1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix

The paper offers a theoretical analysis of long-run economic growth as an outcome of structural changes. We model the microeconomic behaviour of firms in the final good and capital sectors, and the evolution of classes of workers/consumers. We carefully craft economic behaviour onto empirical evidence, and solve the model numerically. The results illustrate the microeconomic properties of the simulated growth patterns. In particular, we observe and explain the interactions between technological change, firm organization, income distribution, consumption behaviour and growth. We confirm the relevance and interdependence of these structural changes, and underline their microeconomic sources.


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix

Cross-country divergence in growth rates has been a solid empirical stylized fact for decades (Denison, 1967, 1979; Maddison, 1987; Barro, 1991; Durlauf and Quah, 1998). The theoretical and empirical assessment of the extent to which the (change in the) structure of the economy is one of the main determinants of growth and, ultimately, of what determines changes in the production structure (e.g. Saviotti and Gaffard, 2008) are more debatable issues.

Since the seminal work by Pasinetti (1981), scholars in the Keynesian and Classical traditions have acknowledged that technological change, changes in the structure of production and the evolution of demand could disrupt the sectoral composition of the economy and the steady path of macroeconomic growth. This work is mainly found in the context of aggregated models (see, for instance, Kurz and Salvadori, 1998; Cesaratto et al., 2003).

From a rather different perspective, since the seminal contribution by Nelson and Winter (1982), the long-term impact of technical change on economic growth has become a rich and consolidated domain of evolutionary growth theory (Dosi, 1982; Dosi et al., 1988; Chiaromonte and Dosi, 1993; Silverberg and Verspagen, 2005). However, within this stream of literature, only a few scholars have attempted to look at the joint effect of supply changes and demand composition on growth and structural change from a sectoral and micro perspective (Verspagen, 1993, 2004; Montobbio, 2002; Ciarli, 2005; Ciarli and Valente, 2005; Lorentz and Savona, 2008; Lorentz, 2009). None of these works looks specifically at the interaction between structural changes in production and organization, earnings distribution and changes in consumption. Saviotti and Pyka (2004, 2008) examined economic growth as resulting from the emergence of new sectors and increased product variety. However, creation of variety is exogenous and links to the demand side are left unexplored.

In the literature investigating the role of the demand side in economic growth, there have been a few major attempts to challenge standard neoclassical consumer theory in some of the most heroic hypotheses on consumer behaviour (see, for instance, Deaton and Muellbauer, 1980a, 1980b; Cowan et al., 1997; Aversi et al., 1999). Demand constrains and is constrained by the response of supply at the micro-level of analysis. Changes in the structure of consumption also depend on firms reactions, as Schumpeter emphasized (Schumpeter, 1934). Within the evolutionary literature, analysis of demand and consumption behaviour is still at an early stage, although a few recent contributions have looked at how consumption ‘needs’ evolve (Swann, 1999; Valente, 1999; Witt, 2001, 2008; Babutsidze, 2007), but have not taken account of the link between demand patterns and changes in the structure of production. Also, none of these contributions attempts explicitly to disentangle at the micro-level the role of distributional changes as the natural channel for the evolution of the consumption structure.

The large and consolidated literature on the two-way link between economic growth and distributional change remains confined to macro-level analyses, since the seminal Kuznet's curve and the works by Pasinetti (1962), Meade (1963), Stiglitz (1969) and Tinbergen (1975), which were extended by Atkinson (1997), Galbraith et al. (1999), Galbraith (1999) and Aghion (2002). In the context of aggregate analysis, the extensive literature on skill-biased technical change implicitly hints at the relation between demand and production structure. In line with Tinbergen (1975), wage dynamics and earnings distribution are argued to reproduce the competition between demand and supply of skills. More recent empirical literature (for a review see Aghion et al., 1999), however, shows that earnings distribution is more complex than reproduction of education-level distribution, with inequalities appearing also within educational classes. Galbraith et al. (1999) and Galbraith (1999), among others, proposed a different view of earnings distribution based on inequality in income and earnings as linked to the sectoral structure of a country. Wage distribution should ultimately depend on the specialization of the economy, at both international (Prebish–Singer hypothesis) and national (à la Kaldor) levels.

At the micro-level of analysis, the literature on firm organization offers an appealing explanation for the too simplistic skill-bias effect (Atkinson, 2007). Recently, Caroli and Van Reenen (2001) show that increased decentralization of production and work organization—for instance, due to the adoption of Information and Communication Technologies—demands greater responsibility and increased wage compensation for executives, but unchanged wages for first-tier workers. This literature implicitly reprises an overlooked stream of contributions (Simon, 1957; Lydall, 1959; Rosen, 1982), which analyse the relation between firms' organizational structure, the composition of workers and executives, and the corresponding wages structure. This work was extended, among others, by Waldman (1984), Abowd et al. (1999) and Prescott (2003) and some empirical contributions have produced corroborative results on the relation between firm size and wage distribution (Brown and Medoff, 1989; Oi and Idson, 1999; Criscuolo, 2000; Bottazzi and Grazzi, 2007).

Galbraith's position is to go beyond the rather bold, all-embracing explanation of technical change being responsible for skill-bias and wage polarization. This explanation risks overlooking the complex set of ‘side-effects’ that follow a firm's decision to adopt technology, which includes changes in the functional division of labour, organizational structure and wage stratification within the firm. In this respect, Simon and Lydall's contributions—and the micro-evidence provided since—offer a useful micro-level perspective of what goes on inside the firm alongside skill-biased technical change. It is at the intersection of this micro- and macro-level literature that our contribution is aimed.

Our conjecture, supported by various theoretical and empirical contributions and detailed in section 2, is that changes in the economic structure and (trade and sectoral) specialization have been accompanied by changes in the organizational structure of firms, which together have brought about changes in the wages and earning structures. Therefore, both micro- and meso-level mechanisms are behind the changes in consumption patterns, which feed back into changes in the production structure at firm and sectoral levels. Thus the original contribution of this work is along two axes.

First, on a theoretical level, we hope to contribute to the growth literature by explicitly introducing income distribution as one of the main channels of changes in the organization of firms into consumption patterns. We suggest and model an explicit relation between organization, technology and wage composition at the firm level, which goes beyond the well-known skill-bias effect in determining the distribution of income at macro-level. We endogenize the role of income distribution by formalizing a relation between changes in earnings distribution and changes in consumption.

Second, from a methodological point of view, we provide a (agent-based) micro-foundation for our conjecture and develop a model where micro-behaviour is directly inspired by the evolutionary literature. We include meso- and macro-level constraints feeding back into the micro-level, such that changes in the micro-level supply side—i.e. technological intensity, organization and firm size—affect the composition of workers/income classes and, as a consequence, consumption behaviour. Demand affects firm size and shapes the market structure. This leads to the emergence of different patterns of growth and income distribution, which in turn become new constraints at the micro-level of decision making.

