Planned spending meets the 45° line, watch a $1 injection multiply into more output.
Warming up the engine…
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)
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.
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.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at Y 50, PE 50.
Equilibrium: Y* = 50.0, PE* = 50.0
Current equations
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. EquilibriumequilibriumThe point where opposing forces balance, quantity supplied equals quantity demanded, so there's no pressure for price to change. is their crossing: firms produce exactly what gets bought. Push autonomous spending up and output rises by MORE than the push, that's the multipliermultiplierThe amount total output changes per dollar of initial spending change, powered by respending: 1/(1−MPC) in the simplest case..
Source: Mankiw, Macroeconomics, ch. 11