Determination of Income and Employment

Written and reviewed by Devendra Dubey, Mathematics & Commerce faculty at UniDrill (M.Sc. Mathematics, Osmania University · 10 years teaching). Based on NCERT Economics Class XII (Introductory Macroeconomics), Chapter 4.

A warehouse full of unsold goods: what happens next?

Picture a country whose factories made more than people wanted to buy. Goods pile up in warehouses. Managers cut production. Workers are laid off. Their lower incomes reduce spending, so sales fall again. Now picture the opposite: shelves are bare, orders exceed stock, and factories hire more workers whose wages create further demand.

This chapter turns that story into a model. It answers two questions. What decides the level of a country's income and output? And why does a small change in spending cause a much larger change in income?

How the model works: hold everything else equal

Macroeconomics cannot track every variable at once. So when it explains one thing, it holds the rest constant. This is ceteris paribus, "other things remaining equal", like solving two equations by first finding $x$ in terms of $y$. This chapter determines national income taking the price of final goods and the rate of interest as fixed, in the style of John Maynard Keynes.

Why can the price level be fixed? First, the model assumes an economy with unused machines, buildings and labour. With idle resources, diminishing returns do not set in, so extra output can be produced without a rise in marginal cost and the price need not change. Second, it is a simplifying step that is relaxed later. Because supply can expand freely at the going price, output is decided entirely by demand. This is the effective demand principle.

Planned or actual? Ex ante and ex post

The same word, such as investment, can mean two different things.

Ex post values come from the accounts and obey the national income identities. Ex ante values are the plans, and they can differ from what happens. The chapter's whole analysis is about ex ante aggregate demand and supply.

The consumption function

The most important determinant of consumption is household income. The simplest consumption function assumes consumption changes at a constant rate with income:

$$C = \bar{C} + cY$$

$\bar{C}$ is autonomous consumption, which occurs even at zero income. $cY$ is induced consumption, which depends on income. The constant $c$ is the marginal propensity to consume (MPC), the change in consumption per unit change in income:

$$\text{MPC} = c = \dfrac{\Delta C}{\Delta Y}$$

MPC lies between 0 and 1. A change in consumption cannot exceed the change in income, so $c \le 1$. If people do not change spending at all when income rises, $c = 0$.

Savings and MPS. Savings is income not consumed, $S = Y - C$. The marginal propensity to save (MPS) is the change in savings per unit change in income. Since $\Delta S = \Delta Y - \Delta C$:

$$\text{MPS} = s = \dfrac{\Delta S}{\Delta Y} = 1 - c, \qquad \text{so } c + s = 1$$

Every extra rupee of income is either consumed or saved, which is why the two always add up to 1.

The book's country Imagenia has $C = 100 + 0.8Y$. Even with no income, its citizens consume ₹100 (autonomous consumption), and each extra ₹100 of income raises consumption by ₹80.

The marginal propensity stays at 0.8, but the average propensity falls as income rises. MPC is a slope; APC is a ratio at a single point.

Investment and aggregate demand

Investment is addition to the stock of physical capital (machines, buildings, roads) and the change in inventories. Investment goods are final goods, not intermediate goods, because they are not used up in one cycle of production. Investment decisions depend a lot on the market rate of interest, but for simplicity this chapter assumes firms plan the same amount each year:

$$I = \bar{I}$$

$\bar{I}$ is autonomous investment, independent of income. Other things, like availability of credit and the interest rate, can change it. Easy credit encourages investment, while a higher interest rate tends to lower it.

Aggregate demand in a two sector model. With only households and firms, ex ante aggregate demand is consumption plus investment:

$$AD = C + I = \bar{C} + \bar{I} + cY = A + cY, \qquad A = \bar{C} + \bar{I}$$

$A$ is total autonomous expenditure. Of its two parts, $\bar{C}$ is a stable subsistence level, while $\bar{I}$ fluctuates over time.

Introducing the government. Government spends $G$ and taxes $T$. Taxes reduce households' disposable income to $Y - T$, so $Y = C + I + G + c(Y - T)$. The term $G - cT$ simply adds to autonomous expenditure and changes nothing qualitatively. Because of this, the rest of the chapter ignores the government. Without indirect taxes and subsidies, GDP equals national income, so $Y$ may be called either.

