Technology and the labour market
In the appendix to Chapter 6 , we learned how the wage-setting and price-setting equations could be expressed in terms of labour demand and labour supply. Consider the wage-setting equation:
$$
W / P=F(u, z)
$$
as the equation corresponding to labour supply. Recall that for a given labour force, $\mathrm{L}$, and where $\mathrm{N}$ is employment, the unemployment rate, $\mathrm{u}$, can be written as
$$
N=(1-u) L
$$
a. Substitute the expression for $u$ into the wage-setting equation.
b. Using the relation you derived in part (a), graph the labour supply curve in a diagram with $N$ on the horizontal axis and $W / P$, the real wage, on the vertical axis.
We write the price-setting equation as follows:
$$
P=(1+m) M C
$$
where $\mathrm{MC}$ is the marginal cost of production. To generalise our discussion in the text, we will write $\mathrm{MC}=\mathrm{W} / \mathrm{MPL}$, where $\mathrm{W}$ is the wage and MPL is the marginal product of labour.
c. Substitute the expression for $M C$ into the price-setting equation and solve for the real wage, W/P. The result is the labour 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 technologyHere, we assume that the MPL falls with employment (again for a given level of technology), a more realistic assumption.
d. Assuming that the MPL falls with employment, graph the labour demand relation you derived in part (c). Use the diagram you drew for part (b).
e. What happens to the labour 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?