The purpose of the model is to produce simulated results fitting the existing empirical evidence and (possibly more relevantly) to root the simulation's equivalents of macro-phenomena onto their underpinning micro-components, by showing how they are generated. The paper introduces a general micro- to macro-framework and provides a detailed description of the model, its rationale and hypotheses. For reasons of space, we focus on the analysis of the main aggregate properties of the model, and identify the most relevant micro-dynamics behind them.

The paper is organized as follows. Section 2 describes the model, the rationale and the underlining assumptions in detail. Section 3 provides an analysis of its properties via numerical simulations: section 3.2 reports the results of the micro- and meso-dynamics and section 3.3 the macro-dynamics of growth and income distribution. Finally, section 4 summarizes the main findings and proposes directions for future research where extensions of this model might be usefully exploited.


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix

We model an unconstrained economy where population grows endogenously as a response to labour demand. Following existing Schumpeterian growth models (see, among others, Chiaromonte and Dosi, 1993; Silverberg and Verspagen, 2005), the economy is composed of two sectors—final and capital goods—and different classes of consumers. We assume that firms in the final good sector can freely borrow from the financial market. Nonetheless, the production capacity of capital good firms, providing capital to final good firms, represents a short-term, partially endogenous, constraint for final good firms. These rather bold assumptions allow us to emphasize, on the one hand, the role of the structural variables over population growth rate and labour market dynamics; on the other hand, they allow us to focus on the aggregate growth patterns emerging from micro-level heterogeneity in consumption and production decisions. The main features of the model are described below.

First, firms produce a good that—for simplicity—satisfies one single need along two characteristics, quality and price. Different quality levels represent competing technologies/designs within the same sector. Firms are therefore heterogeneous with respect to the quality level of the product and compete on the basis of production costs. Consumption decisions—detailed below—are responsible for firm selection.

Second, firms are defined with respect to their organization structure. This consists of number of hierarchical tiers of workers and executives and wage differentials across tiers. The number of workers that a higher tier of executives can coordinate determines the pace at which an increase in firm size generates new working tiers.

Third, the hierarchical structure of wages, linked to firm organization, determines the distribution of earnings and income. Firm selection and increase in firm size (i.e. number of hierarchical tiers) determine the changing composition of workers and executives. This, together with the wage differentials, translates into changes in the distribution of earnings and is in turn responsible for the change in the composition of consumption classes. This is the main mechanism in our model that links changes in the organization of production and consumption via earnings at the micro-level, and that makes growth and inequality patterns to emerge at the macro-level. The ‘national’ minimum wage is the base salary on which firms derive the pyramidal structure of payments. This is determined at the macro-level and results from (un)employment dynamics and the national bargaining that takes place when consumer prices and the average contribution of labour to added value change.

Fourth, the composition of consumption across different classes is endogenously determined by the hierarchical structure of the firm organization. Consumers across classes differ in terms of consumption preferences over the two characteristics. We assume a structure of preferences such that the higher the hierarchical tier that reflects the consumer class, the looser is the selection of firms with respect to prices, and the stricter with respect to the quality of the good. Changes in the distribution of preferences define the demand curve and firms' market shares. Once a consumer class is defined, or emerges, consumption behaviour draws upon the theoretical construction developed by Valente (1999).

Finally, technological change affects the production of capital and its use by final good firms. Changes in production processes are modelled as investment in different capital vintages. By changing vintages, firms alter the capital/labour ratio of their technology, which affects the composition of the labour structure and income distribution in the consumer market. An increase in productivity from a new vintage follows an increase in the amount of resources that capital good firms invest in Research and Development (R&D).

2.1 Final good firms

We model a given population of f∈ {1, 2, . . . , F} firms in the final good sector. Each firm produces one good, which is defined by two characteristics, price and quality. Each firm serves a related share of demand.

2.1.1 Production process and sales

We assume that the level of demand received by a firm is met from current production and inventories, or delayed at no cost. The delayed orders increase the existing backlog of unfulfilled demand. Decisions about the quantity to produce are meant to smooth out short-term volatility, and are aimed at an amount of output that, on average, will be sufficient to meet expected demand with no backlogs, and to maintain a precautionary level of inventory. In detail, production is formalized as follows.

Current expected sales are a convex combination of past expectations inline image and share of total demand faced by a firm (Yt−1):1

  • image(1)

We assume a slow adaptation in sales expectations (as) as an outcome of agents' conservative behaviour. In order to cover unexpected changes in demand, firms maintain a desired level of inventories (inline image), where inline image is a fixed ratio.2

Desired production (inline image) therefore depends on: expected demand (inline image), available inventories (inline image) and unfulfilled demand from the previous simulation steps, the backlog, Bt−1:

  • image(2)

Actual output produced (Qt) may not reach the desired level because of limitations in capital or labour availability:

  • image(3)

At−1 is the level of productivity of labour (Lt−1) embodied in the firms' capital stock (Kt−1) and DKt−1 is the maximum production level allowed by this capital stock. The capital intensity (1/D) remains fixed.3

Then, the gap between actual demand and production is reflected in the inventories or, if these are null and sales exceed production, in the backlog, computed as follows:

  • image(4)
  • image(5)
2.1.2 Labour

We draw upon Simon (1957), Lydall (1959) and Rosen (1981, 1982) and further extensions (Waldman, 1984; Abowd et al., 1999; Prescott, 2003) to represent the firm's labour organization. According to this literature, the size of the firm and the number of its hierarchical tiers—i.e. the proportion of executives and workers—affect the structure of pay.

Given the level of output, firms employ (displace) first-tier workers (inline image) according to the labour productivity of the capital vintages (At−1), and in order to maintain an unused labour capacity (ul) to insure against unexpected labour shortages:

  • image(6)

where the inertial factor εL mimics labour market rigidities, and is interpreted as the elasticity in matching models (see equation (34)). We assume there is quite a slow adaptation in labour markets (large εL and εM).

In addition to first-tier employees, firms need to hire ‘executives’ to manage every batch of v first-tier workers, third-level executives for every group of v second-tier workers, and so on. The number of workers in each tier, given inline image, is thus

  • image(7)

where Λ is the total number of tiers required to manage the firm. Consequently, the total number of workers is

  • image(8)

Ultimately, the constraint on production due to labour is determined by first-tier workers and their productivity only. The ‘managers’, required to organize production, increase the variable costs. We implicitly assume that a firm finds its best organizational configuration given the number of first-tier workers, and given the organizational design proxied by v.

