In this lesson, we will add government spending and taxes to our system of equations. We will treat government spending, G, as fixed, like business investment. We will have tax revenues, T, depend on income, Y. Overall, we have

[1] Y = C + I + G
[2] C = C₀ + c(Y-T)
[3] T = T₀ + tY

Equation [1] says that total output is the sum of purchases by consumers, businesses (for investment), and the government. Equation [2] says that consumption depends on disposable income, which is income after taxes (Y-T). Equation [3] says that taxes are a linear function of income, with a slope of t and an intercept of T₀.

A numerical example of this system might be

[1'] Y = C + I + G = C + $1.8 + $1.7 = $10.2 trillion
[2'] C = $1.54 + (0.6)(Y-T) = $1.54 + (0.6)($10.2 - $1.6) = $6.7 trillion
[3'] T = -$0.44 + 0.2Y = -$0.44 + 0.2($10.2) = $1.6 trillion

In this example, all three equations are satisfied at the values shown.

We saw that with business investment of $1.8 billion, government spending of $1.7 billion, and the intercept and slope of the tax function of -$0.44 and 0.2, respectively, the value of output will be $10.2 trillion. What if potential output is higher, say $12.0 trillion? In that case, the economy would be operating way below potential, in a deep recession, with high unemployment.

Keynes' insight was that the government could use fiscal policy (its choices of G, T₀ and t in our model) to boost demand and bring output to potential. Prior to Keynes, fiscal policy consisted primarily of finding ways to raise money during war time and to pay off debts and achieve budget balance at other times. Note that in equations [1'] - [3'], the government budget surplus (T-G) is -$0.1 billion, which means that the government runs a deficit.