Consider the model presented in class with the following assumptions: The representative firms production function is given by

Y=F(K,L)=2 K L

The labor supply is fixed and given by L = 25 The capital stock is fixed and given by K = 100 Capital and labor markets are perfectly competitive.

3

w is the wage rate r is the rental rate of capital

3.1 Agents: Who are the agents (decision makers) of the model? (1 point)

3.2 Setting up the firms maximization problem (2 points) Write out the expression for firm profits (i.e. the function the firms is aiming to

maximize). What variables are the firm choosing to maximize profits? (1 point)

3.3 Deriving first order conditions for profit maximization

Recall that for a function of two variables, (K, L), the necessary conditions for a maxi-

mum to be obtained are: and

= 0 L

= 0 K

Derive expressions for each of these conditions (5 points). 3.4 Interpreting the first order conditions

Consider the two first order conditions derived above. Explain the economic intuition in terms of marginal benefits and marginal costs. What must be true at an optimum? Why? (5 points).

3.5 Solving for Equilibrium

Recall that an equilibrium consists of expressions for the endogenous variables (K, L, Y , w, r) expressed in terms of exogenous variables and parameters of the model such that:

1. K, L, Y are solutions to the firms profit maximization problem.

2. w, r adjust to clear the labor and capital market. Find expressions for (K, L, Y , w, r) (10 points).