BU.220.610 Chap.5 The IS-LM Model: Output and Interest Rates
The IS-LM Model: Output and Interest Rates
Module 5 moves from the long run to the business cycle, the tendency of the economy to rise above and fall below its central path at potential output. Economists read each new data release to judge where the economy sits in that cycle, and governments adjust fiscal and monetary policy to pull it back toward potential with stable prices. The course's workhorse for that job is the IS-LM model.
Its starting simplification is that prices are fixed in the short run. Firms then have spare capacity and supply whatever is demanded at the