The Marshallian and Schumpeterian Microfoundations of Evolutionary Complexity: An Agent Based Simulation Model

Abstract

The analysis of the Marshallian and Schumpeterian microfoundations of endogenous innovation enables to draw a line between the new emerging evolutionary complexity from biological evolutionary analysis and to overcome its limits. The paper integrates the Marshallian process of imitation and selection with the Schumpeterian creative response. In Marshall initial variety is given and exogenous, the dynamics of the process is driven by the selective diffusion of the best practice and long-term equilibrium stops the generation of externalities; firms are not expected to try and react to unexpected mismatches between planned and actual product and factor market conditions. In Schumpeter firms are allowed to try and react; the quality of knowledge externalities supports their creative response and may keep the system in a self-sustained process of growth. The Schumpeterian creative response can be regarded as a special case of the Marshallian dynamics that takes place when externalities—available to all firms including most performing ones—enable the introduction of innovations that account for the reproduction of superior performances and variety. The levels of reactivity of agents and of the quality of knowledge externalities, provided by the system, account for the growth of output and productivity. This hypothesis is tested by means of an agent based simulation model that shows how these microfoundations of endogenous innovation are able to generate aggregate dynamics based upon the interaction between individual decision making and system properties.

The authors thank the support of the Collegio Carlo Alberto with the project IPER and the University of Torino.

Appendices

Appendix 1: Detailed Description of the Simulated Economy

The economy configuration depends upon the number of agents and their repartition between “smart” and “normal” agents. Smart agents are bigger and have a higher productivity than normal ones. Variable used to configure the economy are the following:

• “agents” it indicates the maximum number of firms the simulated economy is capable to host; at the start of the simulation the market hosts always the maximum allowed number of firms;

• “totMoney” is the fixed amount of money available into the simulated system;

• “labPrice” it quantifies the wage to be payed for a single unit of labour;

• “exitLabour” is the amount of work an enterprise has to employ in order to be considered alive; firms whose input falls under this threshold are automatically removed from the market;

• “smarterRatio” represents the probability a single enterprise can be initially set as smart;

• “normalLab” is the maximum amount of input (work) a normal firm could be given for the first production cycle, the minimum one coincides with the exitLabour, that is the quantity of input a firm needs to employ to survive;

• “smarterLab” is the maximum amount of input (work) a smart firm could be given for the first production cycle, the minimum one coincides with the maximum amount the normal firms could be given (i. e. normalLab);

• “normalPro” is the maximum amount of starting labor productivity (A) for normal firms, being the minimum one a non relevant amount bigger than zero for computational matters”;

• “smarterPro” is the maximum amount of starting labor productivity (A) for smart firms, be the minimum the “normalPro”;

• “turnover” is the probability a new firm enters the market when there is room for that.

The behaviour of the agents is influenced by the following parameters:

• “tolerance” measures the maximum distance from zero, agents consider as equilibrium. As computers are only able to deal with limited precision amounts, this confidence interval makes possible to reach equilibrium position.

• “labRate” represents the higher fraction of the actual input the firms use to compute the input adjustment. Each simulated cycle and for each agent the upgrade for labor is randomly tossed between 0 and the parametrically set value. For each agent:

$$ \varDelta {\mathrm{L}}_{\mathrm{i}}={{\mathrm{L}}_{\mathrm{i}0}}^{\ast}\mathrm{random}\left(\Big]0,\mathrm{labRate}\Big[\right). $$

(14)

Firms that enjoy profit will increase their demand of labour by this ΔL, provided that their profit will be enough to compensate the major expense, due to the fact that no financial institutions have been—intentionally—provided, in the simulated economy firms have to finance the hiring of additional labor with their profit. The affordable increase of labor depends upon the amount of profit(P) and the cost of the labor (w), as in the following equation:

$$ {\mathrm{L}}_{\mathrm{i}1}={\mathrm{L}}_{\mathrm{i}0}+\min\;\left(\varDelta {\mathrm{L}}_{\mathrm{i}},\left({\mathrm{P}}_{\mathrm{i}0}/\mathrm{labor}\ \mathrm{price}\right)\right)\mid {\mathrm{P}}_{\mathrm{i}0}>\mathrm{tolerance}. $$

