Review of the labour market

1. Review of the labour market • In last week’s lecture, we introduced into our system two new endogenous variables (wages W, price level P) and four new exogenous variables (expected price level Pe, labour supply L, factors affecting wage-setting z, firm mark-up over wages μ). • We have two equations W = Pe F(u, z) W = P / (1 + μ ) • To add to our IS-LM framework.

2. Deriving aggregate supply • Setting these two equations equal and dropping W, we get: Pe F(u, z) = P / (1 + μ ) • Remember that unemployment u = 1 – Y/L, so we can solve for output as a function of today’s price level. We will call this relationship “aggregate supply” or AS: F(1 - Y/L, z) = P / [Pe (1 + μ )] • Now F(u, z) was decreasing in u as wages rise slower if unemployment is high. This means that the higher is the right-hand side, the lower is unemployment.

3. Deriving aggregate supply • But the lower is unemployment, the higher is output, Y. • Combining all these we see that the higher is the right-hand side, the higher is output. Y is higher when P is higher, holding fixed Pe and μ. • Our aggregate supply curve graphs output as a function of P, so our AS curve is upward-sloping in P. • What else do we know about our AS curve?

4. Deriving aggregate supply • We know that if P = Pe then u = un. As we showed last week, if P = Pe: F(un, z) = 1 /(1 + μ ) • We can solve this for the natural rate of unemployment, un, as all the other terms are constants. If we have a natural rate of unemployment, then we must also have a “natural rate of output”, Yn: Yn = Nn =(1 – un) L

5. Deriving aggregate supply • The AS curve for a given level of expected price must go through the point (Yn, Pe), or in other terms if Y = Yn, then P = Pe.

6. Deriving aggregate supply • This is true for all AS curves, so higher expected prices must shift the AS curve upwards.

7. Deriving aggregate demand • We have derived an AS equation expressing a relationship between output by firms and the price level. Obviously we will complement this with an equation expressing demand for goods as a function of price. We call this our “aggregate demand” or AD curve. • Our IS equation showed goods demand as a function of government spending G, taxes T and the interest rate i. But i also depended on equilibrium in the LM equation.

8. Deriving aggregate demand • Our IS-LM equations are: IS: Y = C(Y – T) + I(Y, i) + G LM: M/P = Y L(i) • Assume the RBA holds M fixed. • A rise in price will lower the real money supply (M/P) so real money demand has to fall. This means that i must rise. • For a higher i, investment will be lower so goods demand as a whole must also be lower. Our AD graph for output must be downward-sloping in P.

9. Deriving aggregate demand • We could think of a rise in P as shifting the LM curve up, so leading to lower Y and higher i. • A rise in G shifts the IS curve to the right, raising Y for any P, so shifts AD right. Y = Y(M/P, G, T) Derivatives: + , + , -

10. What if RBA sets cash rate? • We can add a complication. Suppose the RBA targets interest rates and allows real money stock to vary- a cash rate- while aiming for a target price level. (This is the way the RBA actually operates.) • In this case the RBA follows an “interest rate rule”, which might be: i = in + a(P – PT) • If the price level exceeds the target price level, the RBA will raise interest rates above the “natural rate of interest”, in. If the price level is below the target rate, the RBA will lower the interest rate below in. • The natural rate of interest is the interest rate when P = Pe, so Y = Yn and u = un.

11. Interest rate rule • Now we have 3 equations, with 3 endogenous variables (Y, i, P): Y = C(Y – T) + I(Y, i) + G M/P = Y L(i) i = in + a(P – PT) • We can substitute for i to reduce this system to: Y = C(Y – T) + I(Y, in + a(P – PT)) + G M/P = Y L(in + a(P – PT)) • These two equations are independent of each other. Once we know P then i is fixed by the interest rate rule, we can determine Y without referring to the LM equation.

12. Interest rate rule • Output is determined by: Y = C(Y – T) + I(Y, in + a(P – PT)) + G • Money supply is determined by: M/P = Y L(in + a(P – PT)) • Our AD curve is given by: Y = Y(in + a(P – PT), G, T) Derivatives: - , + , - • Intuition: A rise in the price level causes the RBA to respond using its interest rate rule and raise i. The rise in i is what causes the AD curve to be sloping down. Since it is the response of the RBA that determines the rise in i, the slope of the AD curve depends on the RBA.

13. AD equation • Our IS-LM equations are two equations in 3 endogenous variables (Y, i, P). We have substituted out for i and derived our AD equation. So we have one equation in two endogenous variables (Y, P). • There are two forms for our AD equation: Fixed M: Y = Y(M/P, G, T) Target P: Y = Y(in + a(P – PT), G, T) • Important: Both of these AD curves slope downwards in P, but note that they slope down for different reasons!

14. AS-AD equilibrium • In our new AS-AD system, we have two equations in (Y, P): AS: P = Pe F(1 – Y/L, z) (1 + μ ) AD: Y = Y(M/P, G, T) Or AD: Y = Y(in + a(P – PT), G, T) • But once we solve for (Y, P), we can go back into the LM equation or interest rate rule: M/P = Y L(i) or i = in + a(P – PT) • To solve for i.

15. AS-AD equilibrium in short-run • For a given Pe (and PT, if the RBA has one), we have the AS curve going through (Yn, Pe). • At point A, where As and AD intersect, we have short-run equilibrium in the goods and money market (on the AD curve) and in the labour market (AS curve).

16. AS-AD equilibrium in medium-run • But this can’t be an equilibrium for long. In wage-setting, workers and firms assumed that P would be equal to Pe. But prices were higher, and so output higher, than expected. • Workers and firms will negotiate higher wages in the future, which will drive prices up even further. • Higher prices will lead to higher interest rates, so driving output down. We move along the AD curve up and to the left. • This continues until expected prices equal prices, and output is back at natural rate.

17. AS-AD equilibrium in medium-run • Higher expected prices shifts the AS curve up, raising current prices and reducing Y. • In the medium-term, we shift along the AD until we are back at equilibrium with P = Pe and Y =Yn.

18. Where do we end up? • In the long-run, we will end up with prices equal to expected prices and output equal to the natural rate. We will also be at the intersection of the AS-AD. AND we will have interest rates equal to their natural rate.

19. Talking through some scenarios • For the rest of today and in the tutorial, we will talk through some “stories” or “scenarios” using this AS-AD framework. It is important that you can replicate both the economic logic of the story and the graphs of the story.

20. A PT ● A´ ● P´ PT´ AD´ Y´ Yn Monetary policy contraction • Let’s say that the RBA wants to reduce the price level in the economy. • The RBA lowers the target price, meaning that current price is above target price, so i has to be raised. • A higher i shifts the AD curve to the left to our new short-run equilibrium.

21. AS´´ A PT ● A´ ● P´ A´´ ● PT´ AD´ Y´ Yn Monetary policy contraction • However we are now below expected prices, so wages have to be reduced. This shifts out AS curve to the right. • In the medium-run we move down along the AD curve back to LR equilibrium.

22. Thursday tutorial • For Thursday, practice the example of the budget deficit decrease in Section 7.5 of the book and Question 7 from the back of the book.