1. Chapter 17. Inflation, unemployment and aggregate supply
ECON320
Prof Mike Kennedy

2. Inflation and unemployment is a major macroeconomic concern: A look at the Canadian experience

3. The Phillips curve
In the late 1950s and early 1960s, most economists believed that there was a stable relationship between the rate of inflation and the unemployment rate, called the Phillips curve
If policy makers chose a particular rate of unemployment they would have to accept the inflation rate given by the curve – there was a trade-off between one and the other (see next slide for Canada)
While the curve appeared to be stable for a number of decades, it proved to be anything but when policy makers tried to exploit it
In this chapter, explanations of why it was both stable and then later shifted will be examined
The relationship explaining this will be the expectations-augmented Phillips curve

4. The Phillips curve for Canada when it appeared to be stable

5. The stable Phillips curve disappears

6. The expectations-augmented Phillips curve
We will first show how the curve works and then go on to discuss the underlying micro foundations
Labour demand is sector i is given by
where
Assume that there is a union for each sector (i) in the economy which has the power to set the nominal wage rate (Wi)
where the term mw > 1 is the mark-up over the opportunity cost of working (b) which is equal to unemployment benefits
Note that the union in setting the wage rate must form an expectation of the price level that will prevail over the life of the contract – this will be key

7. The expectations-augmented Phillips curve con’t
We can substitute into the labour demand equation, the union’s wage setting relationship
At the aggregate level of the economy production is given by
Substituting this into the expression for labour in sector (i) and putting Li on the left hand side we get
and for the aggregate amount of labour

8. The expectations-augmented Phillips curve con’t
The previous equation (reproduced here) can be thought of as the short-run demand for labour and at the aggregate level it is
In the long run actual and expected prices are equal and long-run employment is given by
If we divide the long-run equation into the short run relationship we get something very simple

9. The expectations-augmented Phillips curve con’t
Actual and potential employment are given by, respectively,
Putting these into the above equation and taking natural logs, where we have assumed that N = n we get
Finally we assume (quite correctly) that everybody knows the price level in the previous period P-1
Subtracting the log of P-1 from both sides of the above we get
This is the expectations augmented Phillips curve
It can be used to explain both why the curve was stable for so long and why it shifted from the 1970s onward (see slide 18)

10. How did we get the underlying relationships: The plan of attack
Inflation is a continuous rise in the price level
In the short run, wages are the most important factor determining prices so we start there
We will assume that there is imperfect competition in the goods market (monopolistic competition among firms) and the labour market (a union in each sector which sets the nominal wage)
Employers determine how many people to employ
We will also assume (realistically) that people do not have perfect information about the current price level

11. The origins of nominal rigidities
Assume a large number of firms, each of which has a monopoly in its local market – monopolistic competition.
Workers have skills that apply to a specific firm where they are employed.
If they lose their job they cannot transfer to another firm and so are unemployed, in which case they earn b, real benefits.
When employed, they earn wi = Wi/P real wages.
The worker’s net income would be (wi  – b).
At the same time there is a union for sector i which cares about both the net income of the employee plus employment.
The parameter η > 0 reflects the weight the union attaches to employment in its sector (Li).

12. Price setting
In the short run we assume that K does not change so it can be ignore and the production function is given by
The demand for the firm’s output Yi is:
where σ > 1 is the price elasticity of demand
Since the firm’s total revenue equals TRi = PiYi marginal revenue is
The marginal cost of producing one unit of output (MCi) is the wage rate paid divided by the MPLi.

13. Price setting con’t
We get a price-setting equation by MRi = MCi and solving for Pi
and is the
mark-up of prices over marginal costs
To derive a demand for labour equation, we re-write the demand for Yi in terms of Pi
Now use the production function to eliminate Yi
For convenience we have separated out Li

14. Price setting con’t Dividing each side by we get:
Next set the first and last equation on the previous slide equal to each other so as to eliminate Pi
Note that we have isolated the real wage (Wi/P)
Dividing each side by we get:
Inverting this equation and solving for Li yields the demand for labour
where
and -ε is the elasticity of labour demand wrt the real wage

15. Wage setting The union’s utility curve is:
Maximizing wrt wi (the real wage in sector i) yields
Which becomes
Solving for wages and noting that the term in large brackets is the elasticity of labour demand wrt wages (ε) we get
The real wage that the union sets is a mark-up over the opportunity cost of not working (the outside option)
Note we are assuming for the moment that the union knows the price level

