Equilibrium income

Also called: Macroeconomic equilibrium · Topic: Aggregate Demand, Income Determination and the Multiplier · NCERT: Class 12, Ch 4 "Determination of Income and Employment"

Meaning

Equilibrium income (also called macroeconomic equilibrium) is the level of national income at which ex ante (planned) aggregate demand equals ex ante (planned) aggregate supply. At this level, total planned spending exactly buys the total output that firms plan to produce.

Formula: Y* = (C̄ + Ī)/(1 − c) = Ā/(1 − c)

This is the level of output where the economy settles in the short run. Keynes showed that this level can be below full employment. So an economy can stay stuck with high unemployment unless demand rises [2][4].

Explanation

How it works: AD meets the 45° line

• Aggregate supply (AS): the total output that firms plan to produce.
• Prices are fixed, and resources such as machines and workers are idle. So whatever GDP is demanded is supplied. Supply is perfectly elastic, which means output can rise or fall without any change in price.

• AS is drawn as the 45° line. At every point on it, the horizontal value equals the vertical value, so output supplied = income.

• Aggregate demand (AD): total planned spending. In the two-sector model (households and firms only):

• Consumption function: C = C̄ + cY
  • C̄ is autonomous consumption, the spending people do even when income is zero.
  • c is the marginal propensity to consume (MPC), the share of each extra rupee of income that people spend.
• Investment: I = Ī. This is autonomous investment, which is fixed and does not depend on income.

• So AD = C̄ + Ī + cY.

• Where the lines cross:

• The AD line starts at height (C̄ + Ī) on the vertical axis. Its slope is c.
• c is less than 1, so AD is flatter than the 45° line. The two lines must cross once.
• The crossing point is E, with income OY₁. This is equilibrium income. No firm is surprised by its sales.

The algebra and a worked example

• Start from the equilibrium condition: AD = Y
• C̄ + Ī + cY = Y
• Y(1 − c) = C̄ + Ī

• Y* = (C̄ + Ī)/(1 − c), where (C̄ + Ī) = Ā, total autonomous expenditure

• Example: C = 40 + 0.8Y and I = 10

• AD = 50 + 0.8Y
• Put AD = Y: 0.2Y = 50, so Y* = 250
• Check: C = 40 + 0.8 × 250 = 240

• Saving S = 250 − 240 = 10, which is equal to I = 10

• Saving–investment version: at equilibrium, planned saving = planned investment.

• Income is either spent or saved, so Y = C + S. Also, AD = C + I.
• So if Y = AD, then S = I.

• The saving function is S = −C̄ + (1 − c)Y. In the example, S = −40 + 0.2 × 250 = 10 = I.

• 1/(1 − c) is the investment multiplier. In the example it is 1/0.2 = 5.

How the economy moves to equilibrium: unplanned inventory

• Inventory: unsold goods and unfinished goods kept by firms.
• If AD < Y (excess supply):
• Goods remain unsold, so unplanned inventory accumulation takes place.
• Firms cut output.

• Y falls towards Y*.

• If AD > Y (excess demand):

• Firms sell from their stocks, so inventories run down below the level they planned.
• Firms raise output.

• Y rises towards Y*.

• Output adjusts, not prices. Prices are fixed in this model.

• Ex post, the accounts always balance. Unplanned inventory change is counted as part of actual investment. So actual S = actual I at every income level. Only at Y* are the planned S and planned I equal.
• NCERT exercise: Ā = ₹50 crore, MPS = 0.2 (MPS is the marginal propensity to save, the share of each extra rupee that is saved; MPS = 1 − MPC, so c = 0.8), and Y = ₹4,000 crore.
• AD = 50 + 0.8 × 4,000 = ₹3,250 crore, which is less than Y.
• This gives an excess supply of ₹750 crore. Stocks pile up and output falls.
• Equilibrium income = 50/0.2 = ₹250 crore.

