Technology and the labor market In the appendix to Chapter 7, we learned how the wage-setting and price-setting equations could be expressed in terms of labor demand and labor supply. In this problem, we extend the analysis to account for technological change.

Consider the wage-setting equation

\[
W / P=F(u, z)
\]

as the equation corresponding to labor supply. Recall that for a given labor force, \(\mathrm{L}\), the unemployment rate, \(\mathrm{u}\), can be written as \[
u=1-N / L \]
where \(\mathrm{N}\) is employment.

a. Substitute the expression for \(u\) into the wage-setting equation.

b. Using the relation you derived in (a), graph the labor supply curve in a diagram with \(\mathrm{N}\) on the horizontal axis and \(W / P\) the real wage, on the vertical axis.
Now write the price setting equation as \[
P=(1+m) M C \]
where \(M C\) is the marginal cost of production. To generalize somewhat our discussion in the text, we shall write \[
M C=W / M P L \]
where \(W\) is the wage and \(M P L\) is the marginal product of labor.

c. Substitute the expression for \(M C\) into the price-setting equation and solve for the real wage, \(W / P\). The result is the labor demand relation, with \(W / P\) as a function of the MPL and the markup, \(m\).
In the text, we assumed for simplicity that the MPL was constant for a given level of technology. Here, we assume that the MPL decreases with employment (again for a given level of technology), a more realistic assumption.

d. Assuming that the MPL decreases with employment, graph the labor demand relation you derived in (c). Use the same diagram you drew for (b).

e. What happens to the labor demand curve if the level of technology improves? (Hint: What happens to MPL when technology improves?) Explain. How is the real wage affected by an increase in the level of technology?