We can identify two problems with the Keynesian model as developed so far:

1. nW is exogenous. Even though inflation may temporarily deviate from the wage inflation, this deviation cannot be too large and it cannot last for too long (as real wages would become unreasonable low or unreasonable high). This model has no determination of nW and therefore no complete determination of n. A model that predicts an inflation of around 6% by assuming a wage inflation of 6% is not very useful. The Keynesian model with inflation is therefore incomplete.

2. It is quite unreasonable to assume that nW would be independent of Y. More reasonable would be to model nW as a positive function of Y. If we are in a boom, L will be above its average and unemployment below its average. In such a situation, it is reasonable to expect wage inflation to increase.

To solve these problems, we need to make nw endogenous. We do this by to the Keynesian model adding the Phillips curve.

The Phillips curve

According to the traditional Phillips curve, there is a negative and stable relationship between wage inflation and unemployment.

Fig. 14.9: The Phillips curve.

The Phillips curve is often drawn with n instead of nW on the y-axis, but since these variables may deviate only temporarily, the difference is small. The Keynesian model plus the Phillips curve provides us with a full determination of all variables.

Some comments on the Phillips curve

• The Phillips curve was initially an empirical relationship between wage inflation and unemployment that was observed in many countries. It was usurped rather quickly and many Keynesian economists and integrated into the theory because it allowed them to determine inflation within the model.

• The Phillips curve was not a part of Keynes original theory. The relationship was discovered long after Keynes wrote the "General theory". Therefore, many prefer to view the Phillips curve as an addition to the Keynesian model - not as a part of the Keynesian model.

• The Phillips curve is often interpreted as an important political curve. Some view this curve as giving the government a choice of low inflation or low unemployment (or something in between). Most economists, however, do not share this view - the reason for this will be explained in the next chapter.

• The Phillips curve can also be interpreted in the terms of the business cycle. In a boom, Y is high; U is low and n is high. In a recession, the opposite holds. In a boom, we are at a point up on the left on the Phillips curve, while in a recession, we are at the bottom right. Business cycles may be viewed as oscillations between these two points.

Determination of all endogenous variables

We can illustrate how all the endogenous variables are determined in the following diagram:

Fig. 14.10: The Keynesian model with the Phillips curve.

1. Start at the bottom left. In year 1, AD1 and AS1 apply, the price level is P and GDP is Y.

2. Extend this level of GDP up to the top left diagram and through the 45-degree line to the production function at the top in the middle.

3. In this diagram we can determine how much L we need to produce Y. Extend this amount of labor down to the lower middle graph and through the 45-degree line to the bottom right graph.

4. This diagram shows the relationship between L and U. The higher the unemployment rate U, the lower the amount of labor L and the curve slopes downwards. From L we can determine U which we extend up to the Phillips curve in the right top graph.

5. From the Phillips curve, we can determine wage inflation nz^

6. Going back to the AS-AD diagram, we now the rate at which the AS curve slides up or down. The AD curve slides at a rate determined by nM which is exogenous.

An important case is when the growth in money supply is equal to the wage inflation. In this case, Y is fixed and k = nw = km. If, however, km exceeds the wage inflation, the AD curve will glide upwards at a faster rate than the AS curve. Now Y will increase and if you follow the effect through all the 6 diagrams, you see that L will increase, U will decrease and kw will increase. Y will continue to increase as long as k,., < n„, which means that W will continue to increase until k„. = k,.

W M W M

In the Keynesian model with the Phillips curve, k and kw will eventually be equal to km. As wages are assumed sticky in this model, it may take a long time for kw to become equal to km.

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