Problem set 2 Micro Theory S. Wang Question 2. 1. You have just been asked to run a company that has two factories produc ing the same good and sells its output in a perfectly competitive market. The production function for each factory is Initially, the capital stocks in the two factories are respectively Ki= 25 and K2=100 The wage rate for labor is w, and the rental rate for capital is r. In the short run,the capital stock for each factory is fixed, and only labor can be varied. In long run, both capital and labor can be varied (a) Find the short-run total cost function for each factory (b) Find the company's short-run supply curve of output, and derived demand curve for labor (c) Find the long-run total cost function for each factory and the long-run supply curve of the company (d) If all companies in the industry are identical to your company, what is the long-run industry equilibrium price? (e) Let r=1. Suppose the cost of labor services increases from S1.00 to $2.00 per unit What is the new long- run industry equilibrium price? Can you determine whether the quantity of capital used in the long run will increase or decrease as a result of the increase in the wage rate from S1.00 to S2.00? Question 2.2. Suppose that two identical firms are operating at the cartel solution and that each firm believes that if it adjusts its output the other firm will adjust its output so as to keep its market share equal to What kind of industry structure does this implyProblem Set 2 Micro Theory, S. Wang Question 2.1. You have just been asked to run a company that has two factories produc￾ing the same good and sells its output in a perfectly competitive market. The production function for each factory is: yi = sKiLi, i = 1, 2. Initially, the capital stocks in the two factories are respectively K1 = 25 and K2 = 100. The wage rate for labor is w, and the rental rate for capital is r. In the short run, the capital stock for each factory is fixed, and only labor can be varied. In long run, both capital and labor can be varied. (a) Find the short-run total cost function for each factory. (b) Find the company’s short-run supply curve of output, and derived demand curve for labor. (c) Find the long-run total cost function for each factory and the long-run supply curve of the company. (d) If all companies in the industry are identical to your company, what is the long-run industry equilibrium price? (e) Let r = 1. Suppose the cost of labor services increases from $1.00 to $2.00 per unit. What is the new long-run industry equilibrium price? Can you determine whether the quantity of capital used in the long run will increase or decrease as a result of the increase in the wage rate from $1.00 to $2.00 ? Question 2.2. Suppose that two identical firms are operating at the cartel solution and that each firm believes that if it adjusts its output the other firm will adjust its output so as to keep its market share equal to 1 2 . What kind of industry structure does this imply? 2—1