Someone asked me to explain the difference between real GDP, potential real GDP and Effective demand. They also asked me to explain the UT index and the output gap. They wanted to know how it all fits together. So I want to share my answer here...

You start with real GDP and potential real GDP. The difference between them is the output gap as we all know. However, potential real GDP always marks the center of the business cycle. That is key.

And the center of the business cycle is reflected in the variable effective labor share. The variable that then revolves around effective labor share is capacity utilization. These two variable determine where potential real GDP is in relation to real GDP. Here is the equation for potential real GDP.

Potential real GDP = real GDP - m * (cu - els)/els

m = amplitude constant for business cycle... cu = capacity utilization... els = effective labor share

Now you add in effective demand. The best way to visualize effective demand is as the upper limit of the business cycle.

Real GDP will rise above potential real GDP and eventually hit the upper limit of the business cycle when it hits effective demand.

All 3 together will give you sufficient coordinates to tell exactly where you are in the business cycle.

The difference between real GDP and effective demand is the UT index.

The difference between real GDP and potential real GDP is the output gap.

I made a graph to visualize this. On the y-axis is the UT index. On the x-axis is the output gap. You can see the perfection of the business cycle just pop out. It is the perfect graph to locate where you are in the business cycle. (data is from 1967 to 2012)

The vertical brown line marks the center of the business cycle, where capacity utilization equals effective labor share. To the right of center is the inflationary gap where capacity utilization is more than effective labor share. To the left is the recessionary gap where capacity utilization is below effective labor share. (The x-axis shows where real GDP is in relation to potential real GDP.)

The y-axis is the UT index which shows where real GDP is in relation to effective demand. The UT index simply measures the difference in % terms between effective demand and real GDP. When the UT index goes to zero, you reach the effective demand limit.

Thus, with just 2 variables, capacity utilization and effective labor share, you can locate where you are in the business cycle in relation to its center and to its top limit. Let's do an example...

Take capacity utilization = 81% and effective labor share = 84%.

The x-axis point is...

x = (cu - els)/els = (0.81 - 0.84)/0.84 = -3.6%

You plug 3.6% into the equation for the trend line on the graph, and you get...

UT index = -0.92 * -0.036 + 0.05 = 8.3%

Thus we know approximately that real GDP is 3.6% into the recessionary gap, and 8.3% below effective demand.

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