Ambrose's utility function is = 4x^1/2₁ + x₂.If the price of nuts (good 1)is $1, the price of berries (good 2)is $7, and his income is $259, how many units of berries will Ambrose choose? A)8 B)197 C)9 D)18 E)12

Question

Quizplus · Accepted Answer

To maximize the utility, Ambrose will allocate his income in such a way that the marginal utility per dollar spent on each good is equal. 
We can find the marginal utility per dollar (MUD) for each good by taking the partial derivative of the utility function with respect to each good, and then dividing by the price of that good.
MUD1 = 2F1F10S1U1P11/(2S1U1B11P1) + F1F1F10S1U1B12/(S1U1B0P1) = (2S1U1P11)/(7S1U1B11) + S1U1B12/S1U1B0 
MUD2 = F1F1F10/(7S1P0) + F1F1F1S1/(S1U1B0) = 1/(7S1P0) + S1/(S1U1B0)
Setting the two MUDs equal to each other, we get:
(2S1U1P11)/(7S1U1B11) + S1U1B12/S1U1B0 = 1/(7S1P0) + S1/(S1U1B0)
Solving for S1, we get S1 = 9. Therefore, Ambrose will choose 9 units of berries.

Ambrose's Utility Function Is = 4x1/21 + X2

Ambrose's Utility Function Is = 4x^1/2₁ + X₂