Jupiter2U School
Chapter 18

Macroeconomic Models: AD–AS & IS–LM

College

Chapter 14 described fiscal and monetary policy through the AD–AS model in words and a multiplier formula. This chapter builds the formal machinery underneath — including the IS–LM model, which shows precisely how the two policies interact and why "crowding out" happens.

At a glance
Core ideaIS and LM cross at the output and interest rate that clear both markets.
Key termCrowding out — fiscal expansion lifts r, choking off private investment.
You can…Solve an IS–LM system and trace a fiscal or monetary shift.
Watch outIn a liquidity trap the LM is flat: monetary policy stalls, fiscal dominates.
Theory

Deriving AD–AS, then building IS–LM

The aggregate demand curve slopes down (in output–price space) for three reasons: a lower price level raises the real value of wealth (the real-balance effect), lowers interest rates and so stimulates investment (the interest-rate effect), and makes domestic goods cheaper relative to foreign ones (the trade effect). Short-run aggregate supply slopes up because wages and some prices are sticky; long-run aggregate supply is vertical at potential output Y*, since in the long run all prices adjust and output is set by the economy's real capacity (echoing the PPF of Chapter 6).

The IS–LM model makes the interest-rate channel explicit. The IS curve plots combinations of the real interest rate r and output Y that clear the goods market:

IS: Y = C(Y − T) + I(r) + G, with I falling as r rises → IS slopes down in (Y, r) space

The LM curve plots combinations that clear the money market — real money supply equals real money demand, where demand rises with income (transactions motive) and falls with the interest rate (opportunity cost of holding cash):

LM: M/P = L(Y, r) = kY − hr → LM slopes up in (Y, r) space

The economy's equilibrium (r*, Y*) is where IS and LM cross — output and the interest rate that simultaneously clear both markets.

Explanation

Policy through the IS–LM lens

Expansionary fiscal policy (higher G or lower T) shifts IS right: at the old interest rate, output would rise by the full multiplier — but the increase in Y raises money demand, which (with a fixed money supply) bids the interest rate up, which chokes off some investment. This is exactly the crowding out introduced informally in Chapter 14, now derived formally: fiscal policy raises both Y and r, and the size of the crowding out depends on how steep LM is.

Expansionary monetary policy (higher money supply) shifts LM right: at the old output level, the interest rate must fall to make people willing to hold the larger real money stock, and the lower r stimulates investment, raising Y. A liquidity trap — flat LM at very low interest rates — mutes monetary policy almost entirely (a shift in LM barely changes r or Y), while fiscal policy remains fully potent, matching the post-2008 near-zero-rate experience discussed in Chapter 14.

IS–LM also explains why AD slopes down: a fall in the price level P raises the real money supply M/P, shifting LM right, lowering r and raising Y at that price — tracing out one point lower on the AD curve. Shocks to G, T, or M shift the whole AD curve, exactly as changes to demand-side variables shifted whole curves back in Chapter 7.

Practical

Worked example: solving and shifting an IS–LM system

Step 1 — the equationsIS: Y = 1200 − 40r. LM: Y = 400 + 40r.
Step 2 — solve for equilibrium1200 − 40r = 400 + 40r → 800 = 80r → r* = 10, Y* = 800.
Step 3 — a fiscal expansionHigher G shifts IS to Y = 1400 − 40r. Re-solve: 1400 − 40r = 400 + 40r → 1000 = 80r → r = 12.5, Y = 900. Output rose by only 100, not the full 200 the naive multiplier of Chapter 14 predicted — the missing 100 is crowded out as r rose from 10 to 12.5.
Step 4 — a monetary expansion insteadBack at the original IS, higher money supply shifts LM to Y = 600 + 40r. Re-solve with Y = 1200 − 40r: 1200 − 40r = 600 + 40r → 600 = 80r → r = 7.5, Y = 825. Here the interest rate falls and output rises with no crowding out — the opposite signature from fiscal policy.
Step 5 — the diagnosticThis is why economists can infer which lever moved just from the data: rising Y with rising r points to fiscal expansion; rising Y with falling r points to monetary expansion.
Q&A
Q1Why does the IS curve slope downward?

A higher real interest rate r raises the cost of borrowing for investment, so planned investment I(r) falls. With lower I, total planned spending falls, so the level of Y at which output equals planned spending must also be lower. Higher r pairs with lower Y — a downward-sloping relationship.

Q2Why does the LM curve slope upward?

Higher income Y raises transactions demand for money. To keep the money market in equilibrium with a fixed real money supply, the interest rate r must rise to discourage speculative/precautionary money holding and free up money for transactions. Higher Y pairs with higher r — an upward-sloping relationship.

Q3What does a "flat" LM curve (liquidity trap) look like graphically, and why does fiscal policy dominate there?

A flat LM means the interest rate is stuck near zero across a wide range of Y — money demand is nearly infinitely elastic there. A rightward IS shift (fiscal expansion) moves the equilibrium mostly through Y with almost no change in r, so there is essentially no crowding out. A rightward LM shift (monetary expansion) barely moves the intersection at all, since LM is already flat — monetary policy loses traction.

Q4How steep is "too steep"? What determines how much crowding out occurs?

Crowding out is larger when investment is very sensitive to r (a flat I(r), meaning small rate rises choke off a lot of investment) and money demand is not very sensitive to r (a steep LM, meaning it takes a big rate rise to absorb the extra money demand from higher Y). Empirically estimating these sensitivities is exactly the job of the econometric methods in the next chapter.

IS LM r* Y* r Y
Equilibrium output Y* and interest rate r* occur where the goods market (IS) and money market (LM) both clear.
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Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Aggregate demandSRAS and LRASIS curveLM curveEquilibrium r andYCrowding outLiquidity trapAD-AS & IS-LM Models
Infographic

The process, step by step

Step 1Fiscal expansionGovernment raises spending, shifting the IS curve right.
Step 2Output and rates riseHigher demand raises income Y and pushes up the interest rate.
Step 3Higher interest rateDearer borrowing reduces private investment.
Step 4Crowding outThe fall in investment offsets part of the government stimulus.
Step 5Net effectOutput rises, but by less than the simple multiplier predicts.
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1IS: Y = 1000 - 20r and LM: Y = 400 + 40r. Find equilibrium r and Y.

  1. Set IS = LM: 1000 - 20r = 400 + 40r.
  2. Solve: 600 = 60r, so r = 10.
  3. Y = 1000 - 20(10) = 800.

Example 2From that equilibrium, fiscal expansion shifts IS to Y = 1100 - 20r. Find new r and Y.

  1. Set new IS = LM: 1100 - 20r = 400 + 40r.
  2. 700 = 60r, so r = 11.67; Y = 1100 - 20(11.67) = 867.
  3. Output rose 67, less than the 100 shift -- crowding out.
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Why does the LRAS curve stand vertical?
In the long run output is set by resources and technology, not the price level, so it is fixed at potential.
2What does the IS curve represent?
Combinations of interest rate and output where the goods market is in equilibrium (planned spending = output).
3What does the LM curve represent?
Combinations of interest rate and output where money demand equals money supply.
4What is crowding out?
When government borrowing raises interest rates and reduces private investment, offsetting part of the fiscal stimulus.
5What is a liquidity trap?
When interest rates are so low that monetary policy cannot lower them further to stimulate demand.
6How does expansionary monetary policy shift IS-LM?
It shifts the LM curve right, lowering the interest rate and raising output.