider than before the shock (i.e., the gap between the blue and the green curves increases after the shock). Intuitively, this indicates that a new markup structure has to emerge, where the markup in S2 is lower than before, and this is what we observe in Figure 10c (see also Supplementary Appendix Figure 15a). As the technology shock results in a lower natural price of S2 with respect to S1 and S3, firms in S2 revise downward their markup in the wake of the shock. Therefore, those simulations do not allow us to reject Hypothesis 4. This result highlights why an ABM is an appealing tool to investigate our research question in particular, and a wide range of complex economic questions in general. The evolution of the markups after the technological shock reveals two causal processes operating at different levels: the micro causality linking markups to prices, and the macro causality, from technical coefficients (productivity) to relative prices. Those two causalities are interrelated, but their interplay is essential to the adaptation of the economic system after a shock. 5. Interpretation and lessons Our model is a complex system. It includes three interdependent production sectors, the households, and the bank. These interdependencies are both real (labor and commodities) and monetary (money and debts). Firms in each sector are also in competition with each other for inputs and outlets. In such an environment, the question of the allocation of resources and the relative prices is a nontrivial one. Thanks to the radical decentralization principle of ABM, and guided by the observations of Alchian (1950), we let the firms’ pricing strategies follow an evolutionary process in this complex environment, and let the market answer this nontrivial question: How to fix the markups to ensure the survival and the growth of the firms in each sector, and what are the consequences for the relative price levels? The market is a particular form of organization of collective intelligence. Its forces operate like a massive and parallel trial-and-error process. Therefore, the market cannot bring a fast and unambiguous reply to the above-stated complex problem, but, in the long run, we can see the elements of the answer emerge. We first observe the emergence of a long-run stable and systematic structure of relative prices in the model, with a fair amount of short-run volatility. Although firms set their prices according to idiosyncratic and random innovations on the markup, short-run movements in the markups within the sectors are associated with the permanent trade-off between profit seeking and market-share chasing, in a context of ever-evolving market conditions. In the long run, relative prices appear to “gravitate” around their “natural prices,” that is, around the ratio of the quantities of labor directly, indirectly, and hyper-indirectly required for the goods production in each sector. We therefore succeed in building a model of endogenous formation of markups, interpreted as social norms constantly shaped by market conditions. This method of endogenous determination of behavioral parameters could be useful every time that agents in an ABM are confronted with nontrivial choices, resulting in trade-offs, under radical and strategic uncertainty. Of course, our model relies on restrictive assumptions. One of them is the purely random innovation process and the blind imitation procedure (bankrupt firms imitate any of the surviving firms, independently of their relative level of profits). Abstracting from the individual motivations of firms allows us to highlight the dynamics solely implied by market competition. This surely constitutes an advantage of this approach, as such an observation seems impossible in the real world. However, this does not mean that agents actually behave in such a simple way, which is a criticism of the neo-Schumpeterian school toward the Classical evolutionist representation adopted here (Becker et al., 2006; Nelson, 2016). Our results are therefore only valid within the theoretical framework that we have considered here, and might be modified if those radical behavioral assumptions have to be relaxed and made more complex. Similarly, the model has a very simplified