Consumption and Investment Functions: One Mark Questions, Book Back Answers and Notes

About Consumption and Investment Functions

Medium ~90 min study

In Unit 3 we saw that employment depends on effective demand, \(C + I\). This unit looks at each part separately. How much of their income do households spend and how much do they save? What makes firms decide to buy new machines or build new factories?

The answer on the consumption side is Keynes's psychological law of consumption: when income rises, consumption also rises, but by less than the rise in income. The part not consumed is saved. Saving is a leakage from the spending stream, so for income to stay at a given level, investment must fill that gap. On the investment side, firms compare the expected return on a new asset, the marginal efficiency of capital, with the rate of interest.

This unit has more numbers than the earlier ones. You will be asked to find APC, MPC, APS or MPS from a small table, to calculate the multiplier from a given MPC, or to name the economist linked with the multiplier (Kahn and Keynes), the accelerator (J.M. Clark) or the super multiplier (Hicks). Practise the formulas until the arithmetic is automatic.

What you'll learn

• Calculate APC, MPC, APS and MPS from income, consumption and saving data.
• State the three propositions of Keynes's psychological law of consumption and its assumptions.
• Distinguish autonomous investment from induced investment.
• Explain how the marginal efficiency of capital and the rate of interest decide private investment.
• Work out the multiplier from a given MPC and trace how an initial investment raises income.
• Explain the accelerator, the super multiplier and how their interaction produces business cycles.

Before you start

• National income and the circular flow of income from Units 1 and 2.
• Effective demand, \(ED = Y = C + I\), from Unit 3.
• Ratios, fractions and percentages.

Consumption and Investment Functions explained

Consumption and Investment Functions Explained

Consumption Function and Its Technical Attributes

The consumption function shows how total consumption changes with income, \(C = f(Y)\). Four ratios describe it.

• Average propensity to consume: \(APC = C/Y\)
• Marginal propensity to consume: \(MPC = \Delta C / \Delta Y\)
• Average propensity to save: \(APS = S/Y\)
• Marginal propensity to save: \(MPS = \Delta S / \Delta Y\)

Income is either consumed or saved, so \(APC + APS = 1\) and \(MPC + MPS = 1\). Example: if income rises from ₹1,000 to ₹1,200 and consumption rises from ₹800 to ₹950, then MPC = 150/200 = 0.75 and MPS = 0.25.

Keynes's Psychological Law of Consumption

Keynes stated that as income increases, consumption also increases, but by a smaller amount. The law has three propositions:

1. When income increases, consumption expenditure also increases, but by a smaller amount.
2. The increased income is divided in some proportion between consumption and saving.
3. An increase in income leads to an increase in both consumption and saving.

The law holds under normal conditions, in the short run, and assumes a free capitalist economy with stable habits, tastes and income distribution.

The Investment Function

Investment here means real investment: spending on new machines, buildings and stocks, not buying shares. Autonomous investment does not depend on income or profit. It is usually undertaken by the government for public welfare, such as roads and dams. Induced investment is made by private firms for profit and rises when income and demand rise. A private firm invests when the marginal efficiency of capital, the expected rate of return on an additional unit of capital, is higher than the rate of interest.

The Investment Multiplier

The multiplier is the ratio of the final change in income to the initial change in investment, \(K = \Delta Y / \Delta I\). An initial investment becomes income for someone, who spends part of it, which becomes income for someone else, and so on. Its size depends on MPC: \(K = 1 / (1 - MPC)\). If MPC is 0.8, K = 1/0.2 = 5, so an extra ₹100 crore of investment raises income by ₹500 crore. Leakages such as saving, taxes, imports, payment of past debts and purchase of old assets reduce the multiplier.

The Accelerator and the Super Multiplier

The accelerator shows that a change in demand for consumer goods causes a larger change in demand for capital goods. The accelerator coefficient is the ratio of induced investment to the change in consumption, \(\beta = \Delta I / \Delta C\). The multiplier works from investment to income; the accelerator works from income and consumption back to investment. Hicks combined the two in the super multiplier. The interaction between multiplier and accelerator helps explain why booms and slumps in business cycles can be so sharp.

Common mistakes to avoid

• Mixing up APC and MPC. APC uses totals, C/Y; MPC uses changes, ΔC/ΔY. From the same table they usually give different numbers.
• Getting the multiplier backwards. K = 1/MPS, so a higher MPS means a smaller multiplier, and a higher MPC means a larger one.
• Saying autonomous investment rises with income. It is income inelastic; it is induced investment that responds to income.
• Treating the super multiplier as the simple multiplier. The simple multiplier includes only induced consumption; the super multiplier adds induced investment through the accelerator.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What is the difference between APC and MPC?

APC is total consumption divided by total income at a given income level, C/Y. MPC is the change in consumption divided by the change in income, ΔC/ΔY, and tells you how much of an extra rupee of income is spent.

How does Keynes's psychological law of consumption work?

As income rises, people spend more, but not the whole increase, because they save part of it. So consumption rises by less than income. This gap between income and consumption has to be filled by investment if income and employment are to be maintained.

What is the formula for the investment multiplier?

K = 1 / (1 − MPC), which is the same as K = 1 / MPS. With MPC = 0.75, K = 1/0.25 = 4. The higher the MPC, the larger the multiplier.

What is the difference between autonomous and induced investment?

Autonomous investment does not depend on income and is usually made by the government for welfare, for example building roads or dams. Induced investment is made by private firms for profit and increases when income and demand increase.

What is the accelerator principle?

It says that an increase in demand for consumer goods leads to a proportionately larger increase in demand for the capital goods needed to make them. The idea is associated with J.M. Clark, and it explains why investment swings more widely than consumption.

What are the leakages of the multiplier?

Leakages are parts of extra income that do not go back into spending on domestic output. The textbook examples include saving, hoarding, taxes, payment of past debts, purchase of existing assets and spending on imports. Each one makes the multiplier smaller.

What is the super multiplier?

It is J.R. Hicks's combination of the investment multiplier and the accelerator. An initial rise in autonomous investment raises income through the multiplier, and the rise in income brings induced investment through the accelerator, so the total effect on income is larger than the simple multiplier alone.