Ambrose's brother Patrick has a utility function U(x₁, x₂)  16x^1/2₁  x₂.His income is $82, the price of good 1 (nuts) is $2, and the price of good 2 (berries) is $1.How many units of nuts will Patrick demand?

A) 26
B) 12
C) 14
D) 16
E) 30

Question

Savannah Hicks · Accepted Answer

Final Answer : D, Explanation :   Patrick's utility function is   U ( x 1 , x 2 ) = 16 x 1 + x 2 U(x_1, x_2) = 16\sqrt{x_1} + x_2 U ( x 1 ​ , x 2 ​ ) = 16 x 1 ​ ​ + x 2 ​  , where   x 1 x_1 x 1 ​   and   x 2 x_2 x 2 ​   are the quantities of nuts and berries, respectively. Given his income ($82), the price of nuts ($2), and the price of berries ($1), we can set up the budget constraint as   2 x 1 + x 2 = 82 2x_1 + x_2 = 82 2 x 1 ​ + x 2 ​ = 82  . To maximize utility, we differentiate the utility function with respect to   x 1 x_1 x 1 ​   and   x 2 x_2 x 2 ​   and set the derivatives equal to the ratio of the prices (Marginal Rate of Substitution, MRS, equals the price ratio). The optimal consumption bundle can be found by solving these equations, but since the question only asks for the quantity of nuts, we focus on that.The demand for nuts can be derived by allocating the budget optimally between nuts and berries to maximize utility. Without the detailed steps of solving the utility maximization problem (due to the format constraint), the correct answer is found by applying the utility maximization principle and the given budget constraint, leading to the conclusion that Patrick will demand 16 units of nuts.

Ambrose's brother Patrick has a utility function U(x₁, x₂)  16x^1/2₁  x₂.His income is $82, the price of good 1 (nuts) is $2, and the price of good 2 (berries) is $1.How many units of nuts will Patrick demand?

A) 26
B) 12
C) 14
D) 16
E) 30

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Learning Objectives

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Ambrose's brother Patrick has a utility function U(x1, x2)  16x1/21  x2.His income is $82, the price of good 1 (nuts) is $2, and the price of good 2 (berries) is $1.How many units of nuts will Patrick demand?A) 26B) 12C) 14D) 16E) 30

Definitions

Learning Objectives

Learning Objectives

Related questions

Ambrose's brother Patrick has a utility function U(x₁, x₂)  16x^1/2₁  x₂.His income is $82, the price of good 1 (nuts) is $2, and the price of good 2 (berries) is $1.How many units of nuts will Patrick demand?

A) 26
B) 12
C) 14
D) 16
E) 30