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Utility with food coupons

Question:

In Vancouver the Salvation Army encourages people to make food voucher donations to panhandlers instead of simply giving them cash. You can buy a food voucher for $5 and give it to a panhandler who can use it to purchase food. The Salvation Army says it's a way to ensure that a gift actually goes to food, rather than alcohol or drugs. Suppose a panhandler (PH) consumes two goods: food (F) and drugs (D). The PH has a utility function u = F0D1. This can also be written as u= D. Answer and explain the following using a diagram which is completely labeled.

(a) If drugs and food each cost $1 per unit, and the PH has $20 is cash, how much D and F will he consume.

(b) If instead the PH has $10 in cash and $10 in food vouchers, how much D and F will he consume?

(c) Is the PH better off with $20 in cash, or with $10 in cash and $10 in food vouchers.

Solution:

a)

u = D

PH will only consume drugs. This is because food does not give him additional utility. Whether he consumes 0 units or 1000000 units of food, it does not make a difference. Therefore, he will spend all his income on drugs. He will consume 20 units of drugs.

758_additional utility.png

b)

In this case, he will consume 10 units of drugs, and he is indifferent between consuming 0 units or 10 units of food.

968_Utility with food coupons.png

c) Utility with $20 cash = 20

Utility with food coupons = 10

Therefore, PH is better with $20 cash.

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