Set Y, T, G, and the consumption parameters. The real interest rate r* adjusts so that S = I(r*).
S = Y − C(Y−T) − G = I(r*)
20
3.5
3
0.70
1.0
Consumption C
12.55
Private saving
3.95
Public saving
0.50
National saving S
4.45
Equilibrium r*
5.55%
How to read it
National saving S is fixed (vertical green line) because Y is fixed and consumption depends only on disposable income. Investment I(r) is downward-sloping in r. The real rate r* clears the loanable funds market at the intersection. Try moving G — see how S shifts and r changes.
Watch crowding out happen step by step. Apply a fiscal shock and trace through the four effects on S, r, I, and C.
ΔG > 0: Public saving falls (T−G ↓) → national S ↓ → loanable funds get scarcer → r* ↑ → I(r*) ↓.
Full crowding out in this LR model: ΔI exactly = −ΔG. C is unchanged (Y, T fixed). ΔT < 0: Disposable income ↑ → C rises by MPC·|ΔT|. Private saving falls (since C ↑ by more than disposable income up by MPC less than full). Public saving falls. National S ↓ → r ↑ → I ↓.
Now shock investment demand instead. With S fixed, the equilibrium QUANTITY of I doesn't change — only the price (r).
Investment-demand shocks change r* but NOT total I. With S fixed, total I = S regardless of where the I curve sits. The market clears via the price (r), not the quantity. This is fundamentally different from short-run models with sticky prices, where I shifts can change output.