Microeconomics 2nd Edition by Douglas Bernheim

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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 benefits from socializing are 12 T + T · L, and Louise's utility benefits are 12 L + 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' utility cost of socializing is 2 T 2 , and Louise's is 2 L 2. 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