In period 1, Mr. Consistency and Mr. Hyperbola are each trying to come up with a plan for how much they will exercise in period 2. Exercise is less enjoyable than other leisure activities, leading to a loss of 100 in terms of period 2 utils. Exercise provides health benefits, realized in period 3, leading to a gain of 250 in terms of period 3 utils. They put the following weights on utilities each period:

According to this table, Mr. Consistency's weight on future utility falls by half each period. Mr. Hyperbola's weights are related to Mr. Consistency's; the difference is that Mr. Hyperbola's are reduced a further 30% for periods after the current one.
a. Would Mr. Consistency plan to exercise in period 1? Would he follow through on this plan in period 2?
b. Show that Mr. Hyperbola would not follow through on his exercise plan.
c. Suppose Mr. Hyperbola could sign a contract in period 1 that forced him to give up an amount of money valued at x utile in period 2 if he does not stick with his exercise plan. How high would x have to be to help him commit to hisplan?

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PERIOD TWO PERIODS AFTER AFTER CURRENT CURRENT CURRENT PERIOD ONE ONE Mr. Consistency Mr. Hyperbola 0.5 0.35 0.25 0.175