Hi, my question is about Pareto optimal. There are 2 consumers and 2 commodities

Question

Hi, my question is about Pareto optimal.

There are 2 consumers and 2 commodities. Consumer A's initial endowment is 4 units of good x and 1 unit of y, and the utility function is U=x*y. Consumer B's initial endowment is 0 unit of x and 7 units of B,and the utility function is U=min{x,y}.

Question: 1)show the locus of Pareto optimal allocations.

2) let good x be the numeraire (price=1) and p denote the price of good y. Write the expression for the amount of good y that consumer B will demend at these prices.

Please show all work and thank you in advance for your help!

Explanation / Answer

1. The locus of paraeto optimal allocations is given by equating the slope of utility functions of both A and B as at the equilibrium condition MRS of A = MRS of B

MRS of A = Marginal utility of X / Marginal utility of Y = Y / X

MRS of B = 1 as the goods are perfect Complements consumed in 1 :1 proportion.

So, equating both, Y/X = 1, we get Y = X as the equation of contract curve.

2.The equilibrium condition in this case is Px / Py = 1 ( MRS)

1 / y = 1, so y = 1 unit.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

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