Keynesian Cross

Planned spending meets the 45° line, watch a $1 injection multiply into more output.

Equilibrium: Y* = 50.0, PE* = 50.0

Current equations

PE: PE = 20 + 0.6·Y45°: PE = 1·Y

The simplest engine of macro. Planned spending rises with income (the PE line), but less than one-for-one. The 45° line marks where spending equals output. Equilibrium is their crossing: firms produce exactly what gets bought. Push autonomous spending up and output rises by MORE than the push, that's the multiplier.

Source: Mankiw, Macroeconomics, ch. 11

Shift the curves

Autonomous spending (A: G, I, autonomous C)0

A $1 rise in autonomous spending raises equilibrium output by the multiplier 1/(1−MPC).

The Keynesian Cross model, in writing

Definition

The simplest model of demand-driven output: planned spending rises with income, and equilibrium is where planned spending equals actual output.

Y = C + c(Y - T) + I + G ; multiplier = 1/(1 - c)

The intuition

Spend one extra dollar and it becomes someone's income; they spend a fraction c of it, which becomes someone else's income, and so on. The chain sums to the multiplier, so a $1b stimulus can raise GDP by more than $1b. The flatter the consumption response, the smaller the ripple.

Exam tip

The multiplier is 1/(1-MPC) for spending but -MPC/(1-MPC) for taxes: tax changes have a SMALLER multiplier because the first round is saved partly. Balanced-budget changes still move output.

Related models in Macro Foundations

AS-AD (Aggregate Supply – Aggregate Demand) →Phillips Curve →Business Cycle Phases →Money Multiplier →