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