Microeconomics 2nd Edition by Douglas Bernheim

Exercise 3

Suppose that the demand functions for Coke and Pepsi are the same as in Worked-Out Problem 19.2 (page 679) but that each firm's cost function is C ( Q ) = 0.10 Q + 0.004( Q 2 ). What are Coke and Pepsi's Nash equilibrium prices What are their profits
Worked-Out Problem 19.2

Formula 1

Figure 19.12 Coke's Demand Curves. Figures (a) and (b) show Coke's demand curves when Pepsi's price is $0.60 and $0.40 per can, respectively. A lower Pepsi price shifts Coke's demand curve to the left, since Coke sales are lower for any given Coke price.

Figure 19.13 Coke's Best Responses. Figures (a) and (b) show Coke's profit-maximizing prices when Pepsi's price is $0.60 and $0.40 per can, respectively. They are found by first identifying Coke's profit-maximizing sales quantity [45,000 in (a) and 25,000 in (b)], which occurs where MR = MC, and then finding the corresponding profit-maximizing price [$0.48 in (a) and $0.40 in (b)] from Coke's demand curve.

Figure 19.14 Nash Equilibrium with Differentiated Products. The figure graphs Coke and Pepsi's best-response curves. The Nash equilibrium is the point where they cross, with both firms charging $0.40 per can, more than their marginal cost of $0.30. At the Nash equilibrium, each firm's price maximizes the firm's profit given the price of its rival.