financial sector, and shareholders do not discriminate between firms, provided that they do not accumulate overly large losses. If the model were to be more realistic, shareholders would choose the destination of their excess cash according to some more sophisticated estimates of expected risk and return. Furthermore, a more realistic model would also take into account the fact that workers cannot—as we suppose here for the sake of simplicity—easily move from one sector to another. These extensions are left for future research. Another restriction of our framework is the constant number of firms. Even though we have been able to observe concentration or competition effects within the population of firms, this simplification maintains by construction a minimum of market competition, and limits the amount of market power that firms can acquire. This is a deliberate assumption, as our study has focused on the effect of market competition on firms’ pricing behavior. An extension of the model could develop a model of entry, and allow for an endogenous dynamics of the population of firms which could potentially lead to sectoral oligopolies. None of these limitations are structural, and each of them is waiting to be pushed away. Last but not least, it is worth noting that our model is definitively eclectic, featuring ingredients from different and sometimes competing schools of thought. The model includes the post-Keynesian theory of endogenous money and its SFC approach; it includes the concerns of Leontief for industrial interdependence; it is consistent with the classical idea that industrial prices gravitate toward values that are roughly proportional with the sum of the direct and indirect quantities of necessary labor, as can be found in Sraffa, Pasinetti and Lee; it also relies on Simon’s procedural rationality and on Alchian’s evolutionary behavior. Yet, our model is not a chimera. Every ingredient is used because it plays a judicious role in the construction of the model, and results in a coherent synthesis that goes beyond the theoretical borders that fragment economics. This type of model has then the strong advantage of (re)activating the dialog between parallel and competing schools of thoughts to contribute to the emergence of a new, alternative paradigm in (macro)economics. Footnotes 1 Our approach has affinities with that of Silverberg and Verspagen (1994), who were among the first authors to make a strategy of the firms (namely, the share of R&D expenditures) evolve endogenously through a collective learning process. However, the selection mechanism is more parsimonious in our article, as unsuccessful strategies are simply abandoned when firms go bankrupt. 2 See for instance (Seppecher, 2012; Riccetti et al., 2015; Caiani et al., 2016a). 3 Note one exception, that of Mandel et al. (2015); however, the main assumptions of that model are such that it belongs to the tradition of neoclassical general equilibrium theory, and thus has no other link with our own model. 4 Lowe (1976) also considers that a proper analysis requires three sectors. His preferred model has a consumption sector and an investment sector split into two subsectors, where the first subsector produces fixed capital goods for the consumption goods sector, whereas the second subsector produces machines for itself and the other investment subsector. 5 Such an interest-rate feedback rule is motivated by the need for an adjustment mechanism of the interest rate to inflationary pressures, so that real interest rates rise along a debt-driven boom, and eventually provoke the bust. Those emerging Minskian dynamics are discussed in a simpler version of the present model in Seppecher et al. (2018). 6 Thus, here, what we have is the historic direct unit cost of the goods in inventories (Godley and Lavoie, 2007: 266). 7 The firm chooses the proportions of its two main sources of financing so as to achieve its leverage target. However, if its retained earnings turn out to be insufficient, the firm gets the residual amount by taking a short-term bank loan (see the pseudocode, item 15c, page 19). 