In this exercise, you will look at firm behavior in setting wages and prices and see how this activity affects the level of real wages and the natural rate of unemployment (the equilibrium unemployment rate).
First, let's look at wage determination. The wage that is paid to workers depends on many factors.
As you can see from the graph, we are interested in the relationship between the real wage, W/P, and the unemployment rate. Suppose we formalize the wage setting relationship in the following way:
W = P F(U,z) => W/P = F(U,z)
where z summarizes all things affecting the wage rate, W, other than the unemployment rate, U, and the price level, P. (Note: The wage setting relationship actually depends on the expected price level. The actual price level is used here for simplicity.)
Now let's look at the price-setting relation. Again, we are interested in the relationship between real wages and the unemployment rate. But, now we look at how firms choose the price they charge. A common assumption used for price setting is that price depends on costs. A simple way of mathematically representing that price depends on costs, i.e. wages, is to assume that firms set their price according to:
P = (1 + m)W => W/P = 1/(1 + m)
Here m represents the markup of price over cost.
The wage-setting and price-setting relations determine the real wage paid to workers and the equilibrium unemployment rate (the natural rate of unemployment). You will see that the natural rate of unemployment is a very important variable. In the next exercise you will see how unemployment benefits and markups affect the natural rate of unemployment.