Ambrose's brother Sebastian has a utility function U(x₁, x₂) = 28x^1/2₁ + x₂, where x₁ is his consumption of nuts and x₂ is his consumption of berries.His income is $128, the price of nuts is $2, and the price of berries is $1.How many units of berries will Sebastian demand? A)30 B)60 C)55 D)49 E)There is not enough information to determine the answer.

Question

Quizplus · Accepted Answer

Sebastian's budget constraint is 2x₁ + x₂ = 128. Substituting this into his utility function, we get U(x₁, x₂) = 28x^1/2₁ + 128 - 2x₁ = 26x^1/2₁ + 128. To maximize his utility, Sebastian will choose the value of x₁ that maximizes 26x^1/2₁ + 128. Taking the derivative of this function with respect to x₁, we get dU/dx₁ = 13x^-1/2₁. Setting this equal to zero and solving for x₁, we get x₁ = 16. Substituting this back into the budget constraint, we get x₂ = 96. Therefore, Sebastian will demand 96 units of berries.

Ambrose's Brother Sebastian Has a Utility Function U(x1, X2) =

Ambrose's Brother Sebastian Has a Utility Function U(x₁, X₂) =