8 This assumption avoids the complexities of modeling an entry process of firms, while remaining in line with empirical evidence that suggests that new firms replace a similar number of obsolete firms, without significantly affecting the total number of firms in the market (see, notably, (Bartelsman et al., 2003)). 9 In the case where the bank’s capital is insufficient to cover the bankrupted firms’ losses, the bank goes bankrupt and the simulation breaks off. This remains a rare event, which happens once over the 100 replications of the baseline scenario that we report below. 10 The term “natural prices” follows Pasinetti (1988) terminology in models with several vertically integrated sectors. Pasinetti shows that when the profit rate of such a sector is equal to its growth rate, then prices are exactly proportional to the unweighted sum of the direct, indirect, and hyper-indirect labor required to produce the commodity of a sector. Natural prices thus correspond to the pure theory of labor value that could be found in the Classical school of thought. The natural prices that we calculate in Appendix A are labor values, since these natural prices are computed with a zero rate of profit, which corresponds to the zero growth rate of our economy. Bearing all this in mind, we have chosen to use the term of natural prices. While natural prices have some similitude with another concept, the Classical prices of production, they are not the same. In Sraffa (1960) for instance, the definition of prices of production requires a uniform profit rate across sectors. The prices around which the actual prices in our simulations gravitate are not prices of production because profit rates are not uniform, as is explicit from Table 3. The observed prices in our simulations could then best be defined as imperfect prices of production, resulting from cost-plus pricing procedures. 11 We refer the reader, in particular, to Stock and Watson (1999) for empirical estimates of these correlations. 12 Note that we found similar autocorrelation patterns in alternative indicators of aggregate activity, such as employment. The persistence of the macroeconomic variables in our model seems to be weaker than their empirical counterparts, which typically display unit-root behaviors. In our view, this is due to several features of the model, namely, the absence of the government sector, the very flexible nature of the labor market with only relatively short-term contracts, and the limited number of agents in the model. An autonomous public sector is indeed sometimes used in ABMs to mitigate aggregate fluctuations (Russo et al., 2014; Caiani et al., 2016a). Besides, preliminary simulations with a higher number of agents seem to indicate that bigger populations tend to smooth out aggregate fluctuations, without altering our main results. For computational time reasons, we then use a baseline scenario with a limited number of agents. 13 Comparing the standard deviations of the corresponding band-pass filtered time series, investment is on average almost two times (1.84 with a standard deviation of 0.11 over the 100 replications) more volatile than GDP, while the volatility of consumption is two-third of that of GDP (with a standard deviation of 0.07). These numbers are roughly in line with the ones reported in Stock and Watson (1999: Table 2, p. 30), i.e., respectively, 3 and 0.68. 14 We recall that the productivity of every machine is time-invariant and common to all firms in our model. Therefore we cannot discuss cross-sectional differences or evolution in productivity, which limits the scope of microeconomic stylized facts that we could seek to match. 15 We display once in the main text, here, the robustness over 100 replications of the baseline scenario. In the sequel, we defer to Supplementary Appendix B.2 any proof of robustness across replications, and only discuss outcomes from a typical baseline simulation in the main text. 16 Additional simulations, not displayed here but available upon request, show that varying the number of firms does not affect the emerging hierarchy of markups. References Alchian A. A. ( 1950 ), ‘ Uncertainty, evolution, and economic theory ,’ Journal of Political Economy , 58 ( 3 ), 211 – 221 . Google Scholar Crossref Search ADS Assenza T. , Delli Gatti D. , Grazzini J. ( 2015 ), ‘ Emergent dynamics of a