Ambrose's utility is U(x₁, x₂)= = 4x^1/2₁ + x₂.If the price of nuts (good 1)is $1, the price of berries (good 2)is $4, and his income is $104, how many units of nuts will Ambrose choose? A)67 B)128 C)64 D)10 E)32

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Quizplus · Accepted Answer

To maximize Ambrose's utility, we need to find the quantity of each good that will maximize his total utility given his income and the prices of each good. We can use the equation U(x₁, x₂)F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 4x^1/2₁ F1F1F1S1F1F1F10 x₂ to find the utility from consuming different quantities of nuts and berries. However, since the formula is quite complex, we can use calculus to find the optimal quantity of nuts. Taking the partial derivative of the utility function with respect to x₁ we get: (dU/dx₁)F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 [4x^1/2₁] Setting this equal to zero and solving for x₁ gives us: x₁ = income/(2*price of nuts) = 104/(2*1) = 52 Therefore, Ambrose will choose 52 units of nuts, which corresponds to option C.

Ambrose's Utility Is U(x1, X2)= = 4x1/21 + X2

Ambrose's Utility Is U(x₁, X₂)= = 4x^1/2₁ + X₂