Ambrose's utility function is U(x, y)= x +4y^1/2.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%.

Question

Quizplus · Accepted Answer

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%.

Ambrose's Utility Function Is U(x, Y)= X +4y1/2

Ambrose's Utility Function Is U(x, Y)= X +4y^1/2