macroeconomic agent based model with capital and credit ,’ Journal of Economic Dynamics and Control , 50 , 5 – 28 . Google Scholar Crossref Search ADS Bartelsman E. , Scarpetta S. , Schivardi F. ( 2003 ), ‘Comparative analysis of firm demographics and survival: micro-level evidence for the OECD Countries,’ OECD Economics Department Working Papers 348, OECD Publishing. Becker M. C. , Knudsen T. , March J. G. ( 2006 ), ‘ Schumpeter, winter, and the sources of novelty ,’ Industrial and Corporate Change , 15 ( 2 ), 353 – 371 . Google Scholar Crossref Search ADS Blanchard O. ( 2008 ), ‘The state of macro,’ National Bureau of Economic Research Working Paper (14259). Bruun C. ( 1999 ), ‘Agent-based Keynesian economics—simulating a monetary production system bottom-up,’ Technical report, Aalborg University : Aalborg . Caiani A. , Godin A. , Caverzasi E. , Gallegati M. , Kinsella S. , Stiglitz J. E. ( 2016a ), ‘ Agent based-stock flow consistent macroeconomics: towards a benchmark model ,’ Journal of Economic Dynamics and Control , 69 , 375 – 408 . Google Scholar Crossref Search ADS Caiani A. , Russo A. , Palestrini A. , Gallegati M. ( 2016b ), Economics with Heterogeneous Interacting Agents: A Practical Guide to Agent-Based Modeling . Springer : Switzerland . Caverzasi E. , Godin A. ( 2015 ), ‘ Post-Keynesian stock-flow-consistent modelling: a survey ,’ Cambridge Journal of Economics , 39 ( 1 ), 157 – 187 . Google Scholar Crossref Search ADS Cincotti S. , Raberto M. , Teglio A. ( 2010 ), ‘ Credit money and macroeconomic instability in the agent-based model and simulator Eurace ,’ Economics: The Open-Access, Open-Assessment E-Journal , 4 ( 2010-26 ), 1 – 32 . Google Scholar Crossref Search ADS Cohen K. J. ( 1960 ), ‘ Simulation of the firm ,’ American Economic Review , 50 ( 2 ), 534 – 540 . Coutts K. , Godley W. , Nordhaus W. ( 1978 ), Industrial Pricing in the United Kingdom , Cambridge University Press : Cambridge . Coutts K. , Norman N. ( 2013 ), ‘Post-Keynesian approaches to industrial pricing,’ in Harcourt G. C. , Kriesler P. (eds), The Oxford Handbook of Post-Keynesian Economics , Vol. 1 . Theory and Origins, Oxford University Press : Oxford , pp. 443 – 466 . Dawid H. , Gemkow S. , Harting P. , van der Hoog S. , Neugart M. ( 2011 ), ‘The Eurace@Unibi model: an agent-based macroeconomic model for economic policy analysis,’ Technical Report, Bielefeld University : Bielefeld . Dawid H. , Harting P. , Neugart M. ( 2014 ), ‘ Economic convergence: policy implications from a heterogeneous agent model ,’ Journal of Economic Dynamics and Control , 44 , 54 – 80 . Google Scholar Crossref Search ADS Delli Gatti D. , Gaffeo E. , Gallegati M. , Giulioni G. , Kirman A. , Palestrini A. , Russo A. ( 2007 ), ‘ Complex dynamics and empirical evidence ,’ Information Sciences , 177 ( 5 ), 1204 – 1221 . Google Scholar Crossref Search ADS Dixit A. K. , Stiglitz J. E. ( 1977 ), ‘ Monopolistic competition and optimum product diversity ,’ American Economic Review , 67 ( 3 ), 297 – 308 . Dosi G. , Fagiolo G. , Napoletano M. , Roventini A. , Treibich T. ( 2015 ), ‘ Fiscal and monetary policies in complex evolving economies ,’ Journal of Economic Dynamics and Control , 52 , 166 – 189 . Google Scholar Crossref Search ADS Dosi G. , Fagiolo G. , Roventini A. ( 2010 ), ‘ Schumpeter meeting Keynes: a policy-friendly model of endogenous growth and business cycles ,’ Journal of Economic Dynamics and Control , 34 , 1748 – 1767 . Google Scholar Crossref Search ADS Dosi G. , Pereira M. C. , Virgillito M. E. ( 2016 ), ‘ The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics ,’ Industrial and Corporate Change , 26 ( 2 ), 187 – 210 . Durkheim É. ( 1984 ), The Division of Labour in Society . Macmillan : London . Fabiani S. , Druant M. , Hernando I. , Kwapil C. , Landau B. , Loupias C. , Martins F. , Matha T. , Sabbatini R. , Stahl H. , Stokman A. ( 2006 ), ‘ What firms’ surveys tell us about price-setting behavior in the Euro area ,’ International Journal of Central Banking , 2 ( 3 ), 3 – 47 . Franke R. ( 2017 ), ‘ A simple approach to overcome the problems from the keynesian stability condition ,’ European Journal of Economics and Economic Policies: Intervention , 14 ( 1 ), 48 – 69 . Google Scholar Crossref Search ADS