Bowers Automotive Equipment is planning to launch its new product, a pair of miniature radio transmitters that would allow the owner to locate a car that was misplaced in a crowded parking lot, or even stolen and left somewhere else. One transmitter would be hidden in the car, and the owner would activate it by a hand-held transmitter/receiver that would be carried away from the car in a pocket or handbag. The owner would then zero in on the lost vehicle by moving in the direction of strongest signal. BAE calls this product the Car Finder. Test marketing of this product has resulted in the following initial demand curve being estimated: P = 295.6 — 0.0852Q, where Q is the number of Car Finders.

BAE has assembled 1,500 units in the past month, and notes that average variable cost was $40 and average fixed cost was $60. They expect average variable costs to fall by 20 percent each time cumulative output doubles, however. They estimate that the quantity demanded ini¬ tially will be 1,500 units per month at a price of $149.95, but that the demand curve will shift to the right by about 250 units every month following the product’s launch. Their present plant can produce up to 3,000 units a month, with constant marginal cost, but that output is the absolute maximum. If sales exceed 3,000 units a month, a larger plant will be required. Larger facilities and automated assembly equipment would reduce the average variable costs by 30 percent, however, and marginal costs are expected to be constant at this new level. Overhead costs would increase by 50 percent with the larger plant, which would have a maximum output rate of 6,000 units a month.

Competition is expected in the market if demand increases at the suggested rate. BAE expects Eldridge Electronics to come up with their own version of the product within six months, and Abersen Digital Systems probably will also enter the market within a year. Based on their track records, both these firms are expected to come out with a product which is better in some way, and they would therefore reduce BAE’s market share to 40 percent after six months and to 30 percent after twelve months. Of course, BAE’s engineers will strive to improve the Car Finder as time passes, but the better research facilities at BAE’s competitors mean that the new entrants’ products will probably have a competitive edge. All firms would have similar initial cost structures and would experience similar rates of learning in production.

(a) Is the proposed price the profit-maximizing price for the first month? If not, why do you think BAE chose that particular price level?

(b) Calculate the expected monthly output rates and profits for each of the first six months, presuming that the price stays at $149.95 and that Eldridge will enter the market at the start of the seventh month. Should BAE plan to build the larger plant?

(c) Speculate what would happen if Eldridge were to enter the market after six months with a superior product priced at $169.95 and capture 60 percent of the market, which continued to grow. Should BAE change its price? Calculate the monthly output rates and profits that BAE might expect over months 7 through 12. If you haven’t already recommended building the larger plant, would you recommend it now?

(d) Now speculate that Abersen will enter the market after twelve months with a product supe¬ rior to Eldridge’s but also priced at $169.95. What would you expect to happen to Eldridges price? Should BAE change its price? Explain.

(e) Advise BAE as to the initial and subsequent prices they should set for their new product. Note all qualifications and underlying assumptions.