There is a representative firm that produces output (Y ) by using capital (K) and labor demanded (Nd) through the following Cobb-Douglas production:
Y = zF(K,Nd) = zK0.5Nd0.5.
Thus, the firm’s profit (profit) is given by
(profit) = zK0.5Nd0.5 wNd,
Where w is the wage. Suppose that the government imposes a producer tax, also known as a value-added tax (VAT). The tax rate for each unit of output produced is t, such that the firm can only retain (1 t)Y amount of revenue. Assume that the amount of capital is fixed in this question.
a. Write down the firm’s new profit equation with the producer tax.
b. Determine the effect of this tax on the firm’s revenue (production) with the aid of a graph.
c. How does this tax affect the Nd that maximizes the firm’s profit? Explain with the aid of a graph showing the change in firm’s profit maximizing labor demanded.
d. Determine the effect of this tax on the labor demand curve with the aid of a graph.