Asked by Juliana Ferranti on Jul 29, 2024
Verified
Ambrose's utility function is U(x, y) x 4y1/2.The price of x is $1 and the price of y is $2.If his income rises from $100 to $150, his consumption of y increases by more than 10% but less than 50%.
Utility Function
A mathematical representation that ranks an individual's preferences for various goods and services, aiming to measure their level of satisfaction.
- Comprehend how changes in income affect the demand for various products.
Verified Answer
ZK
Zybrea KnightAug 02, 2024
Final Answer :
True
Explanation :
We can use the Engel curve to determine the change in consumption of y due to the increase in income. The Engel curve for y can be found by holding the utility level constant and solving for y as a function of income and the price of y:
U(x, y) = U(x, y')
P_y' = 2
I = 100
100 = x + 2y'
y' = (100 - x)/2
Setting the above equation equal to the new income level I = 150, we can solve for the new consumption level of y:
150 = x + 2y
y = (150 - x)/2
The percentage change in y consumption is then:
((150 - x)/2 - (100 - x)/2) / ((100 - x)/2) * 100%
= (50/2) / ((100 - x)/2) * 100%
= 50% / (100 - x) * 100%
Since the price of x is $1, we know that x consumption will increase along with y consumption. Therefore, the percentage change in y consumption will be between 10% and 50%.
U(x, y) = U(x, y')
P_y' = 2
I = 100
100 = x + 2y'
y' = (100 - x)/2
Setting the above equation equal to the new income level I = 150, we can solve for the new consumption level of y:
150 = x + 2y
y = (150 - x)/2
The percentage change in y consumption is then:
((150 - x)/2 - (100 - x)/2) / ((100 - x)/2) * 100%
= (50/2) / ((100 - x)/2) * 100%
= 50% / (100 - x) * 100%
Since the price of x is $1, we know that x consumption will increase along with y consumption. Therefore, the percentage change in y consumption will be between 10% and 50%.
Learning Objectives
- Comprehend how changes in income affect the demand for various products.