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 P_{0} and that
the labour market expected the price level P^{e}=P_{1}
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:
1. Suppose the price level is P_{1}, 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 P_{1}
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 righthandside diagram.
2. Next, suppose price moved higher than expected, to P_{2}.
We know that this drives down real wages and spurs production, to
Y_{2} (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 Y_{2}.
3. Finally, suppose prices rose to P_{3}, way higher than
expected. This raises output still further to Y_{3}. We
note this again on the right, marking output to be Y_{3}
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 P_{1}. Now, what if the labour market expected
prices to move, say to P_{3} (that is, expected inflation
was 15%)? We shall see that this yields a new SAS curve:
1. Suppose prices did move to P_{3}, 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 P_{2}. This lowerthanexpected
price hike generates income Y_{2}'. Record this point in
the inflation/income diagram, where the combination of 10% inflation
and output at Y_{2}' is marked by the upper pale blue dot.
3. Finally, let prices rise to P_{1} only, meaning an inflation
rate of 5%. Then income stands at Y_{1}' 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

SAS curve 
