Utility Function - Problem

 

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.?

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