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.
b)
In this case, he will consume 10 units of drugs, and he is indifferent between consuming 0 units or 10 units of food.
c) Utility with $20 cash = 20
Utility with food coupons = 10
Therefore, PH is better with $20 cash.