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

Detail

1. Background: why Keynes built this model

• John Maynard Keynes published The General Theory of Employment, Interest and Money in 1936 [4].
• It came out during the Great Depression of the 1930s. The economic theory of that time could not explain why the whole world economy collapsed so badly. It also could not offer a good policy answer [4].
• Classical belief (before Keynes): free markets would reach full employment (everyone who wants a job gets one) on their own, as long as workers accepted flexible wages [4].
• Keynes's answer: there is no automatic push towards full employment. If total demand is too low, high unemployment can last for a long time [2][4].
• This chapter shows that idea in its simplest form. There are two stages:
• Stage 1: the price level is fixed and only output changes (this section).
• Stage 2: prices are also allowed to change (the fixed-price assumption is dropped).

2. Why keep the price level fixed?

• Fixed price assumption: the economy has unused resources, meaning idle machinery, empty buildings and workers without jobs.
• Chain of reasoning:
• Idle resources exist, so the law of diminishing returns does not apply. (This law says that when you keep adding workers to a fixed factory, each extra worker adds less output.)
• So firms can produce extra output without any rise in marginal cost (the cost of making one more unit).

• Costs do not rise, so firms do not raise prices. The price level stays the same when output changes.

• It is also a simplifying assumption. It is dropped at the second stage.

• Modern support: the IMF lists sticky prices as a core Keynesian idea. Prices, and wages even more, change only slowly when demand or supply changes [4].
• So in the short run, a change in aggregate demand mainly changes real output and employment, not prices [4].

3. Aggregate supply: the 45° line

• Aggregate supply (AS): the total output that firms plan to produce.
• Prices are fixed and resources are idle. So whatever GDP is demanded is supplied.

• This means supply is perfectly elastic: output can rise or fall to any level without any change in price.

• The 45° line:

• National income or output (Y) is on the horizontal axis. Spending or supply is on the vertical axis.
• A line drawn from the origin at 45° has equal horizontal and vertical values at every point.

• So every point on the line means "output supplied = income".

• Example: GDP = ₹1,000 (point A on the horizontal axis). Then ₹1,000 worth of goods is supplied (point B on the 45° line, at a height of ₹1,000).

4. Aggregate demand (short recap)

• Aggregate demand (AD): total planned spending in the economy. In this simple two-sector model (households and firms only), AD = C + I.
• Consumption function: C = C̄ + cY
  • C̄ is autonomous consumption, which people spend 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.

• Graphically, AD is a line that starts at height (C̄ + Ī) on the vertical axis. Its slope is c, and c is less than 1. So the AD line is flatter than the 45° line, and the two lines must cross once.

• Ex ante vs ex post:

• Ex ante means planned (what people intend to do).
• Ex post means actual (what finally happened).
• Equilibrium in this model is defined in terms of planned values.

5. Equilibrium income

• Equilibrium income: the income at which ex ante AD = ex ante AS.
• On the graph, this is the point where AD cuts the 45° line (point E, income OY₁).

• At this income, planned spending exactly buys planned output. No firm is surprised.

• Algebra:

• Equilibrium condition: AD = Y
• C̄ + Ī + cY = Y
• Y − cY = C̄ + Ī, so Y(1 − c) = C̄ + Ī
• Y* = (C̄ + Ī)/(1 − c) (equation 4.4)

• Here (C̄ + Ī) is total autonomous expenditure (Ā). So Y* = Ā/(1 − c).

• Worked example: C = 40 + 0.8Y and I = 10

• AD = 40 + 0.8Y + 10 = 50 + 0.8Y
• Put AD = Y: Y = 50 + 0.8Y, so 0.2Y = 50
• Y* = 50/0.2 = 250
• Check: at Y = 250, C = 40 + 0.8 × 250 = 40 + 200 = 240

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

• Saving–investment version (a standard extension): at equilibrium, planned saving = planned investment.

• Why: Y = C + S (income is either spent or saved), and AD = C + I. If Y = AD, then S = I.

• The saving function is S = −C̄ + (1 − c)Y. In the example, S = −40 + 0.2Y. At Y = 250, S = −40 + 50 = 10 = I.

• Note: 1/(1 − c) is the investment multiplier. In the example it is 1/0.2 = 5. This is covered in the next section.

6. Adjustment through unplanned inventory

• Inventory: stocks of unsold goods and unfinished goods kept by firms.
• Unplanned inventory change: the gap between the stocks firms wanted to hold and the stocks they actually hold. This gap signals that output is not in equilibrium.
• If AD < Y (excess supply, meaning output is more than planned spending):
• Goods remain unsold, so unplanned inventory accumulation takes place.
• Firms see stocks piling up and cut output.

