Consider a potential, voluntary exchange between two people. Assume that both pe

Question

Consider a potential, voluntary exchange between two people. Assume that both people have complete information about each other's preferences and that there are no transaction costs. Initially, Consumer A has 10 of X and 5 of Y, and Consumer B has 5 of X and 10 of Y. Consumers A and B's utility functions are: U_A = XY^2 U_B = X + Y Calculate the marginal rate of substitution between goods X and Y for Consumer A at the current allocation. Calculate the marginal rate of substitution between goods X and Y for Consumer B at the current allocation. Show your work. Is this allocation of resources efficient? If it is, explain why. If it is not, what exchanges will make both parties better off? Explain your answer. For full credit, clearly specify whether A or B would get more X and Y respectively.

Explanation / Answer

1.For consumer A

MRSxy=Mux/MUy

MUx=Y2

MUy=2XY

MRSxy=Y2/2XY

=Y/2X

=5/20

=1/4

b.

For consumer A

MRSxy=Mux/MUy

MUx=1

MUy=1

MRSxy=1

c)An efficient allocation of resources is: That combination of inputs, outputs and distribution of inputs, outputs such that any change in the economy can make someone better off (as measured by indifference curve map) only by making someone worse off (pareto efficiency).An important fact about the Pareto frontier in economics is that at a Pareto efficient allocation, the marginal rate of substitution is the same for all consumers.

Since the MRS for consumer A and B is not the same the resource allocation is inefficient.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.