16. Wage setting con’t
The mark-up factor is greater than one, provided that σ > 1, which it is by assumption
We also assume that ηε > 1
We have already shown how using both wage setting and the price setting equations we can arrive at the expectations-augmented Phillips curve

17. The acceleration view and the natural rate of unemployment
Look again at the expectations-augmented Phillips curve
Now let’s suppose that expected inflation equals last period’s inflation rate
Putting this into the above we get
The implication from this equation is that when the unemployment rate is below the natural rate inflation will accelerate (actually it is the price level that accelerates!)
To keep inflation constant policy should be aimed at keeping the unemployment rate equal to the natural rate.
Such an unemployment rate is often labelled the Non-Accelerating Inflation Rate of Unemployment (NAIRU)

18. The expectations augmented Phillips curve will shift with changes in expected inflation, the long run curve is vertical

19. A structural definition of the natural rate
Recall the equation in slide 8 for long-run employment (when the actual price level was equal to the expected)
Now define
Then from the above we have
Finally assume that unemployment benefits grow with productivity where c < 1 which yields

20. A structural definition of the natural rate con’t
From our definition of the natural rate as
We can see that it will be higher, the larger are the mark-ups for both firms and unions
Note as well the an increase in c, the amount by which benefits are raised when growth improves, will also raises the natural rate
Policies aimed at raising the degree of competition in the economy will lower the natural rate by raising σ, the demand elasticity wrt prices
If the power of unions to set wages were to decline then so would the natural rate
Note that a greater union concern about employment (an increase in η) will also lower the natural rate by lowering the wage mark up

21. Would improving competition raise growth?

22. Is pursuing labour market reform worth the effort?

23. Sticky prices
So far we have assumed that prices of goods adjust instantly while wages are slow to adjust
There is lots of evidence that firms in certain sectors adjust prices infrequently – possibly due to “menu costs”
The model above can be modified to take account of this feature of the economy (see Chap 17 pp 489 to 491)
When this is done the Phillips curve becomes
where ϖ is the fraction of firms that adjust their prices infrequently
Of note is that is that the basic equation has not changed but the slope of the curve has – it is now smaller

24. Supply shocks
The Phillips curve can also be affected by supply shocks that take the form of short-run changes in the mark-ups (mp and mW) and to productivity (B)
To see how this works we first note that unemployment benefits (b) do not tend to move with short-run short-run changes in B but rather with its trend, implying
Substituting this into the equation for the actual level of employment (slide 8, first equation) we get
Next we develop an equation for long-run employment, using the equation from slide 8, and remembering that

25. Supply shocks con’t
As before we can divide the long-run employment equation into the short-run version and get
Remembering that
and
This becomes
where represents supply shocks
The next 7 slides show the importance of taking into account supply shocks

26. In Canada the Phillips appears to have shifted inward

27. The Phillips curve for Canada (A simple accelerationist model assuming no change in the natural unemployment rate)

28. We do know that the natural rate or NAIRU has changed – it seems to have fallen

29. The Phillips curve for Canada (Taking account of a changing natural rate of unemployment)

30. The importance of supply shocks in explaining inflation

31. What could have caused the NAIRU to shift down
What could have caused the NAIRU to shift down? Possibly a decline in unionisation…

32. … or an improvement in competition

33. The aggregate supply curve
The theory of inflation and unemployment implies a systematic relationship between inflation and the output gap
Our strategy is to find short-run and long-run equations for each unemployment rate and substitute them into the expectations augmented Phillips curve
We start from the production function (a supply concept) for GDP
In logs this becomes
which takes care of actual u

34. The aggregate supply curve con’t
Next we find the “natural” or long-run equilibrium level of the supply of output, where long-run values are denoted by “bars”
Using a similar procedure as in the previous slide we get
The expectations augmented Phillips curve is reproduced here from slide 25
Next, use the production relationships and compute

35. The aggregate supply curve con’t
We can substitute the equation we have for cyclical unemployment (the difference between actual and long-run or structural unemployment) into the expectations augmented Phillips curve to get
This is the short-run aggregate supply curve (SRAS) where
An increase in the output gap will raise inflation in the short run because:
The increase requires an increase in employment
Because of diminishing marginal product, marginal costs rise
This ends up in higher prices due to the mark up (mp)
Inflation is also affected by supply shocks (s)
The figure (next slide) shows that the position of the SRAS depends of πe

36. The SRAS curve slopes upward and shifts with πe and supply shocks, the LRAS curve is vertical