(15)

When a firm suffers a loss it simply reduce the labor input, with the lower limit of zero:

$$ {\mathrm{L}}_{\mathrm{i}1}=\min\;\left(0,{\mathrm{L}}_{\mathrm{i}0}-\varDelta {\mathrm{L}}_{\mathrm{i}}\right)\mid {\mathrm{P}}_{\mathrm{i}0}<-\mathrm{tolerance}. $$

(16)

• “techRate” is the fraction of their proceeds the Schumpeterian firms invest to acquire knowledge. Investment has to be financed exactly like labor upgrade. Firms invest in both cases of profit or losses, whereas in the former case the amount of profit will be the maximum affordable investment, in the latter such amount is measured by the savings the enterprise realizes by reducing its input (labor) acquisition. The amount a firm invests can be computed as:

$$ {\mathrm{I}}_{\mathrm{i}1}=\min\ \left(\left({{\mathrm{Y}}_{\mathrm{i}0}}^{\ast }{{\mathrm{Gp}}_0}^{\ast}\mathrm{techRate}\right),{\mathrm{P}}_{\mathrm{i}0}\right)\mid {\mathrm{P}}_{\mathrm{i}0}>\mathrm{tolerance};\kern1em \mathrm{or}\ \mathrm{as}: $$

(17)

$$ {\mathrm{I}}_{\mathrm{i}1}=\min\ \left(\left({{\mathrm{Y}}_{\mathrm{i}0}}^{\ast }{{\mathrm{Gp}}_0}^{\ast}\mathrm{techRate}\right),\left(-\varDelta {{\mathrm{L}}_{\mathrm{i}1}}^{\ast}\mathrm{labor}\ \mathrm{price}\right)\right)\mid {\mathrm{P}}_{\mathrm{i}0}<-\mathrm{tolerance}. $$

(18)

• “techDecay” measures the effects of time on the contribution of knowledge in increasing the productivity (A). The labor productivity (A) is subject either to Marshallian imitation externalities or Schumpeterian knowledge externalities, according to the scenario at work. The production function in the Schumpeterian approach has been operationalized into the simulation as:

$$ {\mathrm{Y}}_{\mathrm{i}1}={{\mathrm{L}}_{\mathrm{i}1}}^{\ast }{{\mathrm{A}}_{\mathrm{i}1}}^{\ast}\left(1+{\mathrm{T}}_{\mathrm{i}1}\right). $$

(19)

Where T represents the technological knowledge the firm is able to exploit, the amount depends both by: (i) knowledge acquisition through investment, (ii) knowledge generation due to the competence rising from past technological knowledge acquisition. To simulate the two effects the level of T at a time is computed as sum of the acquired technological knowledge and the accumulation of a small fraction of the past acquisitions, accordingly with the parameter “techDecay” that measures the fraction of technological knowledge that cannot be cumulated. The level of knowledge is computed as:

$$ {\mathrm{T}}_{\mathrm{i}1}=\sum {{\mathrm{t}}_{\mathrm{i}-\mathrm{j}}}^{\ast}\mathrm{techDecay}+{\mathrm{I}}_{\mathrm{i}1}/\left({{\mathrm{T}\mathrm{p}}_1}^{\ast }{{\mathrm{L}}_{\mathrm{i}1}}^{\ast }{\mathrm{A}}_{\mathrm{i}1}\right). $$

(20)

Where Tp represents the price the firm has to pay to apply a unit of technological knowledge to a unit of product, it is determined at the system level and depends on the effectiveness of the knowledge governance.

• “techLife” represents the number of production cycles a technological knowledge acquisition could be fully exploited.

Type and intensity of externalities are managed by four parameters:

• “risk” measures the risk of failure for imitation and knowledge acquisition, each time a firm acquires knowledge or tries to imitate better practices, a uniform random number E is tossed in the range ]0,1[ and compared with risk value: if the tossed number is less than risk value the result of the action is nullified.