What raises or lowers equilibrium income

• Higher autonomous spending (Ā) shifts AD up, so Y* rises. Examples are more autonomous consumption or more investment.
• Higher MPC (c) makes AD steeper and the multiplier larger, so Y* rises.
• Lower Ā or lower c shifts or flattens AD, so Y* falls.
• Effective demand principle: when prices are fixed and supply is perfectly elastic, output is determined only by aggregate demand. Keynes treated income (Y), output (O) and effective demand (D) as equal: Y = O = D [2].

In India

• The RBI's OBICUS survey: the RBI runs the Order Books, Inventories and Capacity Utilisation Survey (OBICUS) for the manufacturing sector. It gives a quick picture of demand conditions [5].
• The COVID-19 lockdown, Q1:2020-21 (April–June 2020), 50th round, 462 companies [5]:
• Capacity utilisation (CU), the share of factory capacity actually used, fell to 47.3% from 69.9% in Q4:2019-20. Seasonally adjusted CU fell to 48.2% from 68.2% [5].

• The finished-goods inventory to sales ratio rose to 23.6% from 15.1% [5].

• What this shows about the model:

• Sales fell faster than stocks. This is the textbook case of AD < Y leading to unplanned inventory accumulation and falling output.
• Low CU shows idle resources. This is the condition that makes the fixed-price, flat-supply assumption reasonable.
• Output was being limited by demand, not supply. So the economy had settled at an income level well below its capacity.

Don't confuse with

• Full-employment income: equilibrium income is simply where AD = AS. It can sit below full employment. This is called an underemployment equilibrium, a stable income level at which some workers still have no jobs.
• Ex post equality of S and I: actual (ex post) saving and investment are always equal, because unplanned inventory change is counted as investment. Equilibrium needs planned (ex ante) S = planned I.
• Say's law: "supply creates its own demand," so supply leads [3]. Under the effective demand principle, demand leads and output follows.
• Price adjustment: in this model, excess supply is removed by cutting output, not by cutting prices, because prices are fixed.

Prelims Hooks

• Condition: ex ante AD = ex ante AS. On the graph, this is where AD cuts the 45° line.
• Formula: Y* = (C̄ + Ī)/(1 − c). With C = 40 + 0.8Y and I = 10, Y* = 250 and planned S = I = 10.
• Trap: AD < Y → excess supply → unplanned inventory accumulation → output falls. Prices do not fall in this model.
• Trap: at equilibrium, planned saving = planned investment. Actual S = actual I holds at every income level.
• The 45° line stands for aggregate supply under fixed prices. Supply is perfectly elastic only when there are unused resources, so there are no diminishing returns and no rise in marginal cost.
• Keynes's General Theory was published in 1936, in response to the Great Depression [4]. The RBI's OBICUS survey tracks order books, inventories and capacity utilisation in manufacturing [5].

Mains Points

• The case for demand support in a slowdown:
• In Q1:2020-21, CU was 47.3% and the finished-goods inventory to sales ratio was 23.6% [5]. This means low demand, not low supply, was holding output down.
• Equilibrium income is decided by AD. So raising demand through government spending or tax changes can lift output and jobs [4].

• This supports counter-cyclical fiscal policy (spending more in a slowdown and less in a boom) over strict fiscal consolidation (cutting the deficit) during a downturn.

• Limits of the model:

• The result that output changes while prices stay fixed holds only when there is slack, meaning idle capacity and idle workers.
• Near full capacity, extra demand raises prices rather than output. This is why the RBI watches capacity utilisation as an early sign of inflation pressure.

• So policy should match the stage of the business cycle.

• Keynes vs classical economics:

• Classical economists relied on Say's law and believed the economy corrects itself and reaches full employment [3][4].
• Keynes showed that equilibrium income can stay below full employment for a long time [2][4].
• Unplanned inventory changes warn early that planned spending and planned output do not match. Surveys like OBICUS let the RBI and government act before GDP data comes out [5].

Related concepts

• Fixed price assumption
• Aggregate supply
• Effective demand principle

Read more

• Equilibrium income: the 45° line and the effective demand principle