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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
(e) Is Robert with 3B, 6C Pareto efficient?
The point 3B, 6C is pareto efficient as:
Yes, Robert with 3B, 6C is pareto efficient.
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