The Smith and Jones families live next to each other. Each is planning to buy a car. We'll use S to stand for the amount the Smiths spend, and J for the amount the Joneses spend (both in thousands of dollars). The utility benefit the Smiths receive from their car is90 S - S ∙ J
And the utility benefit the Joneses receive from their car is
90J - J ∙ S
Notice that both families care not only about the quality of the car they purchase, but also about how it compares to the other family's car. Spending more money on a car entails a utility cost, because it reduces the amount of other goods consumed. The cost is S2 for the Smiths and J2 for the Joneses. Suppose the families choose S and J simultaneously. Find the Nash equilibrium. Now suppose the Jones 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.