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. We'll 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
12T + T. L
And Louise's utility benefit from socializing is
12L + L.T
For these functions, Thelma's marginal benefit of socializing is
12 + L
And Louise's marginal benefit is
12 + 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. For these functions, Thelma's marginal cost of socializing is 4T, and Louise's is 4L. Suppose they choose T and L simultaneously. Find the Nash equilibrium. How many hours will they spend socializing? Can they do better? Would they be happier if both studied more than in the Nash equilibrium, or less?