2.1.3 Wage, cost and price determination

The labour cost essentially depends on the minimum wage, endogenously determined at macro-level (see section 2.3), and on the firm's hierarchical structure. First-tier wages are set by firms as a fixed multiple ω of the minimum wage inline image:

  • image(9)

As we move upstream in the organizational hierarchy, the wage increases by a fixed-tier multiplier b, which determines the skewness in the wage distribution, in line with Simon (1957) and Lydall (1959).

  • image(10)

As noted in Atkinson (2007), the exponential structure of wage-tier increase is not sufficient to explain the skewness in earnings distribution. On top of their wages, executives can receive wage premiums, inline image. Firms distribute (to managers only) the profits available after paying for capital purchases, inline image. The premium paid to for each manager is proportional to the regular wage:

  • image(11)

Therefore, the overall earnings for a member of tier l are inline image, with inline image. We assume that when facing capital constraint, firms always prioritize capital investment, and whenever there is a positive residual, this is distributed to managers. Distributed profits hence amount to

  • image(12)

where inline image is the capital investment of vintage τh and inline image its price set by the capital good firm g from which it is acquired (see respectively sections 2.1.4 and 2.2.2).

The price is set at firm level as a mark-up on variable costs.4

  • image(13)

Note that the tier-wage structure of variable costs implies diseconomies of scale in labour input, based on the evidence that labour costs are higher for larger firms (Idson and Oi, 1999; Criscuolo, 2000; Bottazzi and Grazzi, 2007). This is due to the necessary increase in the number of tiers of managers required to coordinate a larger number of first-tier workers. Profits (πt) then result as the difference between the value of current sales (Yt) and the variable costs of production:

  • image(14)
2.1.4 Capital and investment

Following Amendola and Gaffard (1998) and Llerena and Lorentz (2004), capital goods are not used as production inputs in the strict sense, but constitute the basis for the firm's production capacity. The accumulation of capital is a pre-condition for any production activity, constraining the actual production level and affecting the efficiency of the labour force. This is also in line with some neo-Schumpeterian models (Verspagen, 1993; Llerena and Lorentz, 2004), which provide evolutionary and micro-foundations for the Kaldor–Verdoorn Law and the cumulative causation mechanism (Verdoorn, 1949; Kaldor, 1966). Therefore, in our model, firms' investment decisions depend on comparisons between current maximum production capacities and expected demand. We assume that capital intensity is constant for all capital vintages and all capital good firms. We also assume that firms can freely access a financial market for capital investment, and we remove profit constraints on the level of investment.5 As a consequence, following a sharp increase in demand, firms may well register short-term negative profits, and require a few time periods before they are able to distribute profits.

The capital stock of a firm, where V indicates the number of capital vintages acquired, kh and τh the amount of capital and date of purchase of vintage h, respectively, is computed as

  • image(15)

where δ is the depreciation rate. The level of productivity embodied in the capital stock is computed as the average productivity across all the vintages available:

  • image(16)

where inline image is the productivity embodied in the h vintage.

Indicating as u the required percentage of unused stock, then the desired amount of new capital (expressed in production units) is

  • image(17)

If inline image is positive, the firm needs to select one of the capital good producers g∈ {1, 2, . . . , G} and place an order for the desired stock. To select among capital good producers we built an index proportional to the productivity of the producers' vintages ag,t−1, and to the inverse of the capital price inline image and time of delivery rg,t:

  • image(18)

where over-signed variables are the non-weighted averages across capital-producing firms, and inline image, inline image, inline image are the final good firm's f constant preferences over capital price, productivity and delivery time. After computing the indexes for all capital good producers, final good firms select the producer with the highest normalized index

  • image

The price of the capital good and the productivity embodied are fixed at the time of the order. However, actual delivery may take place after one or more time steps, depending on the production capacity of the supplier (inline image) and its existing order book (inline image) (see next section 2.2.1). That is, an investment in new capital inline image, bought from capital good firm g, increases the capital stock of the final good firm in period t+ 1 only if inline image.6 While a final good firm is waiting for an ordered capital, it cannot submit new orders, or revise existing ones.

This feature of investment dynamics has three important implications. First, it is in line with the micro-level empirical evidence on the lumpiness of investment (e.g. Doms and Dunne, 1998). Second, it generates a trade-off between immediately acquiring a less productive vintage and waiting longer for a more productive vintage. This also smoothes the cumulative mechanism that increases the probability of first investors being more and more productive with respect to competitors. Third, capital realization places a temporary constraint on economic growth, which is not imposed exogenously, but depends on the accumulation of production capacity in the capital sector.

2.2 Capital sector

Capital goods are produced by firms g∈ {1, 2, . . . , G} belonging to the capital sector. Each capital good is characterized by its vintage τh and embodied productivity level inline image. Capital good firms receive commissions from final good firms, and use their production capacity to fulfil them, in order of receipt. For simplicity, we assume that capital good firms employ labour as the unique input; the introduction of capital input would require a quite complicated intrasectoral input–output relations model, which would have the only effect of changing the scale of our results (by requiring more firms, labour and so on). The commissions determine firm-level demand in the capital sector. In line with the empirical evidence (see, for instance, Doms and Dunne, 1998; Cooper and Haltiwanger, 2006), we assume that the production of capital is just-in-time, with no expectation formation or accumulation of inventories of unsold capital. Firms in the capital sector may increase the productivity of the produced capital investing in R&D, via the hiring of new engineers.

2.2.1 Production process of capital goods

Capital good firms hold books of orders inline image, where the τj,f refers to the date that the order inline image was received from final good firm f. A capital good firm's demand in period t then is the sum of current orders and the backlog of orders received in previous periods that have not been fulfilled (inline image):

  • image(19)

The production function of capital good firms is

  • image(20)

where inline image is the number of first-tier workers in the capital good's firms and AK is the labour productivity, assumed to be constant in this sector. In each period firms sell the available manufactured orders

  • image(21)

and over time cumulate a number of uncovered orders

  • image(22)

assuming that inline image. When the production capacity inline image is smaller than the total order book inline image capital good firms complete the oldest orders first, followed by the next most recent ones, recording the completed share of the oldest, unfinished order, which will be the first to be completed in the next step.

The number of first-tier workers slowly adapts to changes in demand, in order to smooth out short-term volatility. That is, capital good firms modify their labour force in an attempt to fulfil all existing orders and maintain a percentage of extra-capacity uK:

  • image(23)

where εM is the speed of adjustment of labour in the capital sector. Total employment results from the sum of the different tiers, which are generated according to the same coefficient used by firms in the final good sector: one worker to coordinate every v workers in a lower tier. The total number of workers in a firm in the capital sector is therefore

  • image(24)
2.2.2 Wage, costs and price determination

First-tier capital workers' and engineers' wages are also defined as a multiple of the minimum wage (ωK and ωE, respectively), and the same hierarchical wage structure for final good workers (equation (10)) applies to upstream tiers:

  • image(25)

Due to lack of evidence on the organization of engineers' work, we assume they work independently within the same tiers. Given the very low relative numbers of engineers, this assumption does not affect the results.

