Finding equilibrium GDP

Dr. Barry Haworth
University of Louisville
Department of Economics
Economics 202

Is There an Output Gap?

To determine whether there's an output gap we'll need to calculate the amount of equilibrium GDP and then compare that level of GDP to the amount of potential GDP.

We'll begin by considering a simple, hypothetical economy. Assume that, within this simple economy, the price level remains constant and that various other conditions exist which allow us to express aggregate expenditures in terms of a series of equations. Let's look at those equations, ask what they tell us, and then proceed to find how much real GDP must be produced in order to satisfy the demands of this macroeconomy (i.e. we'll find equilibrium GDP, or Y*)

The various expenditure categories within the economy, as well as potential real GDP, are:

C = 0.75(DI) + 400	(C = consumption expenditure, DI = disposable income)
I = 1200	(I = investment expenditure)
G = 1600	(G = government expenditure)
X = 500	(X = exports)
M = 600	(M = imports)
T = 1200	(T = tax revenue)
Y_p = 9000	(Y_p = potential real GDP)

What do these equations mean?

The consumption equation, C = 0.75(DI) + 400, tells us that the marginal propensity to consume is 0.75. That is, every $1 increase in disposable income leads to a 75 cent increase in consumption spending. This provides us with information about how quickly consumers spend any available income. A greater MPC implies that consumers are likely to spend more now, rather than save.

The investment equation, I = 1200, tells us that investment spending (which generally includes expenditure on new capital and unintended changes in inventories) does not vary with changes in variables like GDP and interest rates. That is, if the economy begins to climb out of recession, investors don’t respond by investing more. In reality, this assumption is probably a little restrictive and unrealistic.

The government spending equation, G = 1600, also says that government spending doesn’t vary with changes in GDP, interest rates, etc. Again, this is not very realistic, because this equation implies that the government won’t automatically spend more if the economy goes into recession.

The exports, X = 500, and imports, M = 600, equations are similar to what we’ve just discussed. Neither of these varies with changes in GDP or interest rates, which is not very likely.

The tax equation, T = 1200, shows that there are no income taxes. That is, tax revenues don’t vary with changes in GDP. If we compare the tax and government equations, then we can see that there’s a government budget deficit. In other words, we can see that G > T.

The Potential GDP equation, Y_p = 9000, reveals how much GDP will be at Full Employment. This isn't an expenditure, but rather is a reference point that we can use after solving for equilibrium GDP (Y*) to determine whether an output gap exists or not.

Our first step is to set these equations up in a way that allows us to calculate equilibrium real GDP. This requires finding where aggregate expenditures (AE) equal income (Y). That is, we need to determine where AE = Y. Those steps are worked out below.

First, we must express AE as the sum of all expenditures from the list of equations above. This implies writing out AE as AE = C + I + G + X - M, and then substituting everything into its appropriate spot in that equation.

AE = C + I + G + X - M

AE = [0.75(DI) + 400] + 1200 + 1600 + 500 - 600

Remembering that DI = Y - T, where Y = real GDP, we have:

AE = [0.75(Y - T) + 400] + 1200 + 1600 + 500 - 600

AE = [0.75(Y - 1200) + 400] + 1200 + 1600 + 500 – 600

AE = 0.75Y + 2200

This equation tells us how expenditure changes when people’s income changes. For example, if we wanted to forecast how much (aggregate) expenditure would occur when GDP is $20,000, then we can just plug $20,000 into that equation for Y and solve. The answer would be that AE = $15,000 when Y = $20,000.

Remember, however, that our goal is to find the point where this economy is at equilibrium. We will then compare the GDP that occurs at equilibrium to the GDP we get at full employment (i.e. Potential GDP) and ask how to close any output gap that might exist.

When an economy is in equilibrium, the overall amount of expenditures will equal the total value of output produced (i.e. final goods and services produced in a given period). Within the AE model, the model we’re working with here, equilibrium would occur when AE = Y. Therefore, we only need to substitute Y for AE in the equation above.

Y = 0.75Y + 2200

We now must ask what Y (real GDP) must be in order for this equation to be true. That is, what must Y be in order for Y to equal 0.75Y + 2200? We can use algebra to solve for that answer as follows:

Subtract 0.75Y from both sides and simplify

Y - 0.75Y = 0.75Y - 0.75Y + 2200

0.25Y = 2200

Divide both sides by 0.25 and simplify

0.25Y/0.25 = 2200/0.25

Y = 8800

That is, equilibrium real GDP (Y*) is equal to 8800. Given that Potential GDP is equal to 9000, we calculate the amount of the output gap as the difference between equilibrium GDP and potential GDP. In doing so, we find that there is an output gap of 200 (i.e. Y_p - Y* = 200).

An equally interesting question is to ask how we close this recessionary gap? That topic is the subject of the next handout.