The probability of rain  is now 0.6.

1. How many units of consumption is it optimal for Sam to consume conditional on rain?

2. How many rain coupons is it optimal for Sam to buy?

3. If Sam's brother, Morgan, believes that there is a 50% chance of rain and a 50% chance of sun every day, his expected utility of consumption is U=frac{1}{2}lnc_s+frac{1}{2}lnc_rU=21lncs+21lncr. Is the expected utility function correct?

4. Is Morgan's utility function a monotonic transformation of Sam's utility function?

5. Will Morgan's optimal pattern of consumption be the same as Sam's?

Transcribed Image Text:

Sidewalk Sam, from the previous problem, has the utility function for consumption in the two states of nature u(C₂, Cy, π) = cc where c, is the dollar value of his consumption if it shines, cy is the dollar value of his consumption if it rains, and TT is the probability that it will rain. Sidewalk Sam, from the previous problem, has the utility function for consumption in the two states of nature u(C₂, Cy, π) = cc where c, is the dollar value of his consumption if it shines, cy is the dollar value of his consumption if it rains, and TT is the probability that it will rain.

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