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
 Y = C + I + G
 C = C0 + c(Y-T)
 T = T0 + tY
Equation  says that total output is the sum of purchases by consumers, businesses (for investment), and the government. Equation  says that consumption depends on disposable income, which is income after taxes (Y-T). Equation  says that taxes are a linear function of income, with a slope of t and an intercept of T0.
In equations  - , what are the endogenous variables? What are the exogenous variables? What are the coefficients? Which equations are identities? Which equations are behavioral equations?
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.
Suppose that, in equation , investment is $2.0 trillion instead of $1.8 trillion. How does that change the solution to the three equations? (hint: substitute equations  into equation , then substitute this equation into equation , using $2.0 instead of $1.8)
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.
Suppose that in equation [1'], investment is $1.8 trillion and government spending is $2.2 trillion. What are the new values of Y, C, and T? What is the government deficit? Does the government deficit increase by more, less, or the same amount as the increase in government spending? Explain why this occurs.
Suppose that the government cuts taxes, by changing T0 to -$0.94. What does this do to Y, C, T, and the government deficit?
Suppose that the government cuts taxes by changing t from 0.2 to 0.18. What does this do to Y, C, T, and the government deficit?