Microeconomics 2nd Edition by Douglas Bernheim

Exercise 4

Make the same assumptions about the Smiths and Joneses as in Calculus Problem 2, with the following exception: the utility benefit the Smiths receive from their car is 90 S S · J and the utility benefit the Joneses receive from their car is 90 J J · S. Once again, these functions imply that, when one family buys a nicer car, the other family is less satisfied with its own car. The costs of spending more on a car are the same as before. Suppose the families choose S and J simultaneously. Find the Nash equilibrium. Now suppose that the Jones family, as the social leader, buys its car first. The Smith family sees the car purchased by the Jones family before buying their own car. Solve this game by reasoning in reverse. Do the Smith and Jones families spend more or less on their cars than when they make their decisions at the same time Provide an intuitive explanation for your answer.