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Sem 5 Prep
← Open Economy MacroIncome determination in a closed economy

Formulas for this chapter

Closed economy equilibrium

Y = C(Y) + I Equivalently S = I Shortcut: Y = autonomous spending / MPS

Any question that hands you a consumption function and an investment level. Use the shortcut to get the number fast, then verify with S = I.

Y
Equilibrium national income and production
C(Y)
Planned consumption, a function of income, class case C = 100 + 0.75Y
I
Planned investment, autonomous, class case 150
S
Desired saving, Y minus C(Y), class case S = -100 + 0.25Y

Marginal propensities

MPC = dC / dY MPS = dS / dY MPC + MPS = 1

Whenever a table or a graph gives you two levels of income and the matching consumption or saving. Both are slopes, so both are a change over a change.

MPC
Marginal propensity to consume, less than 1, class case 450/600 = 0.75
MPS
Marginal propensity to save, class case 150/600 = 0.25

Keynesian (closed economy) multiplier

k = 1 / MPS dY = k x dI Round n = MPC^(n-1) x dI

Sizing the effect of a change in investment, or working backwards from a target for income to the injection needed. The round formula is for showing the process.

k
The multiplier, class case 1/0.25 = 4
dI
The autonomous change in investment, class case 100
dY
The resulting change in equilibrium income, class case 400
Step 1 of 24
The ideaTheory

A tank with a tap and a drain

Picture a water tank. A tap pours water in. A drain lets water out. The level in the tank settles where the inflow exactly matches the outflow.

The tank is national income. The tap is investment. The drain is saving.

Open the tap wider and the level rises, but not by the amount of extra water each second: it rises until the drain, which widens as the level rises, is carrying the extra water away again. That single sentence is the multiplier, and the rest of this chapter is arithmetic on it.

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