Godley W. , Lavoie M. ( 2007 ), Monetary Economics, an Integrated Approach to Credit, Money, Income, Production and Wealth . Palgrave Macmillan : Basingstoke . Hall R. L. , Hitch C. J. ( 1939 ), ‘ Price theory and business behavior ,’ Oxford Economic Papers , 2 , 12 – 45 . Google Scholar Crossref Search ADS Kinsella S. , Greiff M. , Nell E. J. ( 2011 ), ‘ Income distribution in a stock-flow consistent model with education and technological change ,’ Eastern Economic Journal , 37 ( 1 ), 134 – 149 . Google Scholar Crossref Search ADS Kirman A. P. , Vriend N. J. ( 2000 ), ‘Learning to be loyal. a study of the marseille fish market,’ in Gatti D. D. , Gallegati M. , Kirman A. (eds), Interaction and Market Structure: Essays on Heterogeneity in Economics . Springer : Berlin; Heidelberg , pp. 33 – 56 . Lavoie M. ( 1992 ), Foundations of Post-Keynesian Economic Analysis . Edward Elgar : Aldershot . Lavoie M. , Stockhammer E. (eds) ( 2013 ), Wage-Led Growth: An Equitable Strategy for Economic Recovery . Palgrave Macmillan : Basingstoke . Lee F. ( 2011 ), ‘ Heterodox microeconomics and the foundation of heterodox macroeconomics ,’ Economía Informa , 367 , 6 – 20 . Lee F. S. ( 1994 ), ‘ From post-Keynesian to historical price theory, part I: facts, theory and empirically grounded pricing model ,’ Review of Political Economy , 6 ( 3 ), 303 – 336 . Google Scholar Crossref Search ADS Lee F. S. ( 1998 ), Post Keynesian Pricing Theory , Cambridge University Press : Cambridge . Lee F. S. ( 2014 ), ‘Heterodox theory of production and the mythology of capital: a critical inquiry into the circuit of production,’ Presented at the Association for Heterodox Economics 2014 annual meeting. Unpublished working paper. Lee F. S. , Irving-Lessmann J. ( 1992 ), ‘ The fate of an errant hypothesis: the doctrine of normal-cost prices ,’ History of Political Economy , 24 ( 2 ), 273 – 309 . Google Scholar Crossref Search ADS Leontief W. W. ( 1936 ), ‘ Quantitative input and output relations in the economic systems of the United States ,’ Review of Economic Statistics , 18 ( 3 ), 105 – 125 . Google Scholar Crossref Search ADS Leontief W. W. ( 1937 ), ‘ Interrelation of prices, output, savings, and investment ,’ Review of Economic Statistics , 19 ( 3 ), 109 – 132 . Google Scholar Crossref Search ADS Lowe A. ( 1976 ), The Path of Economic Growth . Cambridge University Press : Cambridge . Mandel A. , Landini S. , Gallegati M. , Gintis H. ( 2015 ), ‘ Price dynamics, financial fragility and aggregate volatility ,’ Journal of Economic Dynamics and Control , 51 , 257 – 277 . Google Scholar Crossref Search ADS Marglin S. A. ( 1984 ), Growth, Distribution, and Prices . Harvard University Press : Cambridge, MA . Mazzoleni R. , Nelson R. R. ( 2013 ), ‘ An interpretive history of challenges to neoclassical microeconomics and how they have fared ,’ Industrial and Corporate Change , 22 ( 6 ), 1409 – 1451 . Google Scholar Crossref Search ADS Means G. C. ( 1936 ), ‘ Notes on inflexible prices ,’ American Economic Review , 26 ( 1 ), 33 – 35 . Minsky H. P. ( 1975 ), John Maynard Keynes . Columbia UniversityPress : New York, NY . Minsky H. P. ( 1982 ), Can ‘It’ Happen Again? Essay on Instability and Finance . M. E. Sharpe : Armonk . Nekarda C. , Ramey V. ( 2013 ), ‘The cyclical behavior of the price-cost markup,’ Technical Report NBER Working Papers 19099, NBER : Cambridge, MA . Nelson R. R. ( 2016 ), ‘ Behavior and cognition of economic actors in evolutionary economics ,’ Journal of Evolutionary Economics , 26 ( 4 ), 737 – 751 . Google Scholar Crossref Search ADS Nelson R. , Winter S. ( 1982 ), An Evolutionary Theory of Economic Change . Belknap Press : Cambridge, MA . Pasinetti L. L. ( 1977 ), Lectures on the Theory of Production . Columbia University Press : New York, NY . Pasinetti L. L. ( 1981 ), Structural Change and Economic Growth . Cambridge University Press : Cambridge . Pasinetti L. L. ( 1988 ), ‘ Growing subsystems, vertically hyper-integrated sectors and the labour theory of value ,’ Cambridge Journal of Economics , 12 ( 1 ), 125 – 134 . Google Scholar Crossref Search ADS Petrovic P. ( 1987 ), ‘ The deviation of production prices from labour values: some methodological and empirical evidence ,’ Cambridge Journal of