Equilibrium income

At equilibrium, ex ante aggregate demand equals ex ante supply, $Y$. Supply is perfectly elastic at the fixed price, so whatever level of GDP is demanded gets produced.

$$Y = A + cY \;\Longrightarrow\; Y(1 - c) = \bar{C} + \bar{I} \;\Longrightarrow\; Y^* = \dfrac{\bar{C} + \bar{I}}{1 - c} = \dfrac{A}{1 - c}$$

Here is the logic in a table, with $C = 40 + 0.8Y$ and $I = 10$, so $AD = 50 + 0.8Y$.

If demand falls short of planned output, goods pile up as unintended accumulation of inventories, and producers cut output. If demand exceeds output, stocks run down and producers raise output. Only at ₹250 do plans match.

A warning about the equation $Y = A + cY$. The $Y$ on the left is the planned output, and the right side is planned demand. They are equal only in equilibrium. This is not the national income accounting identity, which says ex post output always equals ex post consumption plus ex post investment. When planned output exceeds planned demand, ex post investment includes the unsold goods, so the identity still holds even though the equilibrium condition does not.

Another way to see equilibrium. Since $Y = C + I$ at equilibrium, saving $S = Y - C$ equals investment. In the table's economy, $S = 250 - (40 + 200) = 10 = I$.

The curves in words

Graphs cannot be drawn here, so here is what each line looks like and why.

A change in a parameter that changes the intercept shifts a line; a change in slope swings it. This is what the book calls a parametric shift of a line.

The multiplier: why income rises by more than the spending

Start from equilibrium with $C = 40 + 0.8Y$ and $I = 10$, so $Y^ = 50/0.2 = 250$. Now raise autonomous investment to 20. Then $A = 60$ and $Y^ = 60/0.2 = 300$. A rise of 10 in spending raised income by 50.

The explanation is a chain of rounds. The extra output of ₹10 becomes income for factors. People spend $c = 0.8$ of it on consumption, so demand rises by ₹8, which needs more output of ₹8, which creates ₹8 of income. They spend 80 per cent of that, and so on.

The rounds form a geometric series with ratio 0.8, so:

$$\Delta Y = \Delta A\,\left(1 + c + c^2 + \dots\right) = \dfrac{\Delta A}{1 - c}$$

The ratio of the total increase in income to the initial rise in autonomous spending is the investment multiplier:

$$\text{Multiplier} = \dfrac{\Delta Y}{\Delta A} = \dfrac{1}{1 - c} = \dfrac{1}{s}$$

The larger the MPC, the larger the multiplier. A fall in autonomous spending works in reverse, with the same multiplier.

Beyond the textbook. For the exam: the multiplier is $1/(1 - c)$, so an MPC of 0.8 gives 5. In reality: in an actual economy, part of each extra rupee of income goes to taxes and imports as well as saving, and these leakages make the realised multiplier smaller than $1/(1 - c)$. Why it matters: the formula is a ceiling set by the simplest model, and later chapters add the government and the foreign sector, which is where leakages enter.

Pause and predict: autonomous investment rises by ₹20 crore and the MPC is 0.9. By how much does equilibrium income rise?

Check your answer: the multiplier is $1/(1 - 0.9) = 10$, so income rises by 10 × 20 = ₹200 crore. A high MPC means little leaks into saving in each round, so the effect is large.

The paradox of thrift

Suppose everyone in the economy becomes thriftier, so MPS rises and MPC falls. Surely savings should rise? The model says no: total savings stay the same or fall.

Take the same economy at $Y = 250$ with $c$ falling from 0.8 to 0.5. At the old income, demand falls by $(0.8 - 0.5) \times 250 = 75$. Stocks pile up by 75, and firms cut output by 75. That cuts income by 75, which cuts consumption by $0.5 \times 75$, and so on. The total fall in income is a series with ratio 0.5:

$$\Delta Y = \dfrac{75}{1 - 0.5} = 150, \qquad Y_2^* = \dfrac{50}{1 - 0.5} = 100$$

Savings before: $250 - (40 + 0.8 \times 250) = 10$. Savings after: $100 - (40 + 0.5 \times 100) = 10$. Total savings are unchanged, even though each person is trying to save a larger share. People saved a bigger fraction of a smaller income.

