Question

1. Suppose that at the given distribution of goods individuals A and B have marginal rates of substitution between goods x1 and x2 given by MRSx1,x2A=-4 and MRSx1,x2B=-6 . Further suppose that these two people have strictly convex preferences and ignore corner solutions.

1. Explain using an Edgeworth box whether or not there is a Pareto improving exchange that could be had.
2. Which range of price ratios p1/p2 would induce trade between these two people?

Answer 1

Given:

2 goods x1and x2 are distributed among 2 individuals A & B such that

MRSx1x2 (A) = -4

MRSx1x2 (B) = -6

a) Figure 1 below describes the given information in Edgeworth box.

Since, the total Endowment of goods x1 and x2 among individuals A and B is not given so we assume that total endowment of x1 among both A and B is 6 and total endowment of x2 among A and B is 24.

Now we have drawn 3 of the many possible indifference curves of A and B in the Edgeworth box

At each indifference curve, A(x1, x2) and B(x1,x2) denote the allocation of goods x1 and x2 among A and B.

Note that at each of the 3 points of A(x1,x2), MRSx1x2 (A) = -4. Similarly, at each of the 3 points of B(x1,x2), MRSx1x2 (B) = -6

Now, between each of the 2 over-lapping indifference curves of A and B, there is an area which is called pareto improvement exchange points.

(b) The Pareto improvement trade point between A and B for goods x1 and x2 would be optimal when their relative MRS between goods x1 and x2 is equal to the relative prices of goods x1 and x2.

Thus, when MRSx1x2 (A)/ MRSx1x2 (B) = Px1/Px2

Or, Px1/Px2 = -4/-6 = 2/3.