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B) Second hypothesis
3.1 The Philips Curve
Philips, a New Zealand-born economist, wrote a paper in 1958. In this paper, he showed the relationship between unemployment and the rate of change in money wage rates in the United Kingdom between 1861 and 1957. His paper was published in the quarterly journal, Economica. According to Philips, there is an inverse relationship between the rate of unemployment and the rate of increase in money wages.
If there is a high rate of unemployment then the rate of wage inflation is lower. In other words, there is a tradeoff between wage inflation and unemployment. The Philips curve shows that the rate of wage inflation decreases with the unemployment rate. Thus, w is defined as the wage in the current period. e
W
−1is the wage during the last period. Therefore, wage inflation is defined as follows:1 1
W W W
g W− −
= − (3.1)
where
g
W= wage growth W = present wageW
−1= past wage rateIf u* is defined as the natural rate of unemployment then wage growth is defined as
( *)
g
W= −∈ − u u
(3.2)where U = the unemployment rate in the economy U*= the natural rate of unemployment
If u = u* and
g
W=0, and u > u* theng
Wis negative. The wage rate is decreasing, but if u > u* then the growth rate of wages is rising. The Philips curve implies that wages and prices adjust slowly to changes in aggregate demand. After using wage inflation, it can be further defined as1 1
W W W
g W− −
= − -
1
1 1
W W W− W−−
= −
Advanced Macroeconomics
84
Aggregate supply, wages, prices and employment Dividing
W
−1 from both sides,1
w W 1
g =W− − (3.3)
If we substitute
g
W= −∈ − ( u u *)
into equation (3.3) then1
1 ( *)
W u u
W−
− = −∈ −
1
1 ( *)
W u u
W− = −∈ −
Therefore,
W W =
−1[1 −∈ − ( u u *)]
(3.3a)This means that the present wage depends on the past wage 1− ∈ and the difference between natural unemployment and present unemployment. This also shows the level of wage today relative to the past level for wages to rise above their previous level of unemployment. Unemployment may fall below the natural rate.
The Philips curve rapidly became a cornerstone of macroeconomic policy analysis. It suggests that policy makers could choose different combinations of unemployment rates of inflation.
The Friedman-Phelps amendment
The Friedman-Phelps proposition states that in the long run, the economy will move to the natural rate of unemployment whatever the rate of the change in wages and the inflation rate. There is no tradeoff in the long run. It is a counter argument to the Philips curve. The notion of a stable relationship between inflation and unemployment was challenged by Friedman and Phelps who both denied the existence of a permanent tradeoff between inflation and unemployment (Snowdon and Vane 2005).
3.1.1 Wage Stickiness
The assumption is that wages are slow to adjust. The shift in demand is essential to our derivation of an aggregate supply (AS) curve. Wages are sticky or wage adjustments sluggish when wages move slowly over time rather than being fully and immediately flexible so as to assure full employment at every point in time.
We translate the Philips curve in (3.3) to a relationship between the trade of the change in wages gw and the level of employment N. We define the unemployment rate as a fraction of the full employment labor force N*.
Advanced Macroeconomics
85
Aggregate supply, wages, prices and employment
We assume that u* = 0, then u is defined as
*
* N N u N
= − (3.4)
If we substitute (3.4) into (3.3a) then we obtain the Philips curve. The Philips curve shows the relationship between the wages during this period and the wages during the last period and the actual level of employment.
Thus, 1[1 ( *)]
* W W N N
− N
= + ∈ − (3.5)
where N*= full employment
N = actual level of employment
The above equation shows the relationship between wage employment relations. If we draw the diagram of wages during the last period and actual level of employment, we come up with the following.
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Advanced Macroeconomics
86
Aggregate supply, wages, prices and employment
:
:1
:
1(PSOR\PHQW
Figure 3.1 Wages and employment relationship
The Y axis shows the wages W and the X axis shows the employment. Wages show an upward line. The WN line shows the wage during this period is equal to the wage that prevailed during the last period, with an adjustment for the level of employment.
At full employment (N = N*) the wage of this period is equal to last period’s wage. Equation (3.5) can be defined again as follows:
0 1
[1 ( *)]
* W W N N
N
= + ∈ −
Within a period, the wage increases with the level of employment as shown by WN. If employment is at its neoclassical equilibrium level N*, the wage rate level in this period is equal to that of last period.
:1¶
:1 :1¶¶
:DJHV
1 1(PSOR\PHQW
Figure 3.2 Changes in wages and employment
Advanced Macroeconomics
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Aggregate supply, wages, prices and employment Equation (3.5) implies that the WN relationship shifts over time as in figure 3.2. If there is over- employment during this period, the WN curve will shift upwards at the next period to WN’. If there is less than full employment at this period, the WN line will shift downwards to the next period to WN’’.
The wage and employment relationship changes with time. The WN curve shifts over time if employment differs from full employment. N* is defined as the full employment level. The WN curve shifts upwards to WN’’ in the next period. Therefore, if there is overemployment in the current period then the curve shifts upwards.