3. Simulation Details

In this section, we describe how the firm agents in our simulation make decisions and interact with the three markets. In contrast to traditional economic modeling where the objective functions are optimized simultaneously, our agents act in sequence. The simulation runs as follows:

• Until the stopping criterion is met:

  1.

  For every firm:

  (a)

  Labor and capital markets provide prices based on recent sales.

  (b)

  The firm decides the price of its product.

  (c)

  The product market provides quantity demanded from this firm at this price. The firm produces this amount, provided that it makes a profit. Otherwise, the firm produces the profit-maximizing amount. In doing so, the firm purchases capital and labor at the price computed in step 1a.

  2.

  Firms enter and exit the market.

One cycle through this loop is referred to as a period.

The quantity exchanged does not always have to be equal to the quantity demanded. It will be the minimum of the two: quantity produced or quantity demanded. If there is excess demand, it is left unsatisfied.

3.1 Firm Agents

Firms optimize profit by continuously changing price in small increments (1%) in the direction they think will increase profit. They only know the last change they made in price and the last change they observed in profit. If there was an increase in profits they change the price in the same direction; otherwise, they change the price in the opposite direction. This hill-climbing approach to uncovering the optimal price is successful because the firms' objective function has a single maximum.

3.2 Product Market

The quantity demanded from a single firm at a given price is computed such that the exponential average of quantity exchanged stays on the curve. Specifically, the quantity demanded is given by:

$$\max \left( \frac{P_m - D}{A_D} - q_{avg,m} (n - 1), 0 \right)$$

where P_m is the price submitted by the current firm, nis the number of firms and:

$$q_{avg,m} = (1 - \beta^{1/n}) q + \beta^{1/n} q_{avg,m-1}$$

where q is the last quantity exchanged, m denotes the mth exchange, and $\beta$, the exponential constant, is 0.1.

3.3 Capital and Labor Markets

The rent at which a firm can purchase capital is computed as follows:

1.

Total capital rented in that period is estimated using the exponential average of the capital rented.

2.

The rent at which this amount of capital would be supplied is computed from the supply function.

3.

If the last rent was lower the rent is increased; if the last rent was higher the rent is decreased subject to a maximum 1% change².

The exact formulation is:

$$r = \left( \frac{n k_{avg,m}}{A_K} \right) ^{1/q}$$

where n is the number of firms and :

$$k_{avg,m} = (1 - \beta^{1/n}) k + \beta^{1/n} k_{avg,m-1}$$

where k is the last capital exchange, m is the mth exchange, and $\beta$, the exponential constant, is 0.1.

The wage is determined by the same algorithm, using the average labor hired and the last wage in the following relationship:

$$w = \left( \frac{n l_{avg,m}}{A_L} \right) ^{1/p}$$

where n is the number of firms and :

$$l_{avg,m} = (1 - \beta^{1/n}) l + \beta^{1/n} l_{avg,m-1}$$

where l is the last labor exchanged, m is the mth exchange, and $\beta$, the exponential constant, is 0.1.

3.4 SOE agent

The SOE behaves like the firms, but with an additional employment constraint. After it decides how much labor to hire, it checks to see if its estimate of total employment is at least $\bar{L}$. If not, it hires the difference.