• “imitation” is a variable used to enable the simulation of the imitation process; its value represents the fraction of the gap between the best performing firm labor productivity and the own one each firm can fulfill accordingly with the risk parameter. (See Eq. 25). If the parameter value is zeroed, no enhancement in productivity is allowed for existing firms nor for newcomers.

• “governancePerformance” is used to express the effectiveness of the knowledge management in the simulated environment; its value is set in the range [0,1] the higher the value the lower the cost of knowledge becomes, as follows:

$$ \mathrm{z}=\partial \mathrm{Y}/\partial {\mathrm{T}}^{\ast}\left(1\hbox{--} \mathrm{governancePerformance}\right), $$

(21)

where ∂Y/∂T measures the estimated monetary value of the effect of the new knowledge on the output of the enterprise.

Simulation control is performed by setting up three parameters:

• “randomSeed” is used to set a fixed random distribution based upon the indicated seed; by setting to zero the parameter value each run could be based upon a different random distribution.

• “stopAt” is used to set the number of production cycle to be observed by the simulation; when the number of cycles is reached the simulation is stopped and final results are collected.

• “prFlg” is a switch used to enable printing the values of the parameters directly into the results files.

1.1 A.1 The Computation of the Marginal Value of Technological Knowledge

Assuming c to be the marginal value of the technological knowledge, i.e.:

$$ \mathrm{c}=\partial \mathrm{Y}/\partial \mathrm{T}. $$

(22)

a creative reaction can be performed only if the price of technological knowledge (z) is less than c. In order to study and simulate such situations we need to know the value of c, but it depends upon the prices and the total output of the enterprises.

Starting from the assumption the value of c needs to be only a plausible starting point for figure out z, it has been decided to compute it through a simple two steps procedure:

• (a) all the firms forecast the amount of output (F_i1) they will offer at the end of the current production cycle, without new knowledge acquisition as:

$$ {\mathrm{F}}_{\mathrm{i}1}={{\mathrm{L}}_{\mathrm{i}1}}^{\ast }{{\mathrm{A}}_{\mathrm{i}1}}^{\ast}\left(1+{\mathrm{T}}_{\mathrm{i}1}\right). $$

(23)

• (b) The market after summarizing all the forecasts computes a knowledge price per unit of knowledge and product as:

$$ \mathrm{z}=\mathrm{M}/\sum {{\mathrm{F}}_{\mathrm{i}1}}^{\ast}\left(1\hbox{--} \mathrm{governancePerformance}\right). $$

(24)

Because z represents the cost for an amount of knowledge able to rise of one unit the total product, z has to be multiplied for the product unit the new knowledge is going to be applied: each firm computes the amount of knowledge its investment is worth by dividing the amount it invested by z * A_1i * L_1i; “governancePerformance” is a parameter to be set in the interval [0,1] that quantify how much z differs from c.

Even assuming a null performance of the knowledge governance mechanism, this process over-estimates the z if the production grows, due to the fact the price per unit will fall, as well as it under-estimates z if the whole production fall. Production amount depends not only upon the knowledge acquisition process, it may be influenced by the exit of some enterprises, as well as the decision to reduce or raise the amount of output, so the z value tends to equal c but it never estimate it exactly.¹⁷

With proper levels of knowledge governance that enable each learning agent to access and use the stock of knowledge available at each point in time in the system, including the knowledge being generated by all the other learning agents, knowledge externalities are being recreated as an endogenous process within the system as soon as agents start relying on technological knowledge to feed their—creative—reactions. The lower the costs of accessing and using the stock of existing knowledge, and more specifically, the larger the gap between the actual costs of accessing external knowledge as an input into the internal recombinant generation of technological knowledge and its equilibrium costs, and the larger the opportunities for firms to react creatively to arising mismatches between actual and expected conditions of product and factor markets with the introduction of productivity enhancing innovations (Antonelli 2011).

