The Micro-Macro Reciprocity

9 The Model

9.1 The Basic Structure

9.1.3 The Micro-Macro Reciprocity

Up to this point, the determinants of entrepreneurial behavior have been modelled comprehensively. The founding threshold, thereby, reflects the macro-data of a sector’s economic development, which influence the individuals’ behavior. In traditional economics those data would be taken as exogenous variables legitimized by a ceteris paribus assumption. The methodological framework developed in this work, however, requires a selection module to be introduced into the model to take account of the reciprocity between the micro- and macro-level. Figure 6.1 (chapter 6) summarized the methodological framework in general. Figure 7.1 (section 7.2) specified the framework to

the case of entrepreneurial behavior. Correspondingly, that framework is now going to be completed: a market module is needed—appropriate to generate stylized facts which influence the actors entrepreneurial behavior via the founding threshold. A selection process is used to substantiate competition. The easiest way to take into account the heterogeneity of competitive firms is the implementation of a heterogeneous oligopoly, although other models of competition would be feasible. A change of such a module would only change the results of the model as much as it effects the founding threshold, but it would not change the nature of entrepreneurial behavior in the model. Thus, we obtain a holistic approach while simultaneously focusing on entrepreneurial behavior.

Eventually, we end up with a system which is driven by the endogenous entrepreneurial behavior of individuals.

The Firm

The firm is the total of endowments actors bring into the firm. This is stated in equation 9.8. As emphasized earlier, the subject matter here is not to explicitly model the evolution of firms but to model entrepreneurial behavior. However, the need for a holistic approach asks for a rudimentary treatment of that, since the economic performance of firms also has an influence on actors’ behavior.

For simplicity the firm derives from its initial endowment set fjt. Furthermore, once the firm is founded, its structure is manifest meaning that the firm is not able to adjust to any competitive pressure by restructuring the firm.⁹ The cost structure of a firm consists of fixed cost determined by the venture-capital/human-capital ratio at time t0 (time of founding), with parameter δ limiting the maximal burning rate of firms,

(9.10)

and the variable unit costs, determined by

(9.11) with

(9.12)

Firms learn while accumulating output, and reduce their variable unit cost, by the learning rate lr. The initial variable unit cost, cj0, thereby depends on the initial value, c0, (equal for all firms) and their standardized relative human capital, hcj, to the best practice human capital, hc^max.

Finally, the total cost curve, of firm j looks as follows:

(9.13) Entrepreneurship 100

using an oligopoly model. Although such type of modelling does not perfectly fit the demands laid out above, it does the trick for the purpose analyzed here. Remember, the methodological approach developed allows for a modular construction of models. The sector’s dynamic evolution is decisive for entrepreneurial behavior, but only to the extent facts have an influence on entrepreneurial behavior. Therefore, it is enough to generate some stylized facts of an industry’s evolution in order to model a path-dependent process of entrepreneurial behavior in a continuously changing socio-economic environment.¹⁰ Suppose all firms at time t face their individual demand curve, given in equation 9.14:

(9.14)

pjt:=product price of firm j at time t;

yjt:=price limit of firm j at time t;

η:=price elasticity of demand;

xjt:=output of firm j at time t;

hjt:=oligopolistic interdependence of firm j at time t;

nt:=number of firms at time t.

The price pjt of firm j depends on yjt, which is to be interpreted as the firm’s quality standard which increases its price limit. Furthermore, the firm’s output decision xjt, the demand elasticity η, the oligopolistic interdependence hjt which considers the past price decisions of all other firms, have an influence on the firm’s price.¹¹ With the total cost function in 9.13, the firm’s profit function conclusively looks:

(9.15) πjt:=profit of firm j at time t;

In standard textbook manner the reaction functions of the myopic optimizing firms would be:

(9.16)

(9.17)

Notice that equations 9.16 and 9.17 are considered to be a firm’s forecast. They are a firm’s routinized behavior. A firm sets its price and plans to sell the corresponding output. The price decision is taken as a constant in each period. Equation 9.17, however, will slightly change since the actual output looks different. It is assumed that the turnover

of exiting firms, which drops out in the following period, has a positive effect on the turnovers of the remaining incumbent firms. Hence, an incumbent firm’s actual turnover is increased temporarily; this positive output shock is non-permanent and disappears after some time depending on parameter ρ indicating the persistence of such a shock.

Moreover, firms which produce a positive output are assumed to be able to grow over time with a positive impact, φ(t), of past sales on current sales, whereby this impact is decreasing over time. So that the actual price and output look as follows:

(9.18)

(9.19)

with and

g {1,…, t};

Г:=lag operator with Гxt=xt−1;

xsurv,t:=total turnover of surviving firms at time t;

xexit,t:=total turnover of exiting firms at time t.

Again, though the selection process strongly reminds of a standard textbook optimization problem, the deterministic modelling procedure of the demand side can be tolerated for our purposes here, i.e. modelling entrepreneurial behavior. Certainly, entrepreneurial actions also include the estimation of demand; the specificities, however, do not have a crucial influence on the agents’ behavior. At least the myopic foresight of agents and the routine perspective on their price setting and output production behavior imply a rudimentary bounded rational behavior of firms, too.

Now, as the system is complete, the only thing which is left to do is to present the numeric results obtained by simulation. Before doing that, a short summary will help to recall the basic structure of the model from an intuitive perspective.