Problem 1: When a firm uses K units of capital and L units of labor, it can produce Q units of output with the production function Q = K Sqrt(L). Each unit of capital costs 20, and each unit of labor costs 25. The level of K is fixed at 5 units.

a) Find the equation of the firm short-run total cost curve. b) On a graph, draw the firms's short-run average cost.

Problem 2: The production function Q = KL + M. The input prices of K, L, and M are 4, 16, and 1, respectively. The firm is operating in the long run. What is the long-run total cost of producing 400 units of output?

Problem 3: The bolt-making industry currently consists of 20 producers, all of whom operate with the identical short-run total cost curve ST C(Q) = 16 + Q², where Q is the annual output of a firm. The market demand curve for bolts is D(P) = 110 - P, where P is the market price.

a) Assuming that all of each firm's $16 fixed cost is sunk, what is a firm's short-run supply curve?

b) What is the short-run market supply curve?

c) Determine the short-run equilibrium price and quantity in this industry.

Problem 4: There are currently 10 identical firms in the perfectly competitive gadget manufacturing industry. Each firm operates in the short run with a total fixed cost of F and total variable cost of 2Q², where Q is the number of gadgets produced by each firm. Each firm also has non sunk fixed costs of 128. Each firm would just break even (earn zero economic profit) if the market price were 40. (Note: The equilibrium price is not necessarily 40 when there are 10 firms in the market.) The market demand for gadgets is QM= 180 - 2.5 P , where QM is the amount purchased in the entire market.

a) How large are the total fixed costs for each firm? Explain. b) What would be the shutdown price for each firm? Explain. c) Draw a graph of the short-run supply schedule for this firm. Label it clearly. d) What is the equilibrium price when there are 10 firm currently in the market? e) With the cost structure assumed for each firm in this problem, how many firms would be in the market at an equilibrium in which every firm's economic profits are zero?

Problem 5: A competitive industry consists of 6 type-A firms and 4 type-B firms. Each firm of type-A operates with the supply curve:

Q^S_A= -10 + P when P > 10 OR 0; when P 10

Each firm of type-B operates with the supply curve: Q^S_B= 2P; for P 0:

a) Suppose the market demand is Q^D_market= 108 -10P. At the market equilibrium, which firms are producing, and what is the equilibrium price?

b) Suppose the market demand is Q^D_market= 228 - 10P. At the market equilibrium, which firms are producing, and what is the equilibrium price?