Lecture 12: Aggregate Demand

Mingze Huang

2021-08-05

Aggregate Demand

Recall the policy change effect in IS-LM model, the framework mostly focus on demand side analysis. It enlightens us that we may derive some form of Aggregate Demand (AD) curve from IS-LM model:

\[ \begin{cases} (1 - c_{1})Y^{r} = c_{0}-c_{1}T+I(i)+G & \text{IS relation}\\ \frac{M}{P}=Y^{r}\cdot L(i) & \text{LM relation} \end{cases} \] Since we’ve already got Aggregate Supply (AS) curve on price \(P\) and output \(Y^{r}\). Now our goal is to make an Aggregate Demand (AD) curve on price \(P\) and output \(Y^{r}\) to put on the graph.

Aggregate Demand

(Not required) One way to git rid of \(i\) is to do hardcore mathematical substitution: Rearrange IS relation: \[ I(i) = (1 - c_{1})Y^{r}+c_{1}T-c_{0}-G \] Solving \(i\) by taking inverse function of \(I(\cdot)\): \[ i = I^{-1}((1 - c_{1})Y^{r}+c_{1}T-c_{0}-G) \] Plug it into LM relation: \[ \frac{M}{P}=Y^{r}\cdot L(I^{-1}((1 - c_{1})Y^{r}+c_{1}T-c_{0}-G)) \]

Aggregate Demand

In summary, the higher \(Y^{r}\), the higher the right hand side of equation since both \(Y^{r}\) and \(L(I^{-1}((1 - c_{1})Y^{r}+c_{1}T-c_{0}-G))\) go higher. To hold the equality, price \(P\) should be lower since nominal money supply \(M\) is given.

(Required) Another way to derive the Aggregate Demand (AD) curve is more intuitive:

This curve called Aggregate Demand (AD) curve since it comes from demand side ajustment in IS-LM model.

Aggregate Demand

Aggregate Demand

The intuition goes into IS-LM model:

Aggregate Demand