Question

Jake has a before-tax wage of $10 and pays an income tax of 20 percent, so t=.20. Show his budget constraint for work and leisure for one day. Suppose Jake’s before-tax wage decreases to $8, but tax rate remains constant; however, in turns out that Jake still consumes the same amount of leisure. Show this on a graph. Do these results seem reasonable? What do the results tell you about the relative size of the income and substitution effects for leisure for Jake?

Answer 1

Here, if we use an analog to Slutsky Equation, we get:

Total Effect (TE) = Hicksian Substitution Effect (SE) + Income Effect (IE)

^{$\frac{\mathrm{d}L^{M}}{\mathrm{d} w} = \frac{\mathrm{d} L^{H}}{\mathrm{d} w} + ( - L\frac{\mathrm{d} L^{M}}{\mathrm{d} M})$}

^{Here, Superscripts M and H stand for Marshallian and Hicksian respectively.}

Here, M = Total Income, w = Wage rate, L = Optimal amount of leisure.

per hour Given let L = - Wage w .$.10 Tax rate t 207.b. 2 T = Total time Endowment for a day; Amount of hours of Leisure for a day; Consumption level Pe Beace of consumption good, Total income = ctx W x CT-L) - Total came 0.8 WT - L O &xío CT-L) 841-1) Total expenditure & Pec 16 GENT H Total Total incone expenditure If w becomes $8, Total income = 0.8x8 x CT-L) = 6.4(T-L) = PC Total Expenditure L We are told that for both A and B level of leisure is the same (Lt). These results are reasonable as the total effect is the sum of the income and substitution effect we know that substitution effect is always positives live, the total effect is then decided by the income effect I Here, Total effect o - Income effect & Substitution effect o - (IE Income effect - Substitution effect - 2 IEKO - As income decreases, Leisure decreases - Leisure is a normal good