Question

2. Papa John has preferences over leisure and consumption represented by U(L,C)=3L³C², where L is leisure hours per day and C is dollars of consumption per day. Papa John has 12 hours of time available for leisure and a nonlabor income of $100 per day. What is Papa John's reservation wage?

A. $0.08/hour

B. $0.18/hour

C. $8.33/hour

D. $12.50/hour

Answer 1

(D)

Utility function is given as

U(L,C)= 3L³C²

Marginal Utility of Leisure hours is given as

MU_{​​​​​L}​​​​= 9L²C² (Differentiating w.r.t L)

Marginal utility of consumption is given as

MU_{​​​​​C} = 6L³C

Marginal rate of substitution is given by

MRS= MU_{​​​​​L}​​​​/MU_{​​​​​C}

MRS= 3C/2L

Now, at endowment point

C= $100/day

L= 12 hours

Substituting in MRS, we get

MRS= (3*100)/2*12

MRS= 12.5/hour

Hence , reservation age of John Papa is given as

$12.5/hour