Boxem-Buddies, Inc., has developed a new exercise machine that will appeal to those who like to combine an exercise program with boxing practice. After a successful market-testing pro¬ gram they have estimated the demand curve for this machine to be P = 188.2351 — 0.0023 Q. Their fixed costs are expected to be $200,000 per annum, and marginal costs rise with output, as indicated by the expression MC = 25.8634 + 0.0018Q. The intercept of the market demand curve is expected to shift upward by 10 percent in the second year, with the slope term remain¬ ing the same. If Boxem-Buddies sets the profit-maximizing price in the first year, there will be entry of one firm at the start of the second year. Its cost curve is estimated to be TC = 240,000 + 35Q + 0.002 Q2. Because of its higher costs, it is expected to allow Boxem-Buddies to be the price leader. Moreover, because the innovating firm expects to gain a product differentiation advantage, the entrant will only get a third of the market when the prices are equal.

(a) What are the short-run profit-maximizing price and output levels for the machine in year 1 ?

(b) What is the limit price that would prevent the entry of the new firm? At that price what output would Boxem-Buddies sell?

(c) Suppose BB sets the profit-maximizing price in year 1 and the new firm enters. What price will it set as price leader? What are its output and profit levels in the second year?

(d) In retrospect, should BB have set the limit price? Explain and defend your answer with any underlying assumptions.