Goods and money markets: the IS-LM model
The IS curve shows goods-market equilibrium and the LM curve money-market equilibrium. Where they cross, income and the interest rate are both settled.
The two curves
The model was developed by John Hicks (1937) and Alvin Hansen to put Keynes's ideas into one diagram.
Worked example 1: IS-LM equilibrium
Goods market: C = 200 + 0.8Y, I = 300 − 20r, G = 200. Money market: money demand L = 0.5Y − 50r, money supply M = 1,500 (r in %, Y in Rs. billion). Find the IS and LM equations and the equilibrium.
- IS: Y = 200 + 0.8Y + 300 − 20r + 200 → 0.2Y = 700 − 20r → Y = 3,500 − 100r.
- LM: 0.5Y − 50r = 1,500 → 0.5Y = 1,500 + 50r → Y = 3,000 + 100r.
- Equilibrium: 3,500 − 100r = 3,000 + 100r → 500 = 200r → r = 2.5%.
- Y = 3,500 − 100 × 2.5 = 3,250. Check on LM: 3,000 + 250 = 3,250. ✓
Equilibrium: interest rate 2.5%, national income Rs. 3,250 billion.
Worked example 2: fiscal and monetary expansion
Starting from r = 2.5% and Y = 3,250: (a) government spending rises by 100 to 300; (b) instead, the money supply rises by 100 to 1,600. Find the new equilibrium each time and the crowding out in (a).
- (a) New IS: 0.2Y = 800 − 20r → Y = 4,000 − 100r. With LM Y = 3,000 + 100r: 4,000 − 100r = 3,000 + 100r → r = 5%, Y = 3,500.
- Without any rise in r, Y would have risen by the full multiplier: 5 × 100 = 500, to 3,750.
- Actual rise = 3,500 − 3,250 = 250. Crowding out = 500 − 250 = 250: the higher interest rate cut investment by 20 × 2.5 = 50, and 5 × 50 = 250. ✓
- (b) New LM: 0.5Y − 50r = 1,600 → Y = 3,200 + 100r. With IS Y = 3,500 − 100r: 3,500 − 100r = 3,200 + 100r → r = 1.5%, Y = 3,350.
(a) Fiscal expansion: r rises to 5%, Y to 3,500; half the multiplier effect (250) is crowded out. (b) Monetary expansion: r falls to 1.5%, Y rises to 3,350.
Monetary transmission in the IS-LM model
When is each policy effective?
| Situation | Monetary policy | Fiscal policy |
|---|---|---|
| Vertical (very steep) LM: money demand insensitive to r (classical case) | Very effective | Weak: full crowding out |
| Horizontal LM: liquidity trap at a very low interest rate (Keynesian case) | Ineffective: r cannot fall further | Very effective: no crowding out |
| Steep IS: investment insensitive to r | Weak | Effective |
| Flat IS: investment very sensitive to r | Effective | Weak: strong crowding out |
Combining the two policies
Fiscal and monetary policy interact. A fiscal expansion alone raises Y but also raises r, crowding out private investment. If the central bank accommodates it by raising the money supply at the same time, r can stay unchanged and Y rises by the full multiplier. A tight money, loose budget mix raises r sharply and hurts investment; a loose money, tight budget mix keeps r low and supports private investment while reducing the deficit. Choosing the right policy mix depends on the shapes of the curves and on the main problem: unemployment, inflation or debt.
When the CBSL lowers its policy interest rate, bank lending rates usually fall, and firms such as construction and manufacturing companies find it cheaper to borrow and invest (LM shifts right). When the government borrows heavily, interest rates can rise and crowd out private projects.
Short answer: “What does the LM curve show?” Combinations of income and interest rate at which money demand equals money supply (money market equilibrium).
Structured question: “Given IS: Y = 3,500 − 100r and LM: Y = 3,000 + 100r, find the equilibrium. Show the effect of a rise in G of 100 with a multiplier of 5.” r = 2.5%, Y = 3,250. New IS Y = 4,000 − 100r gives r = 5%, Y = 3,500; 250 of the 500 multiplier effect is crowded out.
Essay: “Explain IS-LM equilibrium and discuss the relative effectiveness of monetary and fiscal policy.” Derive IS and LM, show equilibrium, shift each curve for fiscal and monetary policy, explain crowding out, then the classical, liquidity-trap and IS-slope cases, and the policy mix.
Fiscal moves IS; money moves LM. Fiscal expansion: Y ↑ and r ↑ (crowding out). Monetary expansion: Y ↑ and r ↓.