The aggregate supply & aggregate demand model (AS-AD) is nice because it’s flexible and clear. Often professors will teach it in levels. That is, they teach it with the level of output on one axis, and the price level on the other axis. This presentation is convenient for the equation of exchange, which can be arranged to reflect that aggregate demand (AD) is a hyperbola in (Y, P) space. Graphed below is the AD curve in 2019Q4 and in 2020Q2 using real GDP, NGDP, and the GDP price deflator.
The textbook that I use for Principles of Macroeconomics, instead places inflation (π) on the vertical axis while keeping the level of output on the horizontal axis. The authors motivate the downward slope by asserting that there is a policy reaction function for the Federal Reserve. When people observe high rates of inflation, state the authors, they know that the Fed will increase interest rates and reduce output. Personally, I find this reasoning to be inadequate because it makes a fundamental feature of the AS-AD model – downward sloping demand – contingent on policy context.
At the same time, I do think that it can be useful to put inflation on the vertical axis. Afterall, individuals are forward looking. We expect positive inflation because that’s what has happened previously, and we tend to be correct. So, I tell my students that “for our purposes”, placing inflation on the vertical axis is fine. I tell them that, when they take intermediate macro, they’ll want to express both axes as rates of change. I usually say this, and then go about my business of teaching principles.
But, what does it look like when we do graph in percent-change space?
First, some clear notation.
It follows that:
Therefore, the percent change in AD is:
Solving for π allows us to easily plot the AD curve in (r,π) space.
The distance between the two time periods is irrelevant for the math or the graph. If they are more than one period apart from one another, then the percent change variables can be subscripted with a ‘c’ in order to denote cumulative percent change. Graphed below is the same information for 2019Q4 and 2020Q2 as above, but in terms of percent.
What does this exercise do for us? It’s important to first acknowledge what it doesn’t do for us. Namely, we don’t know the steepness of the SRAS curve. The above evidence is consistent with a relatively flat SRAS that doesn’t move at all. Unfortunately, it is also consistent with a Vertical SRAS that declines dramatically. Of course, the above only reflects an average for the entire economy. We know that service and non-durable consumption were composed by a variety of supply-side responses to the covid-19 recession. Regardless, we can see that from peak to trough, the Covid recession was overwhelmingly an AD shock.
More importantly for students, we can see that the AS-AD model still works in growth-rate space. Demand still slopes down even when we take into account that people expect percent changes in prices, output, and total spending. Neatly, the AS & AD curves and their intersections all still make sense in this space. Yes, the graph space is more conceptually complicated and the math is harder, but the same fundamental message is communicated.
Therefore, we don’t need to fret about price level being on the vertical axis. It does the same job for us pedagogically as does the more complicated percent-change model. For me, the fact that the level and percent-change versions are so consistent makes the mixed model of inflation and output level in (Y, π) space untenable. It introduces unnecessary hand-waiving and assumptions about a policy response function that only serve to confuse and mislead students.