Wage-setting curve?

Question

I am required to draw the graph of the following labor market equations:

Wage-Setting (WS): $W=P^e.(1-0.1u+0.7z)$

Price-Setting (PS): $P=(1+0.44)W$

How should be graph be drawn? I am confused by the so many unknowns here. The graph is supposed to consist of two lines or curves obviously, one for WS and one for PS.

Answer 1

If you assume $P^e=P$, then you can write the two equations as follows:

$$\begin{align*}\frac{W}{P}&=1-0.1u+0.7z \tag{WS}\\ \frac{W}{P}&=\frac{1}{1+0.44} \tag{PS}\end{align*}$$

Now, if you put the real wage $W/P$ on the vertical axis and the unemployment rate $u$ on the horizontal axis then:

• the PS curve is horizontal at $1/1.44$
• the WS curve is a downward sloping line with vertical intercept $1+0.7z$ and horizontal intercept $10+7z$

Here $0.44$ is the mark-up of price over cost. If the mark-up were zero then we would have $P=W$. The variable $z$ is meant to capture factors other than the unemployment rate that affect labour supply (these other factors are exogenous and include things like the unemployment benefit) .