Economics , 11 ( 3 ), 197 – 210 . Riccetti L. , Russo A. , Gallegati M. ( 2015 ), ‘ An agent based decentralized matching macroeconomic model ,’ Journal of Economic Interaction and Coordination , 10 ( 2 ), 305 – 332 . Google Scholar Crossref Search ADS Rotemberg J. J. , Woodford M. ( 1999 ), ‘ The cyclical behavior of prices and costs ,’ Handbook of Macroeconomics , 1 , 1051 – 1135 . Google Scholar Crossref Search ADS Russo A. , Riccetti L. , Gallegati M. ( 2014 ), ‘Growing inequality, financial fragility, and macroeconomic dynamics: an agent based model,’ in Kaminski B. , Koloch G. (eds), ‘ Advances in Social Simulation. Advances in Intelligent Systems and Computing , Vol. 229 . Springer Berlin Heidelberg : Berlin; Heidelberg , pp. 167 – 176 . Seppecher P. ( 2012 ), ‘ Flexibility of wages and macroeconomic instability in an agent-based computational model with endogenous money ,’ Macroeconomic Dynamics , 16 ( s2 ), 284 – 297 . Google Scholar Crossref Search ADS Seppecher P. , Salle I. , Lang D. ( 2018 ), ‘Is the market really a good teacher?’, Journal of Evolutionary Economics , https://doi.org/10.1007/s00191-018-0571-7. Shaikh A. ( 2016 ), Capitalism. Competition, Conflict, Crises . Oxford University Press : New York, NY . Silverberg G. , Verspagen B. ( 1994 ), ‘ Learning, innovation and economic growth: a long-run model of industrial dynamics ,’ Industrial and Corporate Change , 3 ( 1 ), 199 – 223 . Google Scholar Crossref Search ADS Simon H. A. ( 1979 ), ‘ Rational decision making in business organizations ,’ American Economic Review , 69 ( 4 ), 493 – 513 . Sraffa P. ( 1960 ), Production of Commodities: Prelude to a Critique of Economic Theory . Cambridge University Press : Cambridge . Steedman I. ( 1992 ), ‘ Questions for Kaleckians ,’ Review of Political Economy , 4 ( 2 ), 125 – 151 . Google Scholar Crossref Search ADS Stock J. H. , Watson M. W. ( 1999 ), ‘Business cycle fluctuations in us macroeconomic time series,’ in Taylor J. B. , Woodford M. (eds), Handbook of Macroeconomics , Vol. 1 . Elsevier : Amsterdam , chapter 1, pp. 3 – 64 . Tesfatsion L. ( 2006 ), ‘Agent-based computational economics: a constructive approach to economic theory,’ in Tesfatsion L. , Judd K. L. (eds), Handbook of Computational Economics , Vol. 2 . Elsevier/North-Holland : Amsterdam . Thaler R. H. ( 1990 ), ‘ Anomalies: saving, fungibility, and mental accounts ,’ Journal of Economic Perspectives , 4 ( 1 ), 193 – 205 . Google Scholar Crossref Search ADS Wood A. ( 1971 ), ‘Economic analysis of the corporate economy: a survey and critique,’ in Marris R. , Wood A. (eds), The Corporate Economy: Growth, Competition and Innovative . Harvard University Press : Cambridge , pp. 37 – 67 . Appendix A. Assessing the natural prices of the three types of commodities First we define the direct, indirect, and indirect quantities of labor that are necessary to produce a unit of commodity. Our definitions are inspired by those of Pasinetti (1981): The direct labor is the amount of the labor that is used in the firm for the production of the commodity. The indirect labor is the total amount of labor (direct, indirect, and hyper-indirect) that has been expended outside the firm, but which was necessary to produce the intermediate goods that were used by the firm for the production of its commodity. Hyper-indirect labor is the total amount of labor that was expended to produce the machine that was used by the firm to produce its commodity. Next, we calculate l1;l2;l3 ⁠, the amounts of labor, as defined above, required for the production of one unit of good in each sector S1; S2; S3. Starting from the technical coefficients (see Supplementary Appendix Table 14), we obtain the following: Sector 3: We start with Sector 3 because the production technology of this sector is fully self-contained, since it produces investment goods with only labor and its own machines. Thus it is possible to calculate the quantity of labor which is necessary to produce one unit of commodity of this sector by only relying on the technical coefficients of this sector. We wish to calculate, l3, the quantity of total labor which is necessary on average for the production of one unit of investment good. A machine in Sector 3, the average lifetime