Symmetric to the final good sector, prices of capital goods (inline image) are set according to a mark-up rule (µK). In the case of capital good firms, the variable costs include the total labour costs (workers, executives and engineers) divided by the level of production (inline image):

  • image(26)

where inline image and wE are the wages of workers and engineers respectively, and inline image is the number of engineers.

The profits inline image are then computed as the difference between the value of sales and the costs for workers and engineers:

  • image(27)

These profits are cumulated (inline image) by capital good firms and used to finance their R&D activity or are redistributed to executives via premiums.7 The share of redistributed profits is computed as follows:

  • image(28)


  • image(29)

As described in the next section, R&D investments include hiring new engineers to perform the R&D activity.

2.2.3 R&D and innovation in machinery firms

Given the amount of resources devoted to hiring engineering, R&D is aimed at improving the characteristics of a capital good and ultimately maintaining or increasing the capital good firm's market share. The outcome of R&D activity is stochastic, although the probability of obtaining an increase in productivity (pinn) depends on the amount of financial resources devoted to it and, therefore, to the number of engineers employed (inline image):8

  • image(30)

where ζ is a parameter that allows to tune the probability to innovate, for a given amount of resources invested. Firms define the number of engineers they wish to employ as a ratio vK of first-tier workers, constrained by the share ρ of cumulated profits they allocate to R&D:

  • image(31)

If the R&D activity is successful, the characteristics of the newly developed capital vintage are themselves randomly defined, and depend on the outcome of past R&D efforts. The R&D routine follows a stochastic process of the form:

  • 1
    Firms draw a number from a Uniform distribution on [0; 1].
  • 2
    If this number is contained in the interval [0; inline image], the R&D is successful.
  • 3
    If the R&D is successful, the characteristics of the newly developed vintage are randomly drawn as follows:
  • image(32)

where inline image is a normally distributed random function.

2.3 Minimum wage

The minimum wage (wm) is negotiated at the macroeconomic level and defines the lowest bound of firms' wage setting.9 We assume the negotiation to be linked to three main macroeconomic dynamics: (1) labour productivity growth, to maintain pace with the labour contribution to value; (2) consumer prices, to maintain purchasing power over the long run; and (3) unemployment, due, for example, to efficiency wages, corporatism or bargaining. This boils down to an outward shifting ‘wage curve’, which has been well established by empirical evidence (Nijkamp and Poot, 2005; Blanchflower and Oswald, 2006). The shift component is due to full re-negotiation of wages when the increase in both average price (inline image) and aggregate productivity (inline image)—with respect to the previous negotiation in t0—exceeds a boundary ratio (respectively ΩP and ΩA):10

  • image(33)

where inline image is unemployment growth and inline image and inline image are growth in labour productivity and consumer prices, respectively. The ε∈ (0, 1) are the corresponding elasticities of the minimum wage with respect to change in the three macro-dynamics. We use robust empirical estimates for εU (Nijkamp and Poot, 2005; Blanchflower and Oswald, 2006), an equal value for εA and assume a 50 per cent indexation of wages to price changes (εP).

Finally, given our earlier assumption of unconstrained labour resources, we need to derive unemployment rates based on labour hiring. We use the well-established Beveridge curves, which show a negative relation between the rate of vacancies—endogenously determined in the model at micro-level—and the rate of unemployment. We assume that the labour market can be represented by a matching model (Petrongolo and Pissarides, 2001; Yashiv, 2007), and we use a hyperbolic form of the matching function:11

  • image(34)

where CH is the constant and β defines the relation between vacancies Vt−1 and unemployment (inline image refers to the moving average, as defined in footnote 10). Both parameters are set taking account of the mixed empirical evidence from the few available estimates (Nickell et al., 2002; Wall and Zoega, 2002; Teo et al., 2004). A mean value of these estimates is found in Fagiolo et al. (2004), who show that fully random matching models fail to reproduce Beveridge curves, and require the assumption of path dependence in labour supply and demand.

To close the minimum wage setting, we define the number of vacancies Vt−1 as the sum of vacancies in all sectors of the economy: final good firms' workers (inline image), capital good firms' workers (inline image) and R&D employees (inline image), computed respectively as follows:

  • image
  • image
  • image
  • image(35)
  • image
  • image
  • image

Therefore, the friction in the hiring process (εL and εM in the labour demandequations (6) and (24))12 determines the difference between open vacancies and actual number of workers, as shown also in Fagiolo et al. (2004).

2.4 Demand

The demand side of the model represents the mechanisms by which disposable income, generated at micro-level as wages and distributed profits, is converted into physical sales and monetary revenues for the firm. Workers are grouped into income-consumption classes, which constitute aggregate demand.

We assume that social and income factors identify consumer classes. This assumption is common in households surveys for marketing studies (see, for example, CACI, 2005). We assume these factors to be linked to the hierarchical structure of the firm organization and the income it generates: all workers in the same tier are members of the same class.

Each class z∈ {0, 1, . . . , Λt}13 disposes of income composed of current wages and share of profits. The level of consumption for each class is a convex combination of current and past disposable income. The consumption for each class is distributed across firms' revenues on the basis of consumers' preferences. Since consumer choice relies on a stochastic error, we perform a number of repetitions of the purchasing routine for each class. Finally, once each class has consumed, firms compute the quantity sold and their revenues.

In the following sections we describe the variables related to the demand routine: consumer classes disposable income, product definition and consumer choice.

2.4.1 Total income and classes' disposable income

At each time step14 total income is the sum of the wages paid to workers and engineers (Ww), and the distributed profits, or premiums (Wψ):

  • image(36)

where l= 0 in the capital sector firms indicates the engineers. The share of income for class z is then a share of both wages and premiums:

  • image(37)


  • image

is the share of total wages paid by firms to members of class z and

  • image

for higher classes, is the share of the premiums. The shares are computed considering firms from both the final good and capital sectors;

  • image

is the income share of the class of engineers.

Class consumption is a convex combination of current and past income. We implicitly assume that the consumption pattern is based on the convergence of the changes in disposable income over the medium term:

  • image(38)

where γ∈[0, 1] is a parameter determining the ‘speed’ of adjustment of consumption to variations in income. In this model, savings are simply a residual variable that increases (decreases) as income is higher (lower) than consumption.

