Equilibrium Level of Income

Mental Model

Think of $i+g$ as sales and thereby consumption, and $s+t$ as savings.

Determination of Equilibrium Level of Income

Continuing from our previous discussion in The Income Expenditure Model

$$\overline{i}+\Delta inv+g=s+t$$

If $\Delta inv=0$, $I=\overline{i}$

$$\overline{i}+g=s(y-t(y))+t(y)\text{\hspace{1em}(12)}$$

The moment $\overline{i}+g=s+t$, it is the stage where economy will be at equilibrium level of income.

It is important that

$$y\to (s+t)=(i+g)$$

If the savings component is greater than investments¹

$$s+t>i+g⟹\Delta inv>0⟹i\downarrow -e\downarrow -y\downarrow$$

If the investments component is greater than savings²

$$s+t<i+g⟹\Delta inv>0⟹i\uparrow -e\uparrow -y\uparrow$$

Explanation of the inventory mechanism

• When $\Delta inv=0$, there is no tendency for the income or output to change if income is higher than the equilibrium level of income $s+t$ would exceed $i+g$ ($s+t>i+g$) which means the sales would be lower due to fall in consumption and there by there will be unintended accumulation of inventory $\Delta inv>0$.
• Here, the sellers will cut the orders to reduce the unwanted inventory stock and so the firms would cut down their production which would reduce employment and thereby the income starts falling. This will continue to fall until the income falls enough to bring $s+t$ down to $i+g$ and reduce $\Delta inv\to 0$.
• $i+g>s+t$ which means sales will be higher whereas demand and consumption increase and thus there will be unintended inventory shortage $\Delta inv<0$.³
• Here, the seller will increase orders, to reduce the inventory shortage and so the firms would increase their production, which would increase employment and thereby income starts rising. Income continues to rise till it increases $\Delta inv\to 0$.

Stability of Equilibrium Level of Income

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• $(s+t)$ has a positive slope and $(i+g)$ are independent of income, thus it is parallel to $x$-axis
• When $(s+t)=(i+g)$, the level of income determined is at $Y_E$. It is considered as equilibrium level of income.
• This equilibrium level of income is a stable one if there are no outside forces which causes the system to move away from the equilibrium.
• To the left of $Y_E$ say at $Y_1$, $(s+t)<(i+g)$, the firms will eventually increase the investment which will rise the level of income.
• To get the right of $Y_E$ say at $Y_0$, $(s+t)>(i+g)$ the firms will eventually cut down the production leading to fall in income towards $Y_E$. To conclude any disturbance in $Y$, moving away from $Y_E$ will be followed by a movement back toward $Y_E$ through the inventory mechanism. At $Y_E$ the rate of change is $0$, which means stable equilibrium.

Shift in Savings Function

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Increase in savings would shift the $(s+t)$ function from $(s_0+t)\to (s_1+t)$. This leads to a situation $(s_1+t)>(i+g)$ where $\Delta inv>0$.Thus there is then a cutdown in investment and production which leads to reduced employment and thus income falls till $Y_1$. Savings go back to original level.

Paradox of Thrift

One might argue that they can increase savings, but it will eventually lead to further reduction of savings from the initial level.

Suppose the savings increase $20\%\to 30\%$ due to some exogenous reason. Paradox of thrift incrases

• When the savings rate goes upto $30\%$ but the saving volume decreases in economy.
• $i+g$ depends on $y$. (unlike the previous case)

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• Change in assumption that $i+g$ is an increasing function of $y$.
• Increase in savings rate $s_0\to s_1$ not only causes fall in income from $y_0\to y_1$. But also reduces the realized $(s+t)$ i.e., from $(s_0+t)\to (s_1+t)$.
• Thus increase in the desire to save can lead to ultimately decrease in the realized saving $(s+t)$. This is referred to as Paradox of Thrift.

Footnotes

1. Why? ↩

2. Why? ↩

3. Think of $i$ as sales ↩