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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:

UR (BR,CR) = BRCR

UF(BF,CF) = BF CF

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

The marginal rate of substitution for Robert is as follows:

UR (BR,CR) = BR CR

MU = (∂UR)/(∂BR) = CR

MU = (∂UR)/(∂CR) = BR

MRS= ((∂UR)/(∂BR))/((∂UR)/(∂CR)) = CR/BR

The marginal rate of substitution for Fuswal is as follows:

UF (BF,CF) = BFCF

MU = (∂UF)/(∂BF) = CF

MU = (∂UF)/(∂CF) = BF

MRS = ((∂UF)/(∂BF))/((∂UF)/(∂CF)) = CF/BF

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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:

CR/BR = CF/BF

Using the endowments given:

BR + BF = 3+1 = 4

BF = 4 - BR

CR +CF = 2 + 6 = 8

CF = 8 - CR

Putting these values in the MRS equality congition:

CR/BR = (8-CR)/(4-BR)

4CR-BR CR = 8BR-BR CR

CR=2BR

(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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