Thelma and Louise have a big exam tomorrow. Each is trying to decide how much time to spend socializing, and how much to spend studying. Let's use T to stand for the amount of time Thelma spends socializing, and L to stand for the amount of time Louise spends socializing. Thelma's utility benefit from socializing is
12 T + T ∙ L
And Louise's utility benefit is
12L + L ∙ T
Notice that Thelma enjoys socializing more when she does it with Louise, and Louise feels likewise. Unfortunately, socializing will adversely affect their exam scores. Thelma's utility cost of socializing is 2T2, and Louise's is 2L2. Thelma, as the social leader, chooses T and announces her choice to Louise. (Thelma cannot change her mind after declaring her intention.) Then Louise chooses L. Solve this game by reasoning in reverse. Do Thelma and Louise spend more or less time socializing than when they make their decisions at the same time? Provide an intuitive explanation for your answer.
a. At an equilibrium, how many hours do Thelma and Louise spend socializing?
b. Do Thelma and Louise spend more or less time socializing than when they make their decisions at the same time?
c. Why is your answer in part (b) true?