ECON0016: Macroeconomic Theory and Policy
Term 1, Problem set 4
1. A supply shock (25 marks)
(a) Use the 3-equation model to analyse the effect of a reduction in the markup that shifts the PS curve permanently upwards.
Period 1
1. The shock hits, the PS curve shifts up changing equilibrium output to y’e. The PC and the MR curve both shift so that they passes through the new point of medium run equilibrium (the blue dot). Note: if you argue that PC curve does not shift in period 1 but with one-period lag (because workers do not fully realize the PS curve shifts, i.e., workers also have adaptive expectation on medium-run equilibrium output), it is also fine. The dynamics of inflation and output are different though.
2. At the old level of equilibrium output, unemployment is unchanged wage setters want to keep their real wage constant and the nominal wage increases by the level of expected inflation πT
3. Firms set prices as a lower markup over wages (i.e. real wages are higher than expected, due to the shock) so inflation falls to π1< πT
4. The economy moves to the red point, with y=ye (the old equilibrium level), π= π1
5. The central bank is now off its MR curve. Interest rates are assumed only to affect the economy with a one-period lag, so the CB it needs to forecast where the PC will be in the next period. Actual inflation today is π1 so the CB knows expected inflation in the next period will be π1 so forecasts that the PC moves to PC1
6. The CB chooses real interest so that the economy will be at on the intersection of this forecast PC and the MR in the next period
Period 2
1. The reduction in interest rates in period 1 increases investment (and will also have an effect on consumption) so moves the economy along the IS curve. Aggregate demand and output change to y2
2. Inflation expectations are updated to last period’s inflation π2 and the PC shifts to PC1.
3. Output is above the new equilibrium, so unemployment is lower and workers have more bargaining power. They increase their wages by more than expected inflation to reflect this, a total of π2 >π1. The gap π2 – π1 is a measure of the extra bargaining power workers have as a result of lower unemployment/
4. Firms immediately set prices as a markup over wages so prices increase by π2
5. The economy moves to the green point, with y=y2, π= π2.
The central bank then guides the economy along the new MR curve back to the new point of medium-run equilibrium.
(b) List three other factors that can shift the price-setting curve
· Tax rates
· Labour productivity
· Commodity prices
· … and other things which affect the non-labour parts of the production function
(c) How will the response of the economy change if the central bank does not update its output target after the shock?
· Steps 1 -4 in the first period are the same as above.
· The CB then forecasts the PC and sets interest rates so that given this PC the economy in the next period will be on the MR curve i.e. at the green point.
· At this point, output is at the new equilibrium, expected inflation is equal to actual inflation and there are no forces to move the economy away from this point
· What happens next will depend on how the central bank responds to this situation of being away from both its targets. This will be covered in class.
2. Expectational errors and rational expectations
(a) Taking the case considered in part (a) of Q1, write down the expectational error in each period i.e. the difference between actual inflation and expected inflation
|
Period
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Actual inflation
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Expected inflation
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Error (expected inflation less actual inflation)
|
|
1
|
π1
|
πT
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πT-π1>0
|
|
2
|
π2
|
π1
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π1- π2<0
|
|
3
|
π3
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π2
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π2- π3<0
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(b) What is the real consequence of expectational errors
Workers get a real wage different from the one they expected. In the first period the real wage will be higher than expected, because of the shock, in subsequent periods lower than expected.
(c) Rational expectations means using all available information, which includes the three-equation model. Explain carefully how your answer to part (a) would change with rational expectations
· Agents with rational expectations know the answer to parts (a) and (b) of this question.
· If the shock was anticipated, they keep their expectations constant at πT and, if the central bank knows expectations are rational, it will move the economy directly to the new medium run equilibrium. i.e. inflation does not change from πT and the economy moves directly from the old level of equilibrium output to the new.
· If the shock were a surprise (which is in the nature of a shock), period 1 will look exactly as before, but as soon as individuals with rational expectations work out what has happened, they will keep their expectations at πT and the central bank will move the economy directly to the new medium run equilibrium i.e. inflation dips to π1 for just one period
(d) What if only some proportion of individuals form. rational expectations and the rest have adaptive expectations (answer briefly in words)
· The response of the economy would be somewhere in between the two pure cases of adaptive and rational expectations. Those with rational expectations will predict the decisions of those with adaptive expectations and use this in forming their expectations. It’s not possible to say any more in a graphical model.