Question

Peter has a utility function U(x,y)=min{x,4y}. The price of good x is $10, and the price of good y is $5. If Peter's income is $450, how many units of good x would he consume if he chose the bundle that maximizes his utility subject to his budget constraint?

a. 5
b. 10
c. 40
d. 45
e. None of the above

Answer 1

Peter would consume 45 units of good x to maximize his utility subject to his budget constraint. Hence the correct answer is option A

Step-by-step explanation:

To find the number of units of good x that Peter would consume to maximize his utility subject to his budget constraint, we need to compare the utility he would receive from different bundles.

Given that his utility function is U(x,y) = min{x,4y}, we can calculate his maximum affordable consumption of each good by equating the prices with his income.

Since the price of good x is $10, Peter can afford to consume a maximum of 45 units of good x.

Therefore, the correct answer is d. 45.