Macroeconomics/Macroeconomic Equilibrium in the Short Run and the Long Run

Macroecnomic equilibrium in AD-AS model

After examining the AD, SRAS and LRAS curves in AD-AS model, we will examine their Template:Colored em in this chapter. Macroeconomic equilibrium in both SR and LR is located at the intersection of curves, at which $Y\text{ demanded}=Y\text{ supplied}=Y=AE$

• In SR, the SR equilibrium is the intersection point between SRAS and AD curves, but not LRAS curve.
• In LR, the LR equilibrium is the intersection point between LRAS, SRAS and AD curves.

Illustration of an intersection point between SRAS and AD curves, but not LRAS curve:

P
|  LRAS
|   |   /
|   |\ / SRAS
|   | *
|   |/ \
|   |   \  AD
|  /|    \
|---------------- Y

Illustration of an intersection point between LRAS, SRAS and AD curves:

P
|    LRAS
|     |
|    \|/ SRAS
|     *
|    /|\
|   / | \  AD
|  /  |  \
|---------------- Y

Sometimes, there are more than one intersection points when there are three curves, and not all points are macroeconomic equilibrium: e.g. (3 intersection points)

P
|  LRAS
|  \|    /
|   *   /
|   |\ / SRAS
|   | * <----- SR macroeconomic equilibrium
|   |/ \
|   *   \  AD
|  /|    \
|---------------- Y

SR macroeconomic equilibrium

SR macroeconomic equilibrium occurs at which AD and SRAS curves intersect, and does not last long, since it will eventually becomes LR macroeconomic equilibrium by some adjustments of curve(s) (usually SRAS curves without intervention, we may also use some policies to facilitate the adjustment).

Suppose the economy is at LR macroeconomic equilibrium.

P
|    LRAS
|     |
|    \|/ SRAS
|     *
|    /|\
|   / | \  AD
|  /  |  \
|---------------- Y

If AD or SRAS shifts, e.g. SRAS $\searrow$ due to positive supply shock (say, a lot of new oil is discovered):

    P (GDP deflator, 2022=100)
    |    LRAS
    |     | SRAS_0
    |    \|/     
110 |-----*     / SRAS_1
    |    / \   / 
    |   /   \ /
105 |------- *  AD
    | /    /   \
    |---------------- Y (trillion 2022 USD)
         30  32

We can see from the graph that $P\downarrow$ and $Y\uparrow$. Also, original LR macroeconomic equilibrium is located at the point $(Y,P)=(30,110)$, and SR macroeconomic equilibrium is located at the point $(Y,P)=(32,105)$.

Similarly, SR equilibrium can appear also when one or more of AD, SRAS and LRAS curves shift. E.g., $AD\nearrow \mathrm{\&}SRAS\nwarrow \mathrm{\&}LRAS\to$:

P
| LRAS_0  LRAS_1
|     |    |  
|     |  /SRAS_1 
|   \ | /  |/SRAS_0
| \  \|/  /|  
|  \  *<----- SR equilibrium (although located at OLD LRAS)
|   / |\/  | 
|  / \|/\  |
| /   *  \ |    
|/   /|\  \|    
|   / | \  \       
|  /  |  \ |\     
|       AD_0  AD_1
|---------------- Y

Then, we will discuss how SR macroeconomic equilibrium will eventually become LR macroeconomic through some adjustments (without intervention)

Adjustment from SR macroeconomic equilibrium to LR macroeconomic equilibrium

For simplicity, we assume there is no inflation ($\pi =0$), and $P=P^e=100$ (in GDP deflator, which equals 100 in 2022) from now on. Also assume that $\overline{LRAS}$ Template:Colored em, i.e. the AD-AS model in this section is Template:Colored em.

Since SR macroeconomic equilibrium is located at a point at which $Y\ne Y^p$, we can see that SR macroeconomic equilibrium can only be located at a point at wich either $Y<Y^p$ or $Y>Y^p$.

$Y>Y^p$:

P
|  LRAS
|   |   /
|   |\ / SRAS
|   | *
|   |/ \
|   |   \  AD
|  /|    \
|---------------- Y
   Y^p Y

$Y<Y^p$:

P
|       
|   \   | LRAS
|    \ /|    
|     * |
|SRAS/ \|
|   /   |  AD
|  /    |\
|---------------- Y
      Y Y^p

We consider these two cases one by one in the following. Template:Colored proposition

Proof. $Y>(<)Y^p\Rightarrow u<(>)\bar{u}\Rightarrow \text{worker's bargaining power}\downarrow (\uparrow )\Rightarrow w^n\text{ demanded}\downarrow (\uparrow )\Rightarrow \text{production cost}\downarrow (\uparrow )\Rightarrow \mathrm{\Pi }\uparrow (\downarrow )\Rightarrow SRAS\nwarrow (\searrow )$

($u$: unemployment rate, $\bar{u}$: natural unemployment rate,$\mathrm{\Pi }$: profitability) $◻$

Automatic adjustment ($\nwarrow$ shift from $SRA{S}_0$ to $SRA{S}_1$) when $Y>Y^p$:

P
|  LRAS/      
|   | / SRAS_1
|   |/
|   *   /
|  /|\ / SRAS_0
| / | *
|/  |/ \
|   |   \  AD
|  /|    \
|---------------- Y
   Y^p Y

Automatic adjustment ($\searrow$ shift from $SRA{S}_0$ to $SRA{S}_1$) when $Y<Y^p$:

P
|      LRAS
|       |/ SRAS_0
|   \   /     
|    \ /|  / SRAS_1 
|     * | /
|SRAS/ \|/
|   /   *  AD
|  /   /|\
|---------------- Y
      Y Y^p

LR macroeconomic equilibrium

In this section, we will loosen the assumption that $\overline{LRAS}$, i.e. the AD-AS model in this section is Template:Colored em.

The automatic adjustment process is similar in the dynamic model, except that when LRAS shifts, the new LR equilibrium locates at the intersection between new AD, new SRAS, and Template:Colored em curves (not the old one).

For example, automatic adjustment (large $\nwarrow$ shift from $SRA{S}_0$ to $SRA{S}_1$) when $Y>Y^p$ (with $\leftarrow$ shift from $LRA{S}_0$ to $LRA{S}_1$ initially):

P
|      / SRAS_1
|LRAS_1
|\ | /  | LRAS_0
| \|/   |
|  *    |
| /|\   |     
|/ | \  |         
|  |  \ |         
|  |   \| 
|  |    \   /
|  |    |\ / SRAS_0
|  |    | *
|  |    |/ \
|  |    |   \  AD
|  |   /|    \
|---------------- Y
  Y^p     Y

Automatic adjustment ($\searrow$ shift from $SRA{S}_0$ to $SRA{S}_1$) when $Y<Y^p$ (with $\to$ shift from $LRA{S}_0$ to $LRA{S}_1$ initially, and there is LR equilibrium at the beginning, but it becomes SR equilibrium after $LRAS\to$):

P
|      / SRAS_0
|LRAS_0
|\ | /  | LRAS_1
| \|/   |
|  *    |
| /|\   |     
|/ | \  |  / SRAS_1      
|  |  \ | /       
|  |   \|/
|  |    *    
|  |   /|\  
|  |  / | \
|  | /  |  \
|  |    |   \  AD
|  |    |    \
|---------------- Y
   Y    Y^p