Business Application: Deterring Entry of Another Car Company: Suppose that there are currently two car companies that form an oligopoly in which each faces constant marginal costs. Their strategic variables are price and product characteristics.
A: Use the Hotel ling model to frame your approach to this exercise and suppose that the two firms have maximally differentiated their products, with company 1 selecting characteristic 0 and company 2 selecting characteristic 1 from the set of all possible product characteristics [0,1].
(a) Explain why such maximal product differentiation might in fact be the equilibrium outcome in this model.
(b) Next, suppose a new car company plans to enter the market and chooses 0.5 as its product characteristic. If the new company enters in this way and existing companies can no longer vary their product characteristics, what happens to car prices? In what way can we view this as two distinct Hotel ling models?
(c) How much profit would the new company make relative to the original two?
(d) Suppose that the existing companies announce their prices prior to the new company making its decision on whether or not to enter. Suppose further that the existing companies agree to announce the same price. If the new company has to pay a fixed cost prior to starting production, do you think there is a range of fixed costs such that companies 1 and 2 can strategically deter entry?
(e) What determines the range of fixed costs under which the existing companies will successfully deter entry?
(f) If the existing companies had foreseen the potential of a new entrant who locates at 0.5, do you think they would have been as likely to engage in maximum product differentiation in order to soften price competition between each other?
(c) Determine the best response functions p1 (p3) and p3 (p1). Then calculate the equilibrium price.
(d) How much profit will the 3 companies make (not counting the FC that any of them had to pay to get into the market)?
(e) If company 3 makes its decision of whether to enter and what price to set at the same time as companies 1 and 2 make their pricing decisions, what is the highest FC that will still be consistent with the new car company entering?
(f) Suppose instead that companies 1 and 2 can commit to a price before company 3 decides whether to enter. Suppose further that companies 1 and 2 collude to deter entry—and agree to announce the same price prior to company 3’s decision. What is the most that companies 1 and 2 would be willing to lower price in order to prevent entry?
(g)What is the lowest FC that would now be consistent with company 3 not entering? (Be careful to consider firm3’s best price response and the implications for market share.)