The actual cost of access and use of knowledge in an economic system is influenced by the quality of the knowledge governance mechanism the system has been able to elaborate. Knowledge governance consists in an array of institutional settings that combine and integrate market transactions and personal interactions, ex-ante and ex-post coordination both among firms in the economic system and between them and the academic system created by the State. Knowledge governance is intrinsically dynamic. Its ingredients and mechanisms keep changing with the continual introduction of new modes. This dynamics exhibit the typical traits of an emergence process whereby the identification of limits and failures engenders a creative reaction that eventually leads to the articulation of a new mode. Knowledge governance can improve or deteriorate: the outcome is far from deterministic (Antonelli 2015).

1.2 A.2 Simulating Externalities: Marshall Versus Schumpeter

In the Marshallian scenario imitation is limited to less performing firms: the process allows the system to reach the productivity of the best firm at the level that has been tossed during the set up of the simulated economy. In the Marshallian scenario each time a firm takes advantage of imitation it enjoys a productivity upgrade that is a fraction of the gap between its productivity level and the one of the best enterprise in the economy. Imitation is a challenging process, may be an enterprise fails doing its upgrade. The effect of imitation is represented as:

$$ {\mathrm{A}}_{\mathrm{i}1}={\mathrm{A}}_{\mathrm{i}0}+{\left({\mathrm{A}}_{\mathrm{max}}\hbox{--} {\mathrm{A}}_{\mathrm{i}0}\right)}^{\ast }{\mathrm{E}}_0\mid {\mathrm{E}}_1>\mathrm{risk}. $$

(25)

Where A_i0 and A_i1 are the productivity of the i-th enterprise respectively before and after the process, A_max is the productivity of the best firms, E₀ and E₁ are random uniformly tossed numbers: E₀ is tossed in the range ]0,imitation], where imitation is a parametrical value used to manage the process, and E₁ is tossed in the range ]0,1[. Risk represents the probability the imitation process fails.

Newcomers are able to exploit imitation externalities too, accordingly with the risk parameter new enterprises are given either: (i) the labour productivity of the old ones they replace or (ii) the average labour productivity of the system.

A small upgrade of its labor productivity granted to each agent mimics imitation externalities. The upgrade is computed on the basis of the difference between the productivity of the best agent in the system (A_max) and each other agent’s own productivity (A_i). The granted amount is randomly tossed by multiplying the gap (A_max–A_i) by a random number in the interval ]0,imitation[, where “imitation” is a parameter set between [0,1[ (by setting it to zero the effects of imitation are automatically excluded); this upgrade is subject to failure with a probability that is specified by setting up the appropriate model parameter, called “risk”. At the end of each production cycle, for each agent, the gap between its labor productivity (A_i) and the A_max is computed, then by comparing a random trial with the risk, the system decide if the agent would be granted an enhancement or not. If yes the agent is given a labor productivity enhancement that is a randomly tossed fraction of the gap as represented in the previous section. Note that ‘imitation’ does not work for knowledge that has to be bought as a kind of production factor.

A_new and L_new represent, respectively, the labor productivity and the input of a new firm, whereas A_old represents labor productivity of incumbents. The following relations describe how the “new” values are set:

$$ {\mathrm{A}}_{\mathrm{new}}=\mathrm{average}\ \mathrm{A}\mid \mathrm{imitation}>0, $$

(26)

$$ {\mathrm{A}}_{\mathrm{new}}={\mathrm{A}}_{\mathrm{old}}\mid \mathrm{imitation}=0, $$

(27)

$$ {\mathrm{L}}_{\mathrm{new}}={\left(\mathrm{average}\ \mathrm{L}\hbox{--} {\mathrm{exitLabour}}^{\ast }2\right)}^{\ast}\mathrm{random}\left(\left[0,1\right]\right)+{\mathrm{exitLaboour}}^{\ast }2. $$

(28)

