Hi-Techniks, Inc., has recently received a patent on a new product, an electronic cockroach deterrent. This device emits a high frequency noise that drives cockroaches out of the user’s house or apartment into neighboring dwellings. Hi-Techniks plans to produce and market the product themselves, as well as to allow production by any other company that is willing to pay a royalty of $10 per unit produced, under a licensing agreement.

Hi-Techniks estimates its total cost function will be TC = 200,000 + 80Q, up to a maxi¬ mum output rate of 40,000 units per year. Because of learning effects, average variable costs are expected to decline 25 percent in each of the second and third years. The fixed costs of competi¬ tors are expected to be about 20 percent higher, and their variable costs will be similar to those of Hi-Techniks, except for the royalty payment to Hi-Techniks.

Market demand for the product, estimated on the basis of a market survey conducted in New York City, is expected to be represented by the expression P = 300 — 0.005 Q and is expected to remain steady at that level for several years as market awareness of the product spreads and continues to attract new customers. Hi-Techniks expects to be a monopoly for the first year. If entry occurs, each new entrant is expected to gain 1 /(« + 1) of the market, and Hi- Techniks will end up with 2/(n + 1) of the market, where n is the number of firms. Hi-Tech- niks expects three other firms to seek licensing agreements and enter the market after the first year, if the price set by Hi-Techniks allows them to avoid losses. No further entry is expected after these firms enter. Hi-Techniks’ time horizon is three years, and its cost of capital is 15 percent per annum.

(a) What is the profit-maximizing price that Hi-Techniks could set in the first year? How many units would be sold at that price?

(b) Assuming entry of three firms at the end of the first year and that Hi-Techniks will emerge as the low-cost price leader, what price will be profit-maximizing for Hi-Techniks in the second and third years? What sales volume should Hi-Techniks expect in these years?

(c) What is the limit price that would prevent any other firm from entering the market, presum¬ ing that the royalty remains at $10 per unit, and that all three potential entrants would enter at the start of the second year if Hi-Techniks’s price in the first year would allow the en¬ trants to be profitable. (An approximate answer from a graph would suffice, or you may solve this problem algebraically.)

(d) Which is the EPV-maximizing strategy over the three-year time horizon, price skimming or penetration pricing?

(e) What assumptions and qualifications underlie your analysis?