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1. Sidewalk Sam makes his living selling sunglasses at the boardwalk in Atlantic City. If the sun shines Sam makes $30, and if it rains Sam only makes $10. For simplicity, we will suppose that there are only two kinds of days, sunny ones and rainy ones.

 

(a) One of the casinos in Atlantic City has a new gimmick. It is accepting bets on whether it will be sunny or rainy the next day. The casino sells dated “rain coupons” for

$1 each. If it rains the next day, the casino will give you $2 for every rain coupon you bought on the previous day. If it doesn’t rain, your rain coupon is worthless. In the graph, mark Sam’s “endowment” of contingent consumption if he makes no bets with the casino, and label it E.

 

(b) On the same graph, mark the combination of consumption contingent on rain and consumption contingent on sun that he could achieve by buying 10 rain coupons from the casino. Label it A.

 

(c) On the same graph, use blue ink to draw the budget line representing all of the other patterns of consumption that Sam can achieve by buying rain coupons. (Assume that he can buy fractional coupons, but not negative amounts of them.) What is the slope of Sam’s budget line at points above and to the left of his initial endowment?

 

(d) Suppose that the casino also sells sunshine coupons. These tickets also cost $1. With these tickets, the casino gives you $2 if it doesn’t rain and nothing if it does. On the graph above, use red ink to sketch in the budget line of contingent consumption bundles that Sam can achieve by buying sunshine tickets.

 

(e) If the price of a dollar’s worth of consumption when it rains is set equal to 1, what is the price of a dollar’s worth of consumption if it shines?

 

2. Sidewalk Sam, from the previous problem, has the utility function for consumption in the two states of nature

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