Sidewalk Sam, from the previous problem, has the utility function

Sidewalk Sam, from the previous problem, has the utility function for consumption in the two states of nature
u(cs, cr, π) = c1−πs cπr,
Where cs is the dollar value of his consumption if it shines, cr is the dollar value of his consumption if it rains, and π is the probability that it will rain. The probability that it will rain is π = .5.
(a) How many units of consumption is it optimal for Sam to consume conditional on rain?
(b) How many rain coupons is it optimal for Sam to buy?

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