• Y falls towards Y*.

• If AD > Y (excess demand, meaning planned spending is more than output):

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

• Y rises towards Y*.

• 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 planned S and planned I equal.

• NCERT exercise: Ā = ₹50 crore, MPS = 0.2 (so c = 0.8), Y = ₹4,000 crore
• MPS is the marginal propensity to save, the share of each extra rupee that is saved. MPS = 1 − MPC.
• AD = 50 + 0.8 × 4,000 = 50 + 3,200 = ₹3,250 crore. This is less than Y = ₹4,000 crore.
• So the economy is not in equilibrium. There is excess supply of ₹750 crore.
• Stocks pile up and output will fall.

• Equilibrium income would be 50/0.2 = ₹250 crore.

• How India tracks this in real life:

• The RBI runs the Order Books, Inventories and Capacity Utilisation Survey (OBICUS). It covers the manufacturing sector. It gives a quick picture of demand conditions in Indian manufacturing [5].
• Example from Q1:2020-21 (April–June 2020, the COVID-19 lockdown), from the 50th round, which surveyed 462 companies [5]:
  • Capacity utilisation (CU), the share of factory capacity actually used, fell to 47.3%, down from 69.9% in Q4:2019-20. Seasonally adjusted CU fell to 48.2%, down from 68.2% [5].
  • The finished-goods inventory to sales ratio rose to 23.6%, up from 15.1% [5]. Sales fell faster than stocks. This is the textbook "AD < Y → unplanned inventory piles up" case.
  • Low CU also shows idle resources. This is the same condition that justifies the fixed-price, flat-supply assumption.

7. Effective demand principle

• Effective demand principle: when the price level is fixed and supply is perfectly elastic, aggregate output is determined only by aggregate demand.
• Keynes saw national income (Y), output (O) and expenditure or effective demand (D) as equal: Y = O = D [2].

• When effective demand is less than the economy's productive capacity (what it could produce), the result is unemployment and depression [2].

• The break from Say's law:

• Say's law (named after the classical economist J.B. Say) says "supply creates its own demand". Producing goods creates the income that buys other goods [3].
  • In the classical view, supply leads and demand follows. The economy settles at full employment.

• Keynesian short run: demand leads and output follows.

  • Output settles wherever AD cuts the 45° line.
  • This point can be below full employment. That is an underemployment equilibrium: a stable income level at which some workers still have no jobs.

• Policy meaning: demand is shaped by both private and public decisions. So when demand is too low, the government may need to step in, for example through spending or tax changes [4].

Prelims Hooks

• Keynes's General Theory was published in 1936, in response to the Great Depression [4].
• The 45° line stands for aggregate supply under fixed prices. Every point on it has equal values on both axes (output = spending).
• Equilibrium condition: ex ante (planned) AD = ex ante AS. It is not ex post (actual) values, because those are always equal.
• Y* = (C̄ + Ī)/(1 − c). With C = 40 + 0.8Y and I = 10, Y* = 250, and planned S = I = 10.
• Trap: if AD < Y, there is excess supply → unplanned inventory accumulation → output falls. It does not cause prices to fall in this model, because prices are fixed.
• Say's law = "supply creates its own demand" [3]. The effective demand principle = output is determined by AD alone. Match these correctly.
• Perfectly elastic aggregate supply needs unused resources. Then there are no diminishing returns and marginal cost does not rise.
• The RBI's OBICUS survey tracks order books, inventories and capacity utilisation in manufacturing [5].

Mains Points

• Demand-deficient slowdowns: when capacity utilisation is low and unsold stocks are high, output is limited by demand, not by supply. An example is Q1:2020-21, when CU was 47.3% and the finished-goods inventory to sales ratio was 23.6% [5]. This supports using government spending to lift demand, as the effective demand principle suggests [4].
• Limits of the model: the fixed-price, perfectly elastic supply result holds only when there is slack (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. Use this to argue for policy that fits the stage of the business cycle.
• Keynes vs classical economics: Say's law says the economy corrects itself. Keynes said demand shortfalls can cause long-lasting unemployment [2][4]. This debate underlies the choice between counter-cyclical fiscal policy (spending more in a slowdown and less in a boom) and strict fiscal consolidation (cutting the deficit) during a slowdown.
• Inventory signals for policymakers: unplanned inventory changes are the market's own warning that planned spending and planned output do not match. Surveys like OBICUS let the RBI and government spot this early, before GDP data comes out [5].