of which is E(dk) periods, during which its average rate of capacity utilization was equal to u3, will thus produce pr3u3E(dk) units of investment goods over its lifetime. During this same time period, this production has required the use of u3E(dk) units of direct labor. To this direct labor one must add the quantity of hyper-indirect labor that was necessary for the production of this machine. The machine was produced with the help of k3 units of investment goods, fabricated by the same Sector 3, through the use of k3l3 units of direct labor. Thus we have: pr3u3E(dk)·l3=u3E(dk)+k3l3. (4) (pr3u3E(dk)−k3)l3=u3E(dk). (5) l3=u3E(dk)pr3u3E(dk)−k3. (6)Sector 1: We move on to Sector 1, since this sector produces intermediate goods with the help of labor and machines. But we now know the total quantity of labor which is necessary to produce the machines coming out of Sector 3. We thus have the elements that are needed to compute the quantity of labor that is necessary for Sector 1 to produce one unit of intermediate good. Over its lifetime, a machine in Sector 1 will normally produce pr1u1E(dk) units of intermediate commodities, while u1E(dk) will be the amount of direct labor necessary to produce this amount of intermediate goods. With k1 the quantity of investment goods consumed for the creation of this machine, we get: pr1u1E(dk)·l1=u1E(dk)+k1l3. (7) l1=1pr1(1+k1l3u1E(dk)). (8)Sector 2: This is the most difficult sector to deal with, since it requires the use of machines made in Sector 3 as well as intermediate inputs that are produced by Sector 1. Over its lifetime, a machine in Sector 2 will normally produce pr2u2E(dk) units of consumption goods; u2E(dk) will be the amount of direct labor necessary to produce this amount of consumption goods; and pr2u2E(dk)j2 will be the amount of intermediate goods consumed to produce this same amount of consumption goods. With k2 the amount of investment goods that are consumed for the creation of this machine, we get: pr2u2E(dk)·l2=u2E(dk)+pr2u2E(dk)j2l1+k2l3. (9) l2=1pr2(1+k2l3u2E(dk))+j2l1. (10)Computation of natural prices: All the parameters that lead to the computation of the l1, l2, and l3 values are exogenous, with the exception of the sectoral rates of capacity utilization u1, u2, and u3. For the sake of simplicity, we suppose full utilization of capacities, that is, u1=u2=u3=1 ⁠. With these values and those of the technical coefficients in the baseline scenario (see Supplementary Appendix Table 14), we what we call the ex ante relative natural prices by making use of equations (6), (8), and (10): l1l2=0.5. (11) l2l3=2.15. (12) l3l1=0.9302. (13) When there is a technological shock, the technical coefficients take new values. The natural prices described by equations (6), (8), and (10) get modified, and the new relative natural prices l1/l2, l2/l3 and l3/l1 can be computed again. Table A1 displays the results when we still assume that u1=u2=u3=1 ⁠. Table A2 displays the results arising from the same baseline and the same technological shocks, but this time by making use of the realized rates of capacity utilization over a number of runs (what we call the ex post natural prices). When comparing the relative natural prices in Tables A1 and A2, one sees that computations based on the ex ante assumption of full capacity utilization instead of realized rates of utilization barely change the results. This justifies the use of the ex ante natural prices, as we did in the figures of the main text. Gravitation: Knowing l1, l2, and l3, at each period t, we can compute the ϵ1,t and ϵ2,t ⁠, and distances of the relative prices P1,tP2,t and P2,tP3,t from their respective natural prices l1l2 and l2l3 ⁠: ϵ1,t=P1,tP2,tl1l2−1. (14) ϵ2,t=P2,tP3,tl2l3−1. (15) © The Author(s) 2018. Published by Oxford University Press on behalf of Associazione ICC. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - What drives markups? Evolutionary pricing in an agent-based stock-flow consistent macroeconomic model
JF - Industrial and Corporate Change
DO - 10.1093/icc/dty011
DA - 2018-12-01
UR - https://www.deepdyve.com/lp/oxford-university-press/what-drives-markups-evolutionary-pricing-in-an-agent-based-stock-flow-FrXMDbds5O
SP - 1045
VL - 27
IS - 6
DP - DeepDyve
ER -