Kaldor's Business Cycle

Linear KBC

• $I=f(Y,\underset{-}{K})$ This happens because if the capital is already high, investments will reduce due to depreciation considerations as the potential returns have reduced.
• $S=f(Y,\underset{+}{K})$ This happens because if we have more capital, economy is booming, more production, less demand, lesser prices, can spend less to consume more and also save more.

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When MPS > MPI, we have a stable equilibrium and when MPI > MPS, we have an unstable equilibrium. For a stable equilibrium, the investment demand function $I$ should intersect the savings supply function $S$ from above thus figure A gives us stable equilibrium and figure B gives us unstable equilibrium.

Limitation

The limitation of this approach is that both savings and investment functions are linear whereas for business cycles we require non-linearity

Non-linear KBC

In non-linear Kaldor’s BC, there are three levels of income - low, normal and high. Both MPI and MPS will not be the same at all three levels.

MPI¹ will be relatively low, at low and high levels of income. This is due to income inelasticity².

The MPS will be relatively high at low and high levels of income. This is because of income elasticity.

Income Level	MPI	MPS
Low	Low	High
Normal	Normal	Normal
High	Low	High

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Combining the two non-linear investment and savings schedules or functions gives us multiple equilibria, i.e., we have a stable equilibrium at both point $A$ and point $C$, but we have unstable equilibrium at point $B$.

Limitation

The limitation of this approach is that if you are point $A$, you remain at point $A$. If you are point $C$, you remain at point $C$.

But, if you are at point $B$, you move towards point $A$ or point $B$ depending on which side of $B$ you are on.

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As the time progresses, the investments and the saving curves, continue on their migrations, induced by capital accumulation, and as the time progresses, the investments and the saving curves, continue on their migrations, induced by capital decumulation.

• Both $Y_A$ and $Y_C$ are short-term equilibrium levels of output.
• The output fluctuation happens between $Y_A$ and $Y_C$.

Footnotes

1. Slope of investment demand function ↩

2. non responsive ↩