14 Pricing - Eric Rasmusen

Download 14 Pricing - Eric Rasmusen .PDF

960552 Downloads

7.61 MB .pdf

5(pH − 1)[1 − F (pH − 35)] so F (pH − 35) = 1 − 19. ) The payoff function for firm j is πj = (pj − κcj )(α − βj pj + X γi pi ). 5 in which two firms choose the quantities they sell, while Section 14. Thus, even if a player is stuck in the role of low-quality seller in the purestrategy equilibrium, with an expected payoff of 4. I have put primes on the assumptions because they are the special cases, for smooth games, of the general definition of supermodular games in the Mathematical Appendix. If one firm had a capacity that was less than the ordinary Cournot output, that firm would produce only up to its capacity and the other firm would produce more than the ordinary Cournot output, since their outputs are strategic substitutes. p0 (5) If particular functional forms for p(q) and c(qa ) are available, equation (5) can be solved to find qa as a function of qb . Consumer 0 will buy from Apex so long as V − (θxa + pa ) > V − (θxb + pb ), (23) pa − pb < θ(xb − xa ), (24) which implies that which yields payoff (22a) for Apex. When the strategies of the players reinforce each other in this way, the feedback between them is less tangled than if they undermined each other. We already solved the one-quality problem in Vertical Differentiation I, yielding profit of 24. In the bargaining model this would happen if the buyer rejected the first-period offer and the seller could conclude that he must have a low valuation and act accordingly in the second period. The extra z2 is no problem; in comparative statics we are holding all but one exogenous variable constant. That code is an extra fixed cost, but IBM’s 1990 Laserprinter E is an example of a damaged product with extra marginal cost. If n = 1, then qj = 60, the monopoly optimum; and if n = 2 then qj = 40, the Cournot output found in section 3. Now, using the calculus chain rule yields not equation (41) but ∂f ∂f dy1 ∂f dy2 df = + + = 0. ) The price should be either 50, which is the most the strong buyers would pay, or 20, the most the weak buyers would pay. • An ingenious look at how the number of firms in a market affects the price is Bresnahan & Reiss (1991), which looks empirically at a number of very small markets with one, two, three or more competing firms. The instructor will then calculate the market price, rounding it to the nearest dollar to make computations easier. We will start by generalizing the Cournot Game of Section 3. • There are many ways to specify product differentation