Question

A representative consumer has preferences described by the utility function: uc, 1) = ln(c- c) + Inl where c denotes consumption and I leisure. The parameter o captures the level of subsistence consumption. Assume that the total number of hours available to the worker are h = 1. The consumer/worker receives the wage, w, for her labor services. A. Obtain the labor supply curve. B. Introduce a proportional tax on labor income, T. Obtain the new labor supply curve. C. Introduce a proportional tax on consumption, Te. Obtain the new labor supply curve.

Answer 1

A.

Budget:

c + wl = w

where, l = leisure

Equilibrium condition:

du/dc 1/(c-7) 1 MRS = du/dl du/dl = priceratio = = 1/1 1/1

wl =-

Using this in budget, we get:

w + c=

W -C w -1- l= +C W 20

w +G labor Supply =1-1=1-(1- w+ 2w

B. With tax (t) on labor income:

Budget:

c + (w-t)l = w

where, l = leisure

Equilibrium condition:

du/dc du de 1/(c-7) 1/ 1 C 1 -E ==priceratio = ? w -t

(w - t)1=c-

Using this in budget, we get:

w + c=

w -c w+C - 27 2(w - t) w -t W-

labor Supply = 1-1= w + C-27 2(w - t)

C. With tax (t) on consumption:

Budget:

(1-t)c + wl = w

where, l = leisure

Equilibrium condition:

du/dc MRS = du de 1/(c-7) 1/ 1 C = 1 -E 1-t = priceratio = = ?

$wl=(1-t)(c-\overline{c})$

Using this in budget, we get:

$c=\frac{w+(1-t)\overline{c}}{2(1-t)}$

$l =\frac{w-c(1-t)}{w}=1-\frac{c(1-t)}{w}=1-\frac{w+(1-t)\overline{c}}{2w}$

$laborSupply=1-l =\frac{w+(1-t)\overline{c}}{2w}$

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