# MGT 404 – COSTS -COMPETITION MONOPOLY

MGT 404 Ã¢Â€Â“ Economics2016Â PROBLEM SET 2: PRODUCTION Ã¢Â€Â“ COSTS – COMPETITION – MONOPOLY1. True False and Uncertain (20 points)You need to explain your answer in order to obtain full credit. No more than three sentencesper answer.a. (5 points) If the wage rates a firm must pay increase, it may end up with lower total costsfor a given level of output.b. (5 points) A firm should always produce at an output at which long-run average cost isminimized.c. (5 points) The ratio of a monopolistÃ¢Â€Â™s optimal price to its marginal cost is larger when themarket elasticity of demand is greater in absolute value (i.e., more elastic).d. (5 points) A monopolist will always want to produce in the more elastic segment of itsdemand curve.2. Production (10 points)A firm produces output using capital (K) and labor (L) according to the following productionfunction_q= LaKb,where L and K are measured in hours. We assume that a = Ã‚Â½ and b = Ã‚Â½. An hour of labor costs$1 and an hour of capital can be rented at a cost of $4 (or alternatively has an opportunity cost of$4 in terms of other products the firm could produce with that capital).a. (2 points) Does this production function exhibit constant returns to scale? (EXPLAINYOUR ANSWER)b. (2 points) Solve for a general expression for the marginal product of labor and themarginal product of capital. Are they equal? (EXPLAIN YOUR ANSWER) Hint: Notethat for example MP_L =1/2L-.5 K.5 from the notes but use the fact that L=q2/K(rearranging the production function) to greatly simplify the MP_L expression. Use thesame trick to solve for MP_K.c. (1 points) What it the marginal rate of technical substitution?d. (5 points) Assume that the firm wishes to produce 10 units of output at minimum cost.Write down the two equations (but you do not need to solve) that would tell us theoptimal L and K to choose.MGT 404 Ã¢Â€Â“ Economics2016Professor Kevin Williams3. Cost Functions (20 points)The local store TedÃ¢Â€Â™s Tunes is the best music store in town. The cost function for the store is:TC = 20 + 4q + 3q2 + 2q3(Where q is number of records sold.)Please make sure to write out all answers to this question as equations: graphs are not sufficient.a. (5 points) What are the fixed costs of TedÃ¢Â€Â™s Tunes? Give an example of a fixed cost.b. (5 points) What is the average fixed cost function? Explain what happens (and why ithappens) to average fixed costs as quantity increases.c. (5 points) What is the average (total) cost function of the firm?d. (5 points) What is the variable cost function? Give an example of a variable cost.4. The Schott App. (30 points)Peter Schott starts a new company that has a monopoly on a cool new app that gives answers toSOM econ problem sets. His total cost function is:TC = 80 + 3Q + 3Q2which means that MC = 3 + 6Q. The fixed cost of 80 is not a sunk cost.Demand for the app is:Q = 10 Ã¢Â€Â“ (1/8)P.a) (10 points) If Peter is a monopolist, what price does Peter set and what output isproduced? Calculate profit and consumer surplus. What is the deadweight loss whenPeter is a monopolist?b) (10 points) Sharon Oster is tired of the Schott App users being taken advantage of by amonopolist Peter. She proposes that government sets a maximum price for the app of$45. Calculate quantity, change in consumer surplus and PeterÃ¢Â€Â™s profits at this maximumprice.c) (10 points) Judy Chevalier suggests that consumers need even more relief from greedymonopolists. She proposes a maximum price of $25. What do you think Judy is trying todo? What result would her proposal have upon Peter?