Jenny has preferences given by the utility function U(C, L) = C^2 L. So the slop

Question

Jenny has preferences given by the utility function U(C, L) = C^2 L. So the slope of her indifference curve is C/2L . Johnny has the preferences given by the utility function U(C, L) = C L. So the slope of his indifference curve at any point is C/L .

a. Which of them has the relatively stronger preference for consumption over leisure? Explain.

b. They can both earn $10 per hour, they both have a non-labor income of $300 per week and they have 110 hours per week of non-sleeping time. Who works the most hours? How much do each of them make per week?

c. What are their reservation wages?

d. Starting from their preferred choice of work hours at $10 per hour (from part 2), suppose they were offered overtime at $20 per hour how many hours of overtime would each of them want to put in? How much would each of them earn?

I ONLY NEED THE SOLUTION OF d THX.

Explanation / Answer

d.) For Jenny, 933+20*(46.7-L)=2L*20,

so now, Jenny’s choice of leisure is: L=31.1.

and hence 46.7-31.1=15.6.

Jenny provides overtime labor supply of 15.6, with overtime labor income $312. Her total income is: 312+933= $1245

For Johnny, 700+20*(70-L)=20L,

so now Johnny’s choice of leisure is: L=52.5.

and hence 70 - 52.5= 17.5.

Thus Johnny provides overtime labor supply 17.5, with overtime labor income $350.

His total income is: 350+700=$1150.

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