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Given the utility function:

U=lnc + l + lnc' + l'

and the budget constraint:

w(h-l) + w'(h-l')/(1+r) = c + c'/(1+r) where c = current consumption, c'= future consumption, l=current leisure, l'=future leisure, and r is the market interest rate. Suppose that the current wage, w=20 and the future wage w'=22.

What is the market interest rate r ? Show all steps.

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Paramjeet Chawla
Paramjeet ChawlaLv8
28 Sep 2019

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Related questions

Woody lives in Houston, and works at a college restaurant where the minimum wage per hour, w, is paid. The current minimum wage rate per hour is $8. Woody allocates his daily hours either for working or for leisure. That is, for the total 24 hours he has a day, he can choose to work (denoted as H), or do other things (denoted as L). If he works, all the money he earns, w x H, is spent on his consumption. Saving is not poosible. Both consumption and leisure are goods for him.

Woody's utility function is
U(L,C)= Squre root of CL2
MUC=L/(2*Square root of C)
MUL=Sqaure root of C

a) Derive Woody's MRS function. What is the MRS at (L,C) = (20,32)? State the meaning of MRS in terms of leisure and consumption.

b) Derive Woody's budget constraint equation. (Hint: C=w x H, and the total hours a day is 24)

c) What is Woody's optimal (L*,C*) and utility level U*? How many hours does Woody work each day? Clearly state the utility maximization condition.

Worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure:

U(c,l) = lnC + 4lnl

1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl.

Which worker places a higher value on labour market work?

2) Suppose the worker participates in the labour market. Derive worker’s compensated labor supply function and the compensated labour supply elasticity with respect to wage as a function of utility level and wage.

3) Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage.

4) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?

5) Provide the functional form of the income effect from a marginal decrease in income.

6) Provide the functional form of the substitution and total income effects of a marginal increase in wage.

7) Show that the Slutsky equation holds for this worker.

Info: C = w(h-l) + I- T

Question:

1. Suppose both consumption good  and leisure are normal goods, discuss without any graphs what will happen to the household's choice if there is:

a) an increase in dividend income I

b) An increase in wage w

2. Suppose now only the consumption good is normal, and leisure is inferior. Repeat the last question's procedure.

 

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