The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c, b} is Y; K L-4. Cars are capital intensive, hence a > an. The price of cars is pe and the price of beans is po. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm 3. Define an equilibrium for this economy 4. The quantities used by the firm producing cars as a fraction of the total quantities in the economy are K. = nKK and Le = n1,L, for some values 0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to find analogous expressions for K, and Lp. How many equilibrium condi- tions are you left with? What are equilibrium values you are left to solve for?
The economy is populated by two firms. One firm produces cars (c), the other produces beans (b). The production function of each firm i = {c, b} is Y; K L-4. Cars are capital intensive, hence a > an. The price of cars is pe and the price of beans is po. Firms take all prices as given. The unit cost of labor is w and the unit cost of capital is r. The total amount of labor and capital in the economy are, respectively, L and K. 1. Write down the optimality condition for capital and labor of each firm 2. Derive the capital-to-labor ratio of each firm 3. Define an equilibrium for this economy 4. The quantities used by the firm producing cars as a fraction of the total quantities in the economy are K. = nKK and Le = n1,L, for some values 0 < nK <1 and 0 < nL < 1. Use the labor and capital market clearing to find analogous expressions for K, and Lp. How many equilibrium condi- tions are you left with? What are equilibrium values you are left to solve for?
Chapter11: The Firm: Production And Costs
Section: Chapter Questions
Problem 21P
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