Ambrose's brother Bartholomew has an income of $133 and a utility function U(x₁, x₂) . The price of good 1 (nuts) is $2 and the price of good 2 (berries) is $1. How many units of nuts will Bartholomew demand?

Question

Quizplus · Accepted Answer

The optimal choice for Bartholomew can be found by using the marginal rate of substitution (MRS): MRS = MU1/MU2 = P1/P2 = 2/1 = 2 where MU1 is the marginal utility of nuts and MU2 is the marginal utility of berries. Bartholomew's utility function does not involve any income or budget constraints, so he would choose the consumption bundle that maximizes his utility, given the prices of nuts and berries. Therefore, we can calculate his demand for nuts directly using the MRS: MRS = MU1/MU2 = dU/dx1 / dU/dx2 = 2x₁ / x₂ 2 = 2x₁ / x₂ x₁ = 0.5x₂ Now, we can use the fact that Bartholomew's total expenditure on nuts and berries is equal to his income to solve for his demand for nuts: P1x₁ + P2x₂ = $133 2x₁ + 1x₂ = $133 3x₁ = $133 x₁ = $44.33 Therefore, Bartholomew will demand approximately 44 nuts. The closest answer choice is D: 49, which is the best choice.

Ambrose's Brother Bartholomew Has an Income of $133 and a Utility