Suppose that the production function is
Y = 9K0.5N0.5.
With this production function, the marginal product of labour is
MPN = 4.5K0.5N0.5.
The capital stock is
K = 25.
The labour supply curve is
NS = 100[(1 - t)w]2,
where w is the real wage rate, t is the tax rate on labour income, and hence
(1 - t)w
is the after-tax real wage rate.
a. Assume that the tax rate on labour income, t, equals zero. Find the equation of the labour demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers.
b. Repeat part (a) under the assumption that the tax rate on labour income, t, equals 0.6.
c. Suppose that a minimum wage of w = 2 is imposed. If the tax rate on labour income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the mini-mum wage increase the total income of workers, taken as a group?