2.4.2 Product definition

Drawing on the work of Ciarli and Valente (2005), we define the product as a vector of characteristics, which satisfies user needs, in line with the Lancasterian (Gorman, 1959; Lancaster, 1966a, 1966b) and post-Lancasterian (Saviotti and Metcalfe, 1984; Gallouj and Weinstein, 1997) approach to consumer theory. In our model each product satisfies one single need, defined over two characteristics (m), one is the price (ip) of the product and the other one is its quality (iq). The model allows for an exogenous allocation of expenses to different needs for each class (e.g. food, housing, entertainment and so forth). However, the nature, emergence and evolution of needs are still controversial, and their relevance is not generally accepted. The present version of the model is confined to one need and the analysis focuses on the mechanisms linking distributional changes and consumption behaviour.15 We assume that quality levels are heterogeneous across firms, but constant through time, while price is determined by changes in labour and productivity.

2.4.3 Consumer behaviour and firms sales

We model bounded rational consumption behaviour inspired by the literature on experimental psychology, which has the properties of empirically observed behaviour (Gigerenzer, 1997; Gigerenzer and Selten, 2001).16 The original proposal, which resembles lexicographic preferences in the economic literature, has been elaborated to specifically accommodate consumers' purchasing decisions (Valente, 1999).

The model implements independently the purchasing decisions of consumers in each class.17 The consumers in a class are divided into HN+ groups with equal shares of class income inline image. First, a group of consumers in a class assigns to each firm f a pair of perceived values for the price and quality of its good, inline image, where N(. . .) indicates a draw from a normal random function with the specified parameters, and σm determines the ‘error’ variance.18 Repetition of the same choice H times assures random evaluation of the firm's product.

Then, consumers select only the products that (appear to) score equivalent to the best product for each characteristic, i.e. lowest price, highest quality. The equivalence criterion is determined as a range υz,m= (0, 1]: the perceived value of a product characteristic inline image is considered equivalent to the best (perceived) product characteristic inline image if the difference between the two values is smaller than a given percentage υz,m. Formally:19

  • image

The parameter υ can be interpreted as a tolerance level for products whose characteristics are of less-than-optimal quality. For example, when υ= 1.0 the consumers group discards any product with a perceived value even slightly less than optimal. For υ= 0.6, on the other hand, the consumers group is indifferent over goods that are at least 60 per cent as good as the optimal good.

The consumption routine always identifies one or more producers. Indicating with inline image the elements of a set of firms selected by the group ι (ι∈ {1, . . . , H}) of a given class z, each firm within the set is then assigned an equal share of the purchase inline image. We obtain the total units sold (Yt) for a firm by cumulating its sales over all groups and classes:

  • image(39)


  • image(40)

These sales (Yt) are used by the final good firms to set their expectations for the next period's demand (inline image, see equation (1)).


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix

This section analyses the model properties in terms of growth and income distribution, and their relation, given the assumptions on initial conditions (section 3.1). We focus first on the microeconomic dynamics (section 3.2) and second on how these endogenously generate the aggregate growth and income distribution dynamics (section 3.3).

We limit our discussion to the economically relevant results from the model, keeping the technical details of the analysis to a minimum. Further details on the results, including, for example, analysis of the sensitivity to randomness, and stability conditions with respect to a number of structural parameters, can be found in Ciarli et al. (2008).20

3.1 Initialization

The main aim of the analysis is to check whether the interactions among the micro-behaviours formalized above generate sensible results at aggregate level. In order to focus the discussion on the microeconomic effects, we rely on an initialization with minimal heterogeneity across firms. The full list of parameters values is available in the table Appendix.

The economy represented in the following exercise is composed of f= {1, 2, . . . , 50} firms in the final good sector. We assume that the number of firms does not change over time.21

Firms initially differ only with respect to the quality of the service provided, uniformally distributed across firms iqU(98; 102), and are identical with respect to all other initial conditions: product inventories, expected sales, initial demand, mark-up, stock of capital, vintage productivity, wages and so on. At this stage we do not take account of any relation between product price and quality: as a consequence, relative differences in quality across firms are much smaller than the price differences generated by the model dynamics.22

All firms employ a number of first-tier workers necessary to cover the initial demand, which is identical for all the firms, and an executive (second-tier worker) to manage the firm. The tier multiplier (ν) and the wage multiplier (b) are set at values that lie within the observed boundaries (Simon, 1957; Lydall, 1959; Prescott, 2003), respectively 5 and 2.23 We choose an intermediate value for ν and the maximum value for b.24

The capital sector is composed of g= {1, 2, . . . , 15} firms, which are initialized as homogeneous competitors, with an initial first-tier worker, a firm manager and an engineer carrying out R&D activity, paid from the firms' previous accrued profits. Capital good firms initially produce the same vintage, with the same productivity, and have no stock of capital goods to sell.

On the demand side, the labour structure in the final good and capital sectors defines three initial classes of consumers: engineers (employed by the capital sector), first-tier workers and a tier of managers. Starting from the first period, workers contribute to their class's total income out of the pay received (wages, and profit shares/premiums). The three initial income/consumption classes are assumed to have different preferences with respect to the two product characteristics: first-tier workers have a high tolerance towards quality (υ1,q= 0.1), but are highly sensitive to even small price differences (υ1,p= 0.9). For each following class of managers (z+ 1) tolerance of shortfalls in quality reduces and tolerance towards price increases by a fixed multiplier (ς): inline image and inline image, where inline image and inline image are the boundaries of the possible tolerance levels with respect to product quality and price, respectively. Finally, all worker/consumer classes perform H= 50 samples of the purchasing routine.

Unless stated otherwise, the results discussed in the rest of the section are averages obtained over 10 simulation runs with different random properties. In Ciarli et al. (2008) we show that this is a sufficient number of runs to control for variability due to random events.

3.2 Micro- and meso-dynamics

After a few time steps from the start of the simulation, the economic system settles to a stable growth path. We observe that firms' market shares are distributed proportionally to the characteristics of their products, generating an increasing income for consumers via wages and distribution of profits, which spurs further employment and, consequently, sustains moderate growth. However, the simulations reveal many ‘slow’ micro-dynamics, whose effects are generated after periods of building-up, and which eventually lead to (more or less dramatic) changes in the initially stable growth patterns. We can identify three different points in time when the economy undergoes substantial changes, as shown in figure 1.


Figure 1. Aggregate productivity, minimum wage, average income and price. The average price (left axis) results from the minimum wage (left axis), the aggregate productivity (right axis) and the increase in the number of organizational tiers. Average income is also plotted against the left axis.

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At around time step 400, we observe an increase in the minimum wage, which rapidly translates into higher average income and prices. This increase in the minimum wage is due to the slow reaction of labour supply to increasing demand for labour (high number of non-matched vacancies). This translates into an increasing wage, which, in the absence of productivity improvements (if we exclude the initial investment in capital), directly increases consumer prices. When these reach the negotiation level, a series of discrete changes in the minimum wage occurs. However, this does not affect the slow pattern of growth, as it is a monetary adjustment with no real and lasting effects.

