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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.

F. A. Mala
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1 Answers1

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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) .

smcc
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  • Thanks a lot. Very helpful. However, I am still a little muddled about how I would plot the WS curve. – F. A. Mala Aug 15 '23 at 16:09
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    My answer explains that in the second bullet point. Since you do not know the value of $z$, you can just draw a downward sloping line and label the vertical intercept $1+0.7z$ and the vertical intercept $10+7z$. An increase in $z$ will shift the WS curve/line out (in a parallel fashion).

    It is just like when you are not given a specific value for the intercept of a demand curve. For a demand curve, the intercept depends on income. The demand curve shifts out when income rises (for a normal good).

     – smcc Aug 15 '23 at 16:12
  • Great. Thanks a lot. – F. A. Mala Aug 15 '23 at 16:16