In the Schumpeterian scenario, instead, all firms can try and use external knowledge spilling in the system because of its limited capability to generate new technological knowledge and introduce productivity-enhancing innovations. Provided that knowledge externalities are available, each firm is capable to try and increase its productivity: also the best firm can evolve through knowledge acquisition and overcome its initial endowment. This process is subject to fail too: in the model it is subject to the same probability of failure of the imitation process. The innovation equation is split into two components: (i) the decision to try and innovate that depends on the performances and (ii) the knowledge generation function. In the Schumpeterian scenario firms decide to react each time they find themselves in out-of-equilibrium conditions, i.e. when their profit (P) differs from zero, provided a small tolerance range (d). Their reaction consists in the attempt to innovate by investing in knowledge acquisition a fraction of their output (F), but such acquisition has to be financed either by investing extra profits or through savings obtained by reducing the amount of employed labor.

Innovation is subject to failure risks as well as imitation, so results of each trial are subject to failure with a certain probability (risk). Once the new technological knowledge has been acquired it may be exploited during the next years, even obsolescence could reduce its effect on productivity. The decision to try and innovate can be resumed as the amount each enterprise invests each time to acquire new knowledge (Ii):

$$ {\mathrm{I}}_{\mathrm{i}1}=\min\ \left[\left({{\mathrm{Y}}_{\mathrm{i}0}}^{\ast }{{\mathrm{G}}_{\mathrm{p}0}}^{\ast}\mathrm{F}\right),{\mathrm{P}}_{\mathrm{i}0}\right]\mid {\mathrm{P}}_{\mathrm{i}0}>\mathrm{d}. $$

(29)

$$ {\mathrm{I}}_{\mathrm{i}1}=\min \kern0.24em \left[\left({{\mathrm{Y}}_{\mathrm{i}0}}^{\ast }{{\mathrm{G}}_{\mathrm{p}0}}^{\ast}\mathrm{F}\right),\left(-\varDelta {{\mathrm{L}}_{\mathrm{i}1}}^{\ast}\mathrm{labor}\ \mathrm{price}\right)\right]\mid {\mathrm{P}}_{\mathrm{i}0}<-\mathrm{d}. $$

(30)

Provided that innovation is subject to failure, as well as imitation, each investment decision is subject to fail accordingly with a probability parameter (risk). The levels of new knowledge—that may be exploited during the next period—takes into account the effects of obsolescence that limits its effect on productivity accordingly with a decay coefficient (decay).

$$ {\mathrm{T}}_{\mathrm{i}1}=\left\{\left[{\mathrm{I}}_{\mathrm{i}1}/{\mathrm{z}}_1/{{\mathrm{L}}_{\mathrm{i}1}}^{\ast }{\mathrm{A}}_{\mathrm{i}1}\right)\right]\mid \mathrm{E}>\mathrm{risk}\Big\}+\sum {{\mathrm{t}}_{\mathrm{i}-\mathrm{j}}}^{\ast}\mathrm{techDecay}. $$

(31)

Where z₁ represents the current price the firm has to pay to apply a unit of knowledge to a unit of product and E is a uniformly distributed pseudo-random number.

Schumpeterian externalities depend on the quality of the knowledge governance and the accumulation of knowledge. The quality of the knowledge governance mechanisms affects the access costs to the stock of knowledge. The second component of the Schumpeterian dynamic is the accumulation of knowledge that leads to a reduction of the cost of knowledge: by allowing firms to use the knowledge acquired in previous production cycles, paying for the first acquisition only, the model simulates this phenomenon. It is plausible that very old vintages of knowledge have little influence on production. Consequently, in order to account for the effects of obsolescence, at each production step, the amount of the stock of knowledge is reduced by dividing it per a decay parameter.

Both variables are controlled by a parameter: (i) techRate sets the fraction of the production the firms invest, whereas (ii) governanePerformance sets the effectiveness of the knowledge management. By specifying a zero value for techRate the firms remains simply adaptive, without performing any innovative reaction; by setting to zero the governancePerformance the cost of the knowledge becomes very close to c, i.e. to the value of its marginal productivity. Both techRate and governancePerformance manage the main component of the process.

Table 7 Setup of the parameters for the different scenarios

Appendix 2

Fig. 3

The simulation process