The Keynesian cross and the multiplier

The model has three assumptions, and Hyderabad asked for all of them: prices don’t change, there is spare capacity in industry and unemployed labour. Firms can then produce whatever is demanded at the going price, so output is decided by how much people plan to spend.

Start with a closed economy with no government. Planned spending is consumption plus investment. Investment is autonomous: decided by firms’ expectations, not by this year’s income. Consumption rises with income, but by less than income does:

The marginal propensity to save is 1 − c, and MPC + MPS = 1. Lesson 6 looks at consumption in depth; here we only need the straight line.

Say firms produce 800 but buyers plan to spend only 790. The 10 unsold goods pile up in warehouses: firms have invested 10 in inventories they never planned. Actual investment is always equal to saving after the fact, because unplanned inventories take up the slack. But unplanned inventories are a signal: next period firms produce less. If buyers want more than is produced, stocks run down and firms produce more.

Output stops changing only when planned spending equals output: nothing piles up and nothing runs down. That is the equilibrium. Three ways of saying it, all equivalent (Hyderabad 2013): aggregate demand equals output; planned injections equal planned leakages; C + I = Y.

CUET 2025 turned this around: if desired investment exceeds realised investment, the difference is an unintended inventory shortfall. Firms wanted their stocks to be larger than they turned out.

Plot planned spending against output. The 45° line is every point where spending equals output. Equilibrium is where the spending line crosses it. Slide “Try an output level” to any point off equilibrium and read the unplanned inventory change; then move investment or the MPC and watch output respond. Switch to the second view to see the same equilibrium as saving meeting investment.

Set output equal to planned spending and solve:

Why does output rise by more than the rise in investment? Because spending is someone’s income. A firm spends ₹100 building a warehouse; the builders spend 80% of that, ₹80, in shops; the shopkeepers spend ₹64; and so on. Each round is c times the one before.

The bigger the MPC, the more is passed on each round and the bigger the multiplier; the bigger the MPS, the smaller it is. A parallel shift in the consumption function changes C₀, not c, so it moves output but leaves the multiplier alone (CUET 2020). The multiplier works only with prices fixed and idle labour and capacity; at full employment extra spending just raises prices.

A little history that CUET has asked: R. F. Kahn introduced the employment multiplier in 1931, and Keynes built the investment multiplier on it in The General Theory.

Equilibrium output need not be full-employment output. If spending at full employment falls short of full-employment output, there is a deflationary gap: the vertical distance at Y_f between the 45° line and the spending line. If spending would exceed it, an inflationary gap. The gap is in spending; the output shortfall it causes is the gap times the multiplier. Open the “A slump” preset in the lab above to see both.

Saving is a virtue for a household. Is it for an economy? In the lab, switch to “Leakages = injections” and lower the MPC, which raises the saving line. Equilibrium moves left: output falls. But in the new equilibrium saving still equals investment, and investment hasn’t changed, so total saving is exactly what it was. Everyone tried to save more; the economy ended up poorer and saving no more. That is the paradox of thrift, which Keynes popularised (JNU 2018; UGC NET 2023).

If investment also rises with income, the fall in output drags investment down, and saving ends up lower than before: increased saving leads to an eventual fall in saving (Hyderabad 2010).