Why it happens. In equilibrium, saving equals investment. Investment is fixed at 10, so no matter how thrifty people become, the economy can only end up saving 10. The only thing that adjusts is income. The AD line swings down, and equilibrium output falls.

Beyond the textbook. For the exam: higher thrift leaves total saving unchanged or lower. In reality: the result relies on two assumptions of the model, that investment does not respond to saving and that resources are idle so that demand decides output. If more saving brought lower interest rates and so more investment, or if the economy was at full capacity, extra saving could add to investment. Why it matters: it explains why the same behaviour (saving more) can be wise for one household and still reduce income when everyone does it.

Full employment and the two gaps

Equilibrium output also determines employment, given the other factors. But equality of $Y$ and $AD$ says nothing about whether everyone who wants work has it. Full employment income is the level at which all factors of production are fully employed.

Equilibrium only means that, left alone, income will not change, even if there is unemployment.

Worked examples

Worked example: MPC and MPS from data. When income rises from ₹1,000 crore to ₹1,400 crore, consumption rises from ₹900 crore to ₹1,220 crore. Find MPC, MPS and the APC at the higher income.

Common wrong step. Dividing consumption by income at the new level, 1,220 / 1,400 = 0.87, and calling it the MPC. That is the average propensity. The marginal propensity compares changes.

Worked example: equilibrium income. In an economy, $C = 200 + 0.75Y$ and planned investment is ₹100 crore. Find equilibrium income, consumption and saving.

Common wrong step. Dividing by $c$ instead of $1 - c$: 300 / 0.75 = 400. Another slip is stopping at $A = 300$, forgetting the multiplier.

Worked example: is the economy in equilibrium? In the same economy, check income of ₹1,000 crore and of ₹1,500 crore.

At 1,500, ex post consumption is $200 + 1125 = 1325$, and ex post investment is 175, which sum to 1,500. The accounting identity holds, even though the economy is not in equilibrium.

Common wrong step. Saying that at ₹1,500 crore investment is 100 because that was planned. Ex post investment includes the unsold goods, which are counted as inventory investment.

Worked example: the multiplier. In the same economy, autonomous investment rises by ₹40 crore. Find the change in income, consumption and saving.

Round by round, the rise in income is $40 + 30 + 22.5 + \dots$, which adds up to 160.

Common wrong step. Writing $\Delta Y = 40 / 0.75 \approx 53$ or $\Delta Y = 40$. The multiplier divides by $1 - c$, which is the MPS, not by $c$, and the chain does not stop after the first round.

Worked example: the paradox of thrift. An economy has $C = 60 + 0.75Y$ and $I = 40$. People become thriftier, and MPC falls to 0.5. Find the saving before and after.

Income halves, but saving is unchanged at 40, equal to investment.

Common wrong step. Reasoning that MPS doubled from 0.25 to 0.5, so saving must double. A higher share of a smaller income gives the same total saving here, because investment, which equals saving at equilibrium, did not change.

Pause and predict: in the economy above, what is the fall in income in the first round after the MPC drops, and what is the total fall?

Check your answer: at $Y = 400$, demand falls by $(0.75 - 0.5) \times 400 = 100$ in the first round. The total fall is $100/(1 - 0.5) = 200$, from 400 to 200.

Exam traps

Formula sheet

60-second revision

Where this chapter connects

The accounting identities that always hold ex post come from National Income Accounting, and the macro vocabulary is introduced in Introduction. Investment depends on the rate of interest and the availability of credit, both set in Money and Banking, where the money multiplier is a cousin of the investment multiplier. Government spending and taxes, which this chapter folds into autonomous expenditure, are the subject of Government Budget and the Economy, and leakages through imports appear in Open Economy Macroeconomics.