Although different in nature (the minimum wage is not affected), the events that occur at around time 900 do not induce any relevant (immediate) change in the growth pattern. The continuous growth of some of the firms requires that they employ a further tier of managers (i.e. the number of first-tier managers reaches the threshold ν). This leads to a rapid increase in the level of the wages paid by firms, which starts to erode their previous competitive advantage (and which allowed these firms to grow faster). Extra costs force these firms to raise their prices. Since a comparatively larger share of consumption comes from the first-tier workers (highly sensitive to prices), market shares quickly shift to favour smaller firms. These latter in turn begin to approach the same dimensional threshold above, for which they also need an additional tier of executives, so that the process of erosion of competitive advantage affects them too. Soon after this period of imbalance, the system returns to its previous configuration, with the only lasting effect being lower aggregate labour productivity, caused by the higher cost weighting on the same productivity levels (firm-level productivity is obviously unvaried).

Productivity at the firm level remains stagnant due to the fact that, up to period 1200, no technological change occurs. The level and growth of consumption are not sufficient to require final good firms to invest in new capital. This lack of demand in turn affects capital good firms, which do not have the resources to invest in R&D and produce new capital goods with higher embedded productivity.

However, shortly before time 1200, further increases in firm size and changes in the organization of production occur. The differences that firms have established over time are reflected in the larger gaps in their growth rates. Therefore, when just before period 1200 some firms have grown to include a fourth tier of workers, they will suffer a price disadvantage against competitors for a few time periods. The critical mass of consumption that has cumulated over time thus generates an unexpectedly high demand for those firms that still enjoy a price advantage (due to lower labour costs). Such an increase in demand requires an increase in capital stock. In turn, the need for investments generates an intermediate demand that allows capital good firms to start investing in R&D and deliver capital goods with higher embedded productivity.

The final good firms that had lower prices thus also enjoy the advantage of producing using newer capital vintages. When growing larger, they expand their organizational structure (increasing average wages) and enjoy productivity growth. The overall impact for those firms is a reduction in labour costs and prices. The resulting pattern of growth shows a marked increment of average productivity, reflected also in falling prices. Also, the overall market structure is completely altered (figure 2).


Figure 2. Firms dispersion and price dispersion.

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Figure 2 shows in fact a marked increase of market concentration, prompted by a symmetric large increase in price volatility, indicated by the standard deviation of prices. The reason for this is that the stochasticity of innovation has an initially reinforcing effect: more productive firms reduce their prices further, and are targeted by the consumption class of first-tier workers. These firms are then more likely to invest in new capital, and tend, therefore, ceteris paribus, to grow even larger. This latter dynamic allows a cyclical turnover of firms' market shares, when growing firms pair productivity gains with over-generous wages for managers.

3.3 Patterns of growth and income inequality

The previous section provided a summary of the main dynamics of the ‘micro’-level of the model. We now present the simulation results from a macroeconomic perspective, looking at the type of growth and income distribution generated by these micro-dynamics.

The results of the numerical simulations of the model, based on the micro-dynamics described above, endogenously reproduce a typical long-run growth pattern, à la Maddison, which shows a steep take-off after a large number of time steps. Figure 3 shows the GDP series for 100 simulation runs—in logarithmic scale—and their average value. In our simplified model of a closed economy, GDP is the sum of final good firms' production and investment.


Figure 3. GDP (log) series: 100 runs and average. Series for 100 runs and average, in logarithmic scale, for 2000 time steps.

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The simulation results show two clear and distinctive growth patterns, in which the turning point is around step 1250. During the first stage, GDP is characterized by a stable pattern of growth. This occurs after initial capital investment by the final good firms, which generates the initial demand. In this first stage the increase in GDP is driven by what we can term purely demand-led growth: growth in income, through wages and population increases, which induces increased spending for final consumption, and firm expansions which push up wages and employment, inducing a cumulative pattern. In this state of equilibrium growth, investment grows at the rate of capital depreciation and population increase. However, population growth is endogenous in our model. Firms use their profits first to invest, and then redistribute any excess to consumers, contributing to further increasing demand. Note that, unlike standard growth models, the assumed free access to the credit market allows growth in consumption and investments to coexist, and explains the sustainability of the stable growth pattern. Yet, in this first stage, the final demand is not large enough to generate profits in the capital sector to be spent on hiring R&D workers, thus failing to generate productivity-enhancing innovations.

In the second stage of growth, productivity starts to increase (see figure 1), although with high differentiation across firms. This phase shows an increase in variety, with growth rates differing both within and among simulation runs. The results from R&D, in fact, are stochastic, and therefore different simulation runs produce relatively different patterns. The mechanism behind this phase of growth rate that generates a take-off is typically Kaldorian. We refer to this second stage as the cumulative causation growth: the selection of a few firms, together with a critical level of demand, translates into large capital investment for the selected firms, which generates profits and investment in new technology with increased productivity. The growth in productivity then implies a reduction in production costs and prices, an increase in profitability and thus of the income redistributed to households. Both, in turn, sustain the expansion of effective demand via a reduction in prices and a higher available income (Kaldor, 1966).

The two stylized growth patterns are accompanied by a two-stage evolution of inequality. Figure 4 shows the Atkinson index series from 100 independent runs with different random behaviour, and their averages. The Atkinson index of inequality (��t) is computed as follows:


Figure 4. Atkinson inequality index. Series for the first 2000 simulation steps for 100 independent runs, and their average.

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  • image(41)

where Wz,t is the total income for consumer class z, Lz,t is the total number of workers in class z, and inline image is the measure of inequality aversion. Provided that we are not measuring an empirical level of inequality, we use an intermediate value of inline image.

During the demand-led growth phase, the only source of inequality is a new class of consumers (a new tier of managers) enjoying higher salaries and bonus shares. The distribution of income is then highly stable for a given organization of production, and discrete changes in observed inequality depend on the introduction of new manager tiers.

However, when final good firms begin to differ in terms of size and profits (cumulative causation growth phase), the skewness of the wage distribution increases and, together with the increasing distribution of profits, generates the higher average inequality observed. The volatility characterizing this stage of growth at micro-level in terms of productivity and market dynamics also affects income distribution, which follows a cyclical pattern.25

We found that at the end of the simulated periods the model generates the typical Paretian distribution of top incomes.26 In figure 5 we plot the Lorenz curve for an illustrative simulation run. Most of the economic wealth is concentrated in a small number of workers in the executive tiers.


Figure 5. An approximation of the Lorenz curve: curve computed in the last time step of the simulation (2000) for one sample run. The straight connecting lines are an outcome of the assumption that individuals within a working class have the same income.

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Moreover, as reported, for example, by Gottschalk and Smeeding (1997) and Cornia (2003), most of the inequality in distribution observed in our simulated data is explained by earnings inequalities.27 Our results are also in line with the finding that ‘Earnings inequality has risen also because of the fall of minimum wages relative to the average’ (Cornia, 2003, p. 6). An indication of this effect can be seen in the average income and minimum wage series in figure 1.

