Suppose that all workers value their leisure at 90 goods per day. The production function relating output per day Y to the number of people working per day N is
Y = 250N - 0.5N2.
Corresponding to this production function, the marginal product of labour is
MPN = 250 - N.
a. Assume that there are no taxes. What are the equilibrium values of the real wage, employment N, and output, Y? (In equilibrium, the real wage will equal both the marginal product of labour and the value of a day's leisure to workers.)
b. A 25% tax is levied on wages. What are the equilibrium values of the real wage, employment, and output? In terms of lost output, what is the distortion cost of this tax?
c. Suppose that the tax on wages rises to 50%. What are the equilibrium values of the real wage, employment, and output? In terms of lost output, what is the distortion cost of this higher tax rate? Compare the distortion caused by a 50% tax rate with that caused by a 25% tax rate. Is the distortion caused by a 50% tax rate twice as large, more than twice as large, or less than twice as large as that caused by a 25% tax rate? How does your answer relate to the idea of tax smoothing?