Macroeconomics/Aggregate Expenditures

Introduction
In this chapter, we will discuss. Its definition is as follows:

To be more precise, AE means the following:

We will define in the following. For other expenditures, we have defined them in the chapter about GDP, and they have the same definitions here.

We will examine $$C,I^p,G,NX$$ in more details (more than their definitions) one by one in the following sections.

Consumption
Consumption has two components, namely consumption ($$\overline C$$) and  consumption.

Before defining induced consumption, let us define a term which will be used in its definition.

Another similar definition is (MPS).

Then, we can use MPC to define induced consumption.

Then, we can express the consumption function as follows: $$ C=\overline C+MPC\cdot Y_d=f(Y_d), $$ which is a function in $$Y_d$$, and so the of consumption function is MPC (which is positive, and so $$Y_d\uparrow\Rightarrow C\uparrow$$), and  of consumption function is $$\overline C$$ (which is positive).

Then, we will discuss some important factors that affect $$C$$.

Planned investment
$$I^p$$ is, which does not vary with $$Y$$. The following are some important factors affecting $$I^p$$ (which does not include $$Y$$).

Government purchases
Assume $$G$$ is solely determined by the government, and therefore $$G$$ is. So, its change depends on how the government changes $$G$$.

Net exports
Change in $$NX$$ is mainly affected by the between domestic country and foreign countries.

AE function
We can plot the AE aginst GDP graph as follows:

The blue line can be interpreted as the $$AE$$ curve with $$I^p=G=NX=0$$, i.e. the consumption function $$C=\overline C+(MPC)Y$$.

Recall that $$AE+C+I^p+G+NX$$. Since $$I^p,G$$ are, and $$NX$$ does not vary, ceteris paribus (the comparison between domestic country and foreign countries gives same results), we may denote them as $$\overline{I^p},\overline G,\overline{NX}$$, to emphasize their invariance (they are constants which do not vary with $$Y$$).

Then, we can derive the $$AE$$ function (in $$Y$$) by adding back $$\overline{I^p},\overline G$$ and $$\overline{NX}$$ to the consumption function (which shifts the blue line by $$\overline{I^p}+\overline G+\overline{NX}$$ parallelly, since the $$y$$-intercept changes from $$\overline C$$ to $$\overline C+\overline{I^p}+\overline G+\overline{NX}$$): $$ AE=\underbrace{\overline C+MPC\cdot Y}_C+\overline{I^p}+\overline G+\overline{NX}=MPC\cdot Y+\text{constant}=f(Y) $$

We can observe that, at the region the Keynesian cross, $$YAE$$ .

Also, we can see from the $$AE$$ function that, its slope is $$MPC$$, which is the same as that of consumption function.

Adjustment to macroeconomic equilibrium
Sometimes, the economy is at macroeconomic equilibrium, i.e. $$AE>Y$$ or $$AEY\Rightarrow \cancel{C+}I^p\cancel{+G+NX}>\cancel {C+}I\cancel{+G+NX}\Rightarrow I^p>I\Rightarrow I-\Delta inv^{unp}>I\Rightarrow \Delta inv^{unp}<0$$, there is unplanned in inventories. In view of this, firms should refill the inventories by $$\uparrow$$ production $$\Rightarrow I^p\uparrow\Rightarrow Y \uparrow$$, until reaching $$Y=AE$$.

On the other hand, since $$AE<Y\Rightarrow \cancel{C+}I^p\cancel{+G+NX}<\cancel {C+}I\cancel{+G+NX}\Rightarrow I^p<I\Rightarrow I-\Delta inv^{unp}<I\Rightarrow \Delta inv^{unp}<0$$, there is unplanned in inventories. In view of this, firms should cut their production by $$\downarrow$$ production $$\Rightarrow I^p\downarrow\Rightarrow Y \downarrow$$, until reaching $$Y=AE$$.

After reaching the macroeconomic equilibrium, i.e. $$Y=AE\Rightarrow\cancel{C+}I^p\cancel{+G+NX}=\cancel {C+}I\cancel{+G+NX}\Rightarrow I^p=I \Rightarrow I-\Delta inv^{unp}=I\Rightarrow \Delta inv^{unp}=0,$$ and thus there is no unplanned change in inventories, and so $$\overline Y$$ ceteris paribus.

Therefore, eventually, we will reach macroeconomic equilibrium, and macroeconomic equilibrium can occur at arbitrary point at the Keynesian cross.

Recall the economy has a level of potential GDP ($$Y^p$$), but macroeconomic equilibrium may not be located at the point at which $$AE=Y^p$$. Macroeconomic equilibrium is at a point at which $$AE=Y<(>)Y^p\Rightarrow\text{unemployment rate }(u)>(<)\text{ natural unemployment rate }(\overline u)$$.

Also, at macroeconomic equilibrium, $$ Y=AE\Rightarrow Y=MPC\cdot Y+\overline C+\overline{I^p}+\overline G+\overline{NX}\Rightarrow (1-MPC)Y=\overline C+\overline{I^p}+\overline G+\overline{NX} \Rightarrow Y=\frac{\overline C+\overline{I^p}+\overline G+\overline{NX}}{1-MPC} $$

The multiplier effect
In view of the above equation at macroeonomic equilibrium, when the expenditure (variables with a bar on top of it) changes by $$1$$, $$Y$$ changes by $$\frac{1}{1-MPC}$$ in the same direction. Since $$0<MPC\le 1$$, this number is greater than one, and we give this number a name, namely :

The paradox of thrift
Recall that in closed economy in which $$NX=0$$, $$S=I$$. This implies $$S$$ is the key to long run (LR) growth (since $$I$$ is the key to LR growth). Thus, it has a positive effect on the economy.

However, in the short run (SR), $$S\uparrow\Rightarrow \text{private saving}(S_{\text{private}})\uparrow\Rightarrow C\downarrow\Rightarrow Y\downarrow\Rightarrow C\downarrow\cdots$$. This can push the economy into, and thus have a negative effect on the economy.

Here is the paradox, since what appears to be favourable in LR may be unfavourable in SR.

However, the existence of this paradox is questionable, since it is argued that $$S\uparrow\Rightarrow \text{loanable fund supply}\searrow(\&\;\overline{\text{loanable fund demand}})\Rightarrow r\downarrow\Rightarrow I\uparrow$$, which offset the $$\downarrow$$ in $$C$$.

Aggregate demand (AD) curve
In the following, we will loosen the assumption that $$\overline P$$. After that, we can use the AE curve to derive aggregate demand (AD) curve.

$$P$$ affects AE as in the following proposition:

Since at macroecnomic equilibrium, $$Y=AE$$, $$P\uparrow(\downarrow)\Rightarrow AE\searrow(\nwarrow)\Rightarrow Y\downarrow(\uparrow)$$, and thus we have established the (inverse) relationship between $$P$$ and $$Y$$ at macroeconomic equilibrium. We can assume that the economy is at macroecnomic equilibrium unless otherwise specified, since it is likely that the economy is at macroeconomic equilibrium, considering that the economy will adjust to the macroeconomic equilibrium eventually.

This inverse relationship between $$P$$ and $$Y$$ is reflected by AD curve.

Illustration of (a portion of) the downward sloping AD curve: P AD curve is essential in the AD-AS model, which will be discussed later.
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