Asked by Victoria Rodriguez on May 19, 2024
Verified
Elmer's utility function is U(x, y) minx, y2.If the price of x is $20, the price of y is $30, and Elmer chooses to consume 4 units of y, what must Elmer's income be?
A) $540
B) $880
C) $440
D) $200
E) There is not enough information to tell.
Min Function
In mathematics, a function that identifies the smallest value in a set of numbers.
Income
Represents the money received, especially on a regular basis, for work or through investments.
Price of X
The amount of money required to purchase a specified amount of good or service 'X'.
- Evaluate the outcomes of income fluctuations on consumption preferences.
- Utilize the principle of fiscal constraints when examining consumer selections.
Verified Answer
MG
Manbir GhumanMay 19, 2024
Final Answer :
C
Explanation :
To find Elmer's income, we need to use the fact that he chooses to consume 4 units of y. Let's set up the equation:
U(x,4) = min{10x, 4y}
We know that the price of x is $20, so we can rewrite the equation:
U(20,4) = min{200, 120}
Since Elmer chooses to consume 4 units of y, we know that the minimum is 120. So:
U(20,4) = 120
Now we can use the utility function to solve for Elmer's income:
U(x,y) = 10 min{x, y}
120 = 10 min{20, 4}
120 = 10(4)
120 = 40x
x = $440
So Elmer's income must be $440.
U(x,4) = min{10x, 4y}
We know that the price of x is $20, so we can rewrite the equation:
U(20,4) = min{200, 120}
Since Elmer chooses to consume 4 units of y, we know that the minimum is 120. So:
U(20,4) = 120
Now we can use the utility function to solve for Elmer's income:
U(x,y) = 10 min{x, y}
120 = 10 min{20, 4}
120 = 10(4)
120 = 40x
x = $440
So Elmer's income must be $440.
Learning Objectives
- Evaluate the outcomes of income fluctuations on consumption preferences.
- Utilize the principle of fiscal constraints when examining consumer selections.