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Edgeworth Box Assignment - Rob Crusoe Problem

(a) Draw Edge worth box and clearly label axes + points.

The edgeworth box is as follows:

(b) Draw indifference curves with utility = 6.

The indifference curve with utility 6 are as follows:

U^R (B^R,C^R) = B^RC^R

U^F(B^F,C^F) = B^F C^F

(c) Find MRS (Marginal rate of substitution) of C for B.

The marginal rate of substitution for Robert is as follows:

U^R (B^R,C^R) = B^R C^R

MU = (∂U^R)/(∂B^R) = C^R

MU = (∂U^R)/(∂C^R) = B^R

MRS= ((∂U^R)/(∂B^R))/((∂U^R)/(∂C^R)) = C^R/B^R

The marginal rate of substitution for Fuswal is as follows:

U^F (B^F,C^F) = B^FC^F

MU = (∂U^F)/(∂B^F) = C^F

MU = (∂U^F)/(∂C^F) = B^F

MRS = ((∂U^F)/(∂B^F))/((∂U^F)/(∂C^F)) = C^F/B^F

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(d) Find Pareto-efficient allocation. Mark on graph as "a" points Pareto optimum.

Pareto efficiency is attained where the MRS of both the consumers is equal:

C^R/B^R = C^F/B^F

Using the endowments given:

B^R + B^F = 3+1 = 4

B^F = 4 - B^R

C^R +C^F = 2 + 6 = 8

C^F = 8 - C^R

Putting these values in the MRS equality congition:

C^R/B^R = (8-C^R)/(4-B^R)

4C^R-B^R C^R = 8B^R-B^R C^R

C^R=2B^R

(e) Is Robert with 3B, 6C Pareto efficient?

The point 3B, 6C is pareto efficient as:

6=2*3

Yes, Robert with 3B, 6C is pareto efficient.

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