Finally, we explore the relation between GDP and inequality. In figure 6 we plot the values of the Atkinson index, for given levels of GDP (at constant prices, in log scale).


Figure 6. The relation between GDP and inequality. Levels of the inequality index vs. levels of GDP, with the 95 per cent confidence interval.

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Figure 6 shows that our model, notwithstanding its limitations, is able to generate a sort of Kuznets curve, albeit the negatively sloped portion is shorter than that predicted in the theory. This result shows that, while higher levels of production and income lead to higher levels of inequality, after the income level reaches a threshold the inequality stops growing, and rather begins to fall. The increasing part is clearly due to the increasing wage differential, while at very high levels of income and demand, firms sacrifice profit shares to capital investment.

It is interesting to look at the relation between inequality and GDP growth, which is still highly controversial on both empirical and theoretical grounds (among many others, Aghion et al., 1999; Eicher and Turnovsky, 2007). We plot this relation in figure 7.


Figure 7. The relation between GDP and inequality. Levels of the inequality index vs. GDP growth, with the 95 per cent confidence interval.

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Figure 7 shows that higher levels of inequality increase GDP growth in the following period. This is easily explained in our model at the micro-level: first, demand plays a crucial role in our model, determining the critical level above which contributing to further increasing demand take-off and sustained growth. Second, when demand increases, both average wages (through the new tier of executives) and employment (though at a slower pace once technological progress is possible due to investment) increase. Hence, an increase in the number of hierarchical tiers, together with an increase in profit shares, generates more consumption. Nonetheless, we do not make any assumptions about the elasticity of consumption across wage classes. We only assume a difference in preferences which, on average, would push first-tier workers to be more selective about prices than managers. Therefore, if there were distributional mechanisms at work, and the increase in average wages was equally distributed across the new class of executives and the other working tiers, the level of the demand would be the same. The same would apply to the rate of growth.

We thus find a relevant result: if it is verified that different classes of income have different preferences in terms of prices and qualities from the beginning, then the initial difference in income, and thus in preferences, is what triggers the take-off, via the selection of firms on the basis of their costs. But, in our model, further inequality cannot be justified by a higher growth rate.


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix

4.1 The scope of the analysis: a summary

In this paper we investigated the properties of a growth model that embeds the relation between technological and organizational change, income distribution and the dynamics of consumption affecting macroeconomic growth. We developed an agent-based micro-founded model with the aim of integrating these phenomena within a coherent theoretical framework. Microeconomic behaviours are modelled in line with the large and consolidated evolutionary theory of technical change and economic growth, while the macro-framework borrows from the structuralist literature—including the presence of a capital sector and endogenous consumption classes. In terms of these two streams of literature, the main original feature of the model is the explicit introduction of micro-mechanisms representing income distribution, one of the main channels between changes in the organization of firms and changes in consumption patterns.

The results of the simulations—reported in detail above—are driven by the structural conditions and interaction mechanisms formally represented. We summarize these as follows.

First, the organization of production—given by the required number of workers that a manager can supervise and the number of tiers characterizing the firm—generates price dispersion, defines different wage classes and directly affects income distribution.

Second, the formation of wage classes and the related income structure determine differences in consumption preferences.

Third, the differences in consumption preferences play a crucial role as soon as firm dynamics generate a sufficient heterogeneity. Heterogeneity of firms and consumption patterns lead to changes in the market structure (i.e. oligopolistic competition), and the income structure (i.e. higher profits).

Fourth, the composition of production in terms of product characteristics determines the heterogeneity required for consumer choice. In this paper we observed only the emergence of price differences (through process innovation).28

As already mentioned, these results relate to the analysis of the main aggregate properties of the model. As a preliminary counterfactual, we analysed the effects of different initial structural conditions, to check for sensitivity of the model to the crucial parameters. These are not reported in full due to space constraints. We provide only a brief summary and direct the interested reader to Ciarli et al. (2008). We analysed how the results obtained in this paper change with respect to a number of parameters that determine structural properties: (1) product characteristics and mark-up values (composition of production); (2) consumer preferences and their differences across classes (consumption patterns); (3) the multiplier defining the number of workers per executive and the rate of process innovation (organization and production structure); and (4) the multiplier determining earnings distribution (income structure). The results confirm the relevance of the initial structural conditions on both economic growth and distribution. While the model always shows endogenous growth under any combination of the structural conditions, the relation is highly non-linear. It ranges from exponential growth, similar to what we found in this paper, to an almost stagnant economy. Also, the effect on inequality is mostly non-linear, as is the relation between growth and inequality (we obtain high growth with a rather equal economy, as well as highly uneven economic stagnation).

4.2 Research agenda

The results obtained and discussed above—both those from our study and those related to the effects of structural parameters (Ciarli et al., 2008)—are encouraging and worthy of further investigation. We plan to extend the model by endogenizing some of the presently parametrized structural conditions, in order to analyse the scenarios under which structural changes emerge, and their dynamic effects, which mainly relate to:

  • • 
    Final demand: the (radical) change in the product characteristics (i.e. product innovation), the conditions for their emergence and the effects on consumption (i.e. consumer perception, quality and time of reaction to novelty, etc.). The model would provide micro-foundation for the relation between variety and economic growth, in line with some of the findings in the literature (Saviotti and Pyka, 2004, 2008) for the macro-level.
  • • 
    Linked to this, the relationship between product innovation and the creation and/or substitution of needs (i.e. evolution of consumer preferences). A recent and flourishing literature explores this domain (Witt, 2001, 2008), to which this model could originally contribute.
  • • 
    Intermediate demand: changes in the organization of firms and sectors (i.e. outsourcing, emergence of new inputs sectors and changes in the intersectoral linkages).

All these issues are on our future research agenda, which will be based on the fundamentals proposed in the present work.


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix
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  • 1

    We suppress the firm index to improve readability. It is implicit that each equation is replicated for each firm, and we refer to the definition of parameter values to identify differences across firms.

  • 2

    We assume an inventory/sales ratio that corresponds to the lower empirically observed values (see, for example, McCarthy and Zakrajšek, 2000; US Census Bureau, 2008), to avoid level effects that may be linked to the accumulation of inventories, and to reduce the propagation of production fluctuations.

  • 3

    This assumption is sustained by evidence from numerous empirical studies, starting with Kaldor (1957). The capital investment decision in section 2.2.3 ensures that the actual capital intensity remains fixed over time.

  • 4

    A common assumption in evolutionary models, supported by empirical evidence that dates back to Hall and Hitch (1939), and more recently to Blinder (1991) and Hall et al. (1997).

  • 5

    This is not to say that Modigliani and Miller (1958) theory is correct, nor are we denying that the financial structure influences the investment strategy (e.g. Fazzari et al., 1988).

