EC212 · LESSON 06 / 08

6. Building IS–LM

Spending determines goods-market income, but interest affects investment while income affects money demand. We must solve both markets together.

Understand

What is this lesson explaining?

IS collects Y–i pairs where AE = Y. Higher interest reduces investment, spending, and equilibrium income, giving a downward slope with Y horizontal and i vertical.

LM collects pairs where M/P = L(Y,i). Higher Y raises money demand; with fixed M/P, i must rise to reduce other money holdings. LM therefore slopes upward.

KEY MODEL

IS:Y = A − bi

LM:i = dY − f

Y, iReal income and interest rate (percentage-point units)A, bIS intercept and positive income sensitivity to interestd, fLM slope and a real-money-supply term, with d > 0

See it on a graph

The graph is right here

Read the axes and original point first. Then change one value at a time and watch the curve or point move.

KEY MODEL

IS:Y=600−40i

LM:i=0.025Y−5

E₀=E₁ : Y=400, i (%)=5

IS₀LM₀IS₁LM₁

IS shift (Y units): 0 Y units of IS shift Change money supply M: 0 model units

Higher spending shifts IS right; more money shifts LM right/down → equilibrium Y=400, i=5. If both change, identify the market behind each curve.

Blue dashed: original · Solid: new state · E₀/A: original point · E₁/B: new point. Coincident points share a label; use the explanation to read each result.

A curve shifts when one of its non-axis conditions changes. An adjusting point on a fixed curve is movement along that curve, not a shift of it.

Quick check

NO TYPING

IS: Y = 500 − 20i and LM: i = 0.05Y − 5. Which is equilibrium?

Takeaway

Remember these two ideas

✓

Let IS be Y = 600 − 40i and LM be i = 0.025Y − 5. Substitute LM into IS: Y = 600 − 40(0.025Y − 5).

Common mix-upA change in Y alone does not shift LM because Y is an axis variable. Changing M/P shifts the LM relationship.

Assumptions and sources

Closed economy, fixed P, and zero expected inflation so i also represents the real rate. Curves are not in special horizontal or vertical cases.

EC212 tutoring outline: chapters 1–8 (local course outline)
Mankiw, Macroeconomics, 8th edition, chapter 11, pp. 314–325