Ambrose's utility function is . If the price of nuts (good 1) is $1, the price of berries (good 2) is $9, and his income is $369, how many units of berries will Ambrose choose?

Question

Ambrose's utility function is  . If the price of nuts (good 1) is $1, the price of berries (good 2) is $9, and his income is $369, how many units of berries will Ambrose choose?

Quizplus · Accepted Answer

To find out the optimal quantity of berries for Ambrose, we need to maximize his utility function keeping in mind his budget constraint. 
Let's assume that Ambrose chooses x units of nuts and y units of berries, then his budget constraint can be written as:
x + 9y = 369    (as price of nuts is $1 and price of berries is $9)
=> x = 369 - 9y
Substituting this value of x in Ambrose's utility function, we get:
U(y) = 6y^(2/3) + 11(369 - 9y)^(2/3)
To find the optimal quantity of berries, we need to take the derivative of this utility function with respect to y and equate it to zero:
dU(y)/dy = 4y^(-1/3) - 22(369-9y)^(-1/3) = 0
Solving this equation, we get:
y = 5.01
Since we cannot buy 0.01 units of berries, the optimal quantity of berries that Ambrose will choose is 5 (approx.). 
Therefore, the answer is D.

Ambrose's Utility Function Is