2. Model

This section describes the decision-making processes of the agents in an economy with one product market,and two input markets (capital and labor). Firms are the only agents we model explicitly and they interact with the three markets. There is a special firm, namely the state-owned enterprise (SOE), which has different constraints than the rest of the firms. All firms, including the SOE produce identical products. We do not explicitly model consumer agents but rather impose specific input supply functions and an output demand function.

This model can be solved analytically if firm agents are assumed to be homogeneous. All of the functions are differentiable, so the solution involves simultaneously solving the equilibrium conditions and all the first order conditions to the maximization problems, to get market-clearing prices and quantities. However, heterogeneous agents are a defining component of transition economies so this simplification would rob the simulation of all potential interest.

2.1 Firms

The private firms maximize profits at every period, taking prices of their output and inputs as given. The firms' objective function is:

$$\max_{K,L} \Pi = \max_{K,L} PF(K,L) - rK - wL$$

where F(K,L) = A K^a L^b (Cobb-Douglas production function).

L is labor demand, K is capital demand, and, P, w and r are the market-clearing prices of output, labor services and capital services, respectively. If the parameters of the Cobb-Douglas production function (A, a, and b) are the same across firms, the firms are homogeneous.

Typically, the standard economic approach to solving such a maximization problem is to use calculus. In our simulation, the firm agents instead use local methods, drawn from the field of artificial life, which are described in the Simulation Details section. In particular, the firm agents use locally available prices instead of the market-clearing prices.

2.2 The State-Owned Enterprise (SOE)

The SOE maximizes profits at every period but it has to satisfy an employment constraint. The labor demanded in the industry has to be at least $\bar{L}$. The SOE's objective function is:

$$\max_{K,L} \Pi = \max_{K,L} PF(K,L) - rK - wL$$

subject to

$$Q_L^D \geq \bar{L}$$

where Q_L^D is industry labor demand. The production function, F, is also Cobb-Douglas, the parameters of which may be different than those of private firms.

Like the private firms, the SOE uses an optimization method that requires only local information to maximize this objective function.

2.3 Input Supply

The supply functions of inputs are increasing (at a decreasing rate) functions of the input prices.

$$Q^S_L = A_L w^p,\ p<1 \mbox{ and } A_L>0$$

$$Q^S_K = A_K r^q,\ q<1 \mbox{ and } A_K>0$$

where Q^S_L is quantity supplied in the labor market and Q^S_K is quantity supplied in the capital market.

2.4 Consumer Demand

The market demand for the firms' output is linear¹:

$$P = A_D Q^D + D,\ D>0 \mbox{ and } A_D<0$$

As with the input suppliers' supply curves, this market demand function is provided exogenously.

2.5 Equilibrium Conditions

Demand in every market is equal to supply in every market. There are three markets: two input (capital and labor) markets and one output market. The equilibrium conditions for these three markets are:

$$\begin{eqnarray*}Q^D &=& Q^S \\ Q^D_L &=& Q^S_L \\ Q^D_K &=& Q^S_K \\ \end{eqnarray*}$$

where Q^D is the quantity demanded in the output market and the subscripts L and K refer to the labor and capital markets.