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From the AS curve to the SAS curve
 

To move from the AS curve to the SAS curve again is only a mechanical step. Here the question is: how can the firms' supply decisions, which the AS curve visualizes in a price/income diagram, be displayed in an inflation/income diagram?

The coordinate systems for both graphs are shown in the figure below. The AS curve derived previously is given in the left diagram. It is assumed that last year's price level was P0 and that the labour market expected the price level Pe=P1 for this year. What is this year's income? Well, this is obviously determined by this year's actual price level. And, given last year's price level, this year's prices are determined by how much inflation we had in the meanwhile. Let us put some numbers in the graph:

AS to SAS - Fig. 1

1. Suppose the price level is P1, as had been expected. Then firms supply potential income. Note that by prices being what they were last year, and being expected to move to P1 this year, the labour market expected inflation to be 5%. So if inflation really does turn out to be 5%, income is at potential income, as marked by the red dot in the right-hand-side diagram.
2. Next, suppose price moved higher than expected, to P2. We know that this drives down real wages and spurs production, to Y2 (which exceeds Y*). We mark this in the inflation/income diagram by noting that if inflation is 10% (while it was expected to equal 5%) income rises to Y2.
3. Finally, suppose prices rose to P3, way higher than expected. This raises output still further to Y3. We note this again on the right, marking output to be Y3 when inflation equals 15%.

Running a line through the three points combines all the points that may be obtained by tracing income levels at all kinds of inflation rates. This line is the SAS curve.

When deriving the red SAS curve we assumed that prices were expected to move to P1. Now, what if the labour market expected prices to move, say to P3 (that is, expected inflation was 15%)? We shall see that this yields a new SAS curve:

AS to SAS - Fig. 2

1. Suppose prices did move to P3, as expected. Then potential output is being produced. As shown in the diagram on the right, now income is at Y* if inflation stands a 15%. This blue point is off the previous (red) SAS curve.
2. Now suppose prices move to P2. This lower-than-expected price hike generates income Y2'. Record this point in the inflation/income diagram, where the combination of 10% inflation and output at Y2' is marked by the upper pale blue dot.
3. Finally, let prices rise to P1 only, meaning an inflation rate of 5%. Then income stands at Y1' as marked by the lower pale blue dot in the inflation/income graph.

Running a new line through these three new points gives a new (blue) SAS curve.

The lesson to be learned here is that while the SAS curve is upward sloping, its position depends on expected inflation. The higher expected inflation (the expected price level), the higher is the position of the SAS curve (the AS curve). Whenever actual inflation is as expected (no matter whether expected inflation is 0%, 7% or 20%) potential income obtains. This is captured in the algebraic equation

Formula SAS curve
 

Copyright 1997-2013, Manfred Gärtner. All rights reserved.