  • 6

    Where inline image are the cumulated orders of firm g in t− 1.

  • 7

    The scheme of distribution of premiums is the same as for final good firms.

  • 8

    This is in line with Nelson and Winter (1982) and most of the evolutionary models developed since, and follows the scheme presented in Llerena and Lorentz (2004).

  • 9

    We are aware that heterogeneous occurrences in the income distribution across countries are partly due to institutional differences in the minimum wage settings (e.g. Gottschalk and Smeeding, 1997; Cornia, 2003), and to the existence of an informal economy (e.g. Cornia, 2003). The present version of the model would allow us to study the joint role of minimum wage on income inequality, analysing the wage-setting parameters that we assume in this paper. This is left for future studies.

  • 10

    Changes in productivity (inline image) and consumer prices (inline image) are computed as moving averages of the type inline image. We thus consider that the bargaining bodies evaluate variable trends and overlook short cyclical changes—smoothing adapting expectations—and that they perceive recent changes as more relevant (assuming a small value for d).

  • 11

    Börsch-Supan (1991) provides estimates on the German labour market using the hyperbolic form.

  • 12

    This can also be interpreted as labour market friction, which, in matching models, determines the level of unemployment as a function of the number of matches and vacancies. In our model the number of matches corresponds to the workers actually hired (function of εL and εK).

  • 13

    Where Λt is the number of tiers of the larger firm in the market, and z= 0 is the class of engineers in capital sector firms.

  • 14

    We omit the time index for clarity of exposition.

  • 15

    The qualitative change of demand due to the emergence of new needs or the evolution of needs, and innovation in terms of changes in the quality of the product are all relevant source of structural change. Their analysis requires a self-standing paper and is therefore part of our research agenda based on further versions of the model.

  • 16

    The algorithm implemented, devised to represent generalized decision making, respects the requirements of many findings in experimental psychology, such as generating a simple and explicit motivation for a decision (Shafir et al., 1993).

  • 17

    As noted, the routine is generally applied for each need defined in the configuration of demand. This is not necessary here because our model is configured with only one need for each class.

  • 18

    The reader may object that price, unlike quality, is generally easy to assess. However, it is frequently the case that consumers fail to assess the true costs of a purchasing option (e.g. maintenance and usage costs). Moreover, this method allows us to represent the heterogeneity within a class.

  • 19

    The best price is a minimum value, while the highest quality is a maximum value.

  • 20

    The simulated data and the files implementing the model are available on request from the authors. The simulation program was implemented using Lsd (Valente, 2008), which allows even non-expert programmers to easily investigate an existing model, replicate predefined results and generate new ones.

  • 21

    This is a strong assumption, and ideally we need to analyse the model behaviour abstracting from possible spin-offs or entry of new firms. Both sources of market dynamics would require the addition of several ad hoc elements, either in the form of incentives to split production (which are not only cost based) or in the form of a full initialization of the features of new firms. We believe that such an extension would require full analysis, in a self-standing paper.

  • 22

    However, in the conclusions we briefly report on the results that we obtained when the relative differences in quality across firms are much larger, and a positive relation between price and quality is introduced.

  • 23

    In referring to the tier multiplier Simon (1957, p. 32) states that ‘this number varies within only moderate limits in a given company, and even among a number of companies. At executive levels it is seldom less than three, and seldom more than ten, and usually lies within narrower bounds’. Similarly, he argues (p. 33) that ‘the value of b can change from situation to situation, but one can find figures quoted in the range of 1.25 to 2. While we would expect to encounter instances of larger or smaller ratios, averages can be expected to be relatively stable’.

  • 24

    This is because, as frequently pointed out after presentations of this paper, and as indicated by a large amount of evidence, wage gaps have increased substantially in the last 50 years.

  • 25

    An increasing and oscillating pattern of inequality is reported, for example, by Fiaschi and Marsili (2006) for the Gini coefficient computed on Italian labour income. See, also, the evidence on earnings dispersion over the last 40 years, in different OECD countries, in Atkinson (2007).

  • 26
  • 27

    Both Gottschalk and Smeeding (1997) and Cornia (2003) refer to high-income countries, which is the reference for the last step of our simulations.

  • 28

    The introduction of new characteristics and new needs (product innovation), which generates new sectors, would sparkle similar selection mechanisms, although this is part of future analysis of more refined versions of the present model.


  1. Top of page
  4. 2. THE MODEL
  5. 3. RESULTS
  8. Appendix
Table A1. Parameters setting: initial values
inline imageWage income50
inline imageProfit income100
inline imageMinimum wage1.25152
inline imageAggregate productivity0.18
inline imageAverage price1
inline imageMoving average of aggregate productivity0.18
S0Firm stock0
Q0Firm production1
inline imageExpected sales1
c0Production cost125
A0Embodied labour productivity1
inline imageCapital good firm price1
inline imageCapital good firm workforce1
z0Market shares0.02
inline imageEmbodied labour productivity in capital vintage τ01
Table A2. Parameters setting: parameter values
asSpeed of adaptation of sales expectations0.9
inline imageDesired ratio of inventories0.1
DCapital coefficient0.4
εLLabour market friction (final good firms)0.9
ulUnused labour capacity0.05
νTier multiplier5
ωMinimum wage multiplier1.11141
bExecutives wage multiplier2
δCapital depreciation0.001
uUnused capital capacity0.05
inline image, inline image, inline imagePreference weights in capital supplier choice1, 1, 1
εMLabour market friction (capital good firms)0.9
uKUnused labour capacity in the capital sector0.2
ωKWage multiplier in the capital sector1
AKLabour productivity (capital good firm)1
ωEEngineer's wage multiplier1.5
µKMark-up (capital good firm)0.5
ζParameter innovation probability10,000
νKTargeted worker–engineer ratio (capital good firm)5
ρR&D investment share0.7
σaStandard deviation productivity shock0.01
εUWage curve unemployment elasticity0.1
εAWage curve productivity elasticity0.1
εPWage curve inflation elasticity0.5
ΩAIncrease in average productivity for a wage renegotiation to occur0.05
ΩPIncrease in average price for a wage renegotiation to occur0.05
dSmoothing parameter in the computation of the moving averages0.05
CHBeveridge curve constant0.2
βBeveridge curve parameter6
γSmoothing parameter in consumers expenditures0.8
HNumber of consumer class subgroups50
σmVariance in the evaluation of characteristics0.05; 0.1
ςInter-class multiplier for tolerance levels0.2
υ1,qFirst income class tolerance towards quality0.1
υ1,pFirst income class tolerance towards price0.9
inline imageMaximum tolerance towards quality0.9
inline imageMinimum tolerance towards price0.1
inline imageHouseholds' inequality aversion (Atkinson Index)0.5