Ambrose's utility is U(x 1 , x 2 )   4x 1/2 1  x 2 .If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $108, how many units of nuts will Ambrose choose?A) 128B) 64C) 67D) 11E) 32

Question

Ambrose's utility is U(x 1 , x 2 )       4x 1/2 1     x 2 .If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $108, how many units of nuts will Ambrose choose?A) 128B) 64C) 67D) 11E) 32

Kayla Marie · Accepted Answer

Final Answer : B, Explanation :   Given the prices and income, we can use the budget constraint to find the optimal consumption of nuts. The budget constraint is given by   P 1 X 1 + P 2 X 2 = I P_1X_1 + P_2X_2 = I P 1 ​ X 1 ​ + P 2 ​ X 2 ​ = I  , where   P 1 P_1 P 1 ​   and   P 2 P_2 P 2 ​   are the prices of goods 1 and 2, respectively,   X 1 X_1 X 1 ​   and   X 2 X_2 X 2 ​   are the quantities of goods 1 and 2, respectively, and   I I I   is the income. Substituting the given values,   1 X 1 + 4 X 2 = 108 1X_1 + 4X_2 = 108 1 X 1 ​ + 4 X 2 ​ = 108  . Without additional information on preferences, we cannot determine the exact allocation between nuts and berries. However, if Ambrose spends all his income on nuts (good 1), ignoring the utility function's specifics due to the question's formatting issues, he would purchase   108 / 1 = 108 108 / 1 = 108 108/1 = 108   units of nuts. Since this option is not available and the question's specific utility function details are unreadable, we cannot accurately solve for   X 1 X_1 X 1 ​   without clearer information on preferences. The correct answer choice is based on the assumption that clearer information or a specific utility maximization problem would lead to one of the provided options being correct. Given the options and the typical approach to such problems, option B seems like a plausible choice if we were to follow standard economic theory on consumer choice, but without the specific utility function's correct interpretation, this remains speculative.

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 $108, how many units of nuts will Ambrose choose?

A) 128
B) 64
C) 67
D) 11
E) 32

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Learning Objectives

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Ambrose's utility is U(x1, x2)   4x1/21  x2.If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $108, how many units of nuts will Ambrose choose?A) 128B) 64C) 67D) 11E) 32

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Learning Objectives

Learning Objectives

Related questions

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 $108, how many units of nuts will Ambrose choose?

A) 128
B) 64
C) 67
D) 11
E) 32