Consider an economy with a single worker whose utility is given by , = ², where c denotes consumption and denotes labor (measured in hours of work). The hourly

real wage rate (measured in consumption units) is given by 1. Assume that both the labor

market and the market for the consumption good are competitive.

a) Calculate the optimal choice of the worker (illustrate graphically in the l-c

space, with labor hours on the horizontal axis and consumption on the vertical

axis).

b) The government decides to levy a 50 percent proportional wage tax. Recalculate

the worker's optimal choice and derive the worker's utility level.

(illustrate graphically).

c) Show that shifting to a lump-sum tax system would yield higher tax revenues

than those obtained under the wage tax regime, while maintaining the worker's

utility level unchanged.

d) What is the excess burden of the wage tax regime?

e) Draw the labor supply and the labor demand curves in the l-w space, with labor hours on the horizontal axis and the wage rate on the vertical axis. Illustrate the excess burden (EB) of the wage tax by the area of the Harberger triangle associated with the labor supply curve. (hint: EB is given by the difference b/w the potential-tax trapezoid (PT) and the actual-tax rectangle (AT), associated respectively with the lump-sum and wage tax regimes. Both tax regimes are calibrated to yield the same worker's surplus, measured by the area above the labor supply curve and below the net-of tax wage rate).

f) Show that the area is equal to the excess burden measure calculated in part f.