problem1. KopyKat is a firm which specializes in printing business cards and résumé’s, using the new laser technology. The manager has estimated that weekly demand can be approximated through P = 25 – 0.001Q, where P is price and Q is output per week. The firm’s cost function is C = 25,000 + 13Q + 0.002Q^2, where C is total cost. (MR = 25 – 0.002Q; MC = 13 + 0.004Q)
(i) Find out the firm’s profit maximizing output and price.
(ii) The night supervisor thinks that extending KopyKat’s hours through two hours in the evening would substantially raise volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead the manager to decide if the store can remain open later in the evening on a permanent basis?
(iii) A former employee decides to sue KopyKat, alleging employment discrimination. Though management claims innocence, they agree to settle out of court. The settlement needs KopyKat to pay the employee $10,000 per month for the next year. Find out the optimal output and price for the firm under these new conditions.
problem2. Firm Z is a U.S. based firm which sells farm equipment and faces demand given by P 3,000 – Q, where P denotes price in dollars and Q is quantity of units sold per month. In its East coast factory, the firm’s fixed costs are $250,000 per month, and its marginal cost of manufacturing the equipment is $1,000 per unit. (Part (a) MR = 3000 – 2Q; part (b) MR = 2,500 – 2Q; part (d) MR = 2,800 - 4Q)
(i) Find the firm's profit-maximizing price and output. What is its profit?
(ii) Over the last year, the US dollar has appreciated (gained value) versus the Japanese yen with the result which Japanese imports of farm equipment to the US have raised. Firm Z’s marketing department judges which it now would have to cut price by $500 per unit in order to sell the same profit-maximizing quantity as estimated earlier (The price equation will shift in-ward toward the origin). Is the price-cut consistent with a profit maximizing strategy? Describe.
(iii) Assume that a new market for firm's product emerges in South America. Firm Z has begun selling the equipment in various test markets there and has found the elasticity of demand to be EP = –3 for a wide range of prices (between $1,500 and $2,500). The cost of shipping to South America is $200 per unit. One manager argues which the foreign price must be set at $200 above the earlier profit-maximizing price to cover the transportation cost. Do you agree that this is the optimal foreign price? Justify your answer.
(iv) Assume that the firm has manufactured the optimal level of output in part (a). But before this quantity is sold, demand unexpectedly falls to: P = 2,800 - 2Q, (equivalently Q = 1,400 - 0.5P). One manager recommends cutting price to sell the whole inventory; another favour maintaining the price in part (a) (selling less than the total inventory). Do you concur with either manager? What optimal price would you set?