Question

Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $80 and can buy apples at $2 per pound and kumquats at $1 per pound His utility function is Uſa, k) -5a +3k. That is, his constant marginal utility for apples is 5 and his constant marginal utility for kumquats is 3. What bundle of apples and kumquats should Andy purchase to maximize his utility? Why? Andy should maximize his utility buy purchasing apples (lbs.) and Kumquats (lbs.). (Enter your responses rounded to the nearest whole number.)

Answer 1

Given

Marginal utility from apples=MUa=5

Marginal utility from kumquats=MUk=3

Price of apple=Pa=$2 per pound

Price of kumquats=Pk=$1 per pound

Let us calculate marginal utility per dollar spent in case

(MUa/Pa)=5/2=2.50

(MUk/Pk)=3/1=3.00

Since (MUk/Pk)>(MUa/Pa), consumer will buy kumquats to maximize utility.

Maximum number of units of kumquats that can be bought in $80=80/Pk=80/1=80

Andy should maximize his utility by purchasing 0 apples (lbs) 80 kumquats (lbs)