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Consider an individual with preferences given by ?(?, ?) = 2?^1/2 . C^1/2 where C is...

Consider an individual with preferences given by ?(?, ?) = 2?^1/2 . C^1/2 where C is consumption and L is leisure. Suppose the total time available each day is 16 hours, the wage rate is $8, the price of the consumption good is normalized to $1, and non-labour income is $50. (i) What is the individual’s reservation wage? Will the individual participate in the labour market? (ii) What is the optimal time spent working given these preferences and budget constraint?

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Homework Answers

Answer #1

Given

U(C,L)=2L^(1/2).C^(1/2)

MUL=dU(C,L)/dL=L^(-1/2)C^(1/2)

MUC=dU(C,L)/dC=L^(1/2)C^(-1/2)

MRS=MUL/MUC=L^(-1/2)C^(1/2)/L^(1/2)C^(-1/2)=C/L

i)

Reservation wage is equal to MRS if individual does not work. In this case,

C=Non labor income (V)=$50

L=16

So,

Reservation wage=C/L=50/16=$3.125 per hour

Current wage ($8) is higher than the reservation wage. So, individual will participate in the labor market.

ii)

Set MRS=wage rate for utility maximization

C/L=8

C=8L

Budget constraint is given by

C=V+(16-L)*w=50+(16-L)*8=50+128-8L=178-8L

Set C=8L

8L=178-8L

16L=178

L=11.125

So, Optimal time spent on working=16-11.125=4.875 hours

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