A small economy has only two consumers, Boris and Vanessa.Boris's utility function is U(x, y)= x + 16y^1/2.Vanessa's utility function is U(x, y)= x + 2y.Boris is endowed with 160 units of x and 60 units of y.They make trades to reach a Pareto optimal allocation of resources in which both persons consume positive amounts.How much y does Boris consume? A)32 units B)19 units C)14 units D)16 units E)There is not enough information to determine how much y he will consume.

Question

Quizplus · Accepted Answer

To find the Pareto optimal allocation, we need to find the point where the indifference curves of both individuals are tangent to each other. This occurs where the marginal rate of substitution (MRS) of one individual is equal to the MRS of the other individual. 
Boris's MRS is given by MUx/MUy = (1/2)x/y, while Vanessa's MRS is given by MUx/MUy = 5x/y. 
We can set these equal to each other and simplify to get x = 10y. 
We also know that Boris consumes 160 units of x and 60 units of y, so we can substitute x = 10y into his budget constraint to get 160 = 10yP1 + 60P2, which simplifies to y = 16. 
Therefore, Boris will consume 16 units of y in the Pareto optimal allocation.

A Small Economy Has Only Two Consumers, Boris and Vanessa