Description 1. ABC Company is the manufacturer of a low-noise air-purification system. Since three months ago, ABC has been receiving more orders than it can fulfill and has had to turn down some orders. Its current capacity is 10,000 units/month, but ABC received orders totaling 12,000 units in each of the past three months. Currently, ABC sells its system at a price is $200 per unit, its fixed cost is $500,000/month, and its variable cost is $100/unit. To expand its capacity, ABC will have to lease additional manufacturing machines, each of which will cost $50,000/month to lease and can add 1000 units to ABC’s capacity. Note that currently, half of ABC’s variable cost is materials, and the other half is labor cost (wages for workers). All existing workers are already working full time. So, to expand production, ABC has to hire new workers, who are expected to be paid 90% of the hourly wage of existing workers but produce only 75% of the hourly output of existing workers. (a) ABC decided to keep its price at $200 but expand its capacity to 12,000 units/month to deal with the demand increase. What is ABC’s monthly profit after its capacity expansion, assuming the orders come in at the rate of 12,000 units/month? (b) Suppose that ABC signed a long-term contract for leasing the additional machines when it expanded its monthly capacity to 12,000 units. ABC’s CEO now wants to consider a 5% price increase for the product. What are the incremental breakeven unit sales for this price increase? Assume that ABC’s capacity cannot be reduced to save capacity cost (since it has a long-term lease). If the 5% price increase will reduce orders by 8%, should ABC implement the price increase? (c) Comment on ABC’s initial decision to expand its monthly capacity to 12,000 units. In particular, are there situations in which ABC’s capacity increase is a bad decision? What information may be useful when deciding whether to expand capacity or how much to expand capacity? Explain your answer. What other alternatives to capacity expansion can ABC consider? 2. Canon has developed a new, high-end, high-resolution printer, which can print 40 pages per minute. Its market research identified two target segments of customers: 2,500 large businesses and 7,500 university labs. A large business has a valuation of $850 for the new printer, whereas a university lab has a valuation of $610. Canon’s variable cost for the printer is $450/unit; all fixed costs are sunk. Assume that each customer needs at most one new Canon printer (i.e., no customer will buy multiple units). (a) Suppose that Canon cannot price discriminate the two segments of customers, i.e., it can charge only one price for its printer. What is Canon’s optimal price for the new printer? What is its maximum profit? (b) Suppose that Canon can install an extra chip in the printer to slow down printing to 15 pages per minute. Such a chip costs Canon $20 to make and install for each printer. The slower version of the printer is valued at $650 by a large business customer and $600 by a university lab. With second-degree price discrimination, what are Canon’s optimal prices for the two versions of the printers, and what is its corresponding total profit? (c) Let N be the total number of large businesses and university labs in the market. Let f be the fraction of customers that are university labs, i.e., ?? represents the total number of university labs. How do the optimal prices in part (a) and part (b) depend on ?? Explain your answer and derivations.
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