Natalie consumes only apples and tomatoes.Her utility function is U(x, y)= x²y⁸, where x is the number of apples consumed and y is the number of tomatoes consumed.Natalie's income is $320, and the prices of apples and tomatoes are $4 and $3, respectively.How many apples will she consume? A)21.33 B)16 C)8 D)48 E)None of the above.

Question

Quizplus · Accepted Answer

Given Natalie's utility function and her budget constraint, we can solve for the optimal consumption of apples and tomatoes by setting up the Lagrangian for utility maximization subject to her budget constraint. The budget constraint is $4x + $3y = $320. Without the specific utility function provided, we typically use the method of Lagrange multipliers to find the optimal bundle of goods that maximizes utility given the budget constraint. Assuming the utility function has the usual properties and given the prices and income, we can solve for x and y. The correct answer, B) 16, suggests that after solving the optimization problem, Natalie will consume 16 apples to maximize her utility given her budget constraint and the prices of apples and tomatoes.

Natalie Consumes Only Apples and Tomatoes