This is for equation reference only, for example, when you’re lost as hell during lectures! I will make real cheat sheets that explain what things are.

Calculating GDP

\[Y = C_a + I_a + G_a + NX_a\]


Simple Short-Run Model

Equilibrium GDP \(Y_e\) occurs when \(Y_e = AE\), the aggregate expenditure.

We have a few basic metrics:

All our models will be linear, that is, \(AE = A + zY\). This should make it easy to identify \(A\) and \(z\). The term with no \(Y\)-dependency is called autonomous and with is called induced.

Assuming linearity also gives us the really nice equation \(Y_e = \frac{A}{1-z}\).

This also gives a relation for change in marginal propensity to spend: \(Y_{e_2} = \frac{1-z_1}{1-z_2}Y_{e_1}\).

Super Simple Model

In our simple model, we ignore government and trade, so that we can say

\(\begin{align} AE & = C + I \\ & = \underbrace{(a + I_0)}_{A} + \underbrace{(b)}_zY \end{align}\)


Adding Government

We now add government expenditure.

\(\begin{align} AE & = C + I + G \\ & = \underbrace{(a + I_0 - bT_0 + G_0)}_{A} + \underbrace{b(1-t)}_{z}Y \end{align}\)

where the only changes from above are that

Adding Trade

Adding the most annoying thing of all: the rest of the world.

\(\begin{align} AE & = C + I + G + NX \\ & = \underbrace{(a + I_0 - bT_0 + G_0 + X_0)}_{A} + \underbrace{(b(1-t) - m)}_{z}Y \end{align}\)

where the variables are the same except

Government Policy

The budget balance is \(T - G\) where \(T\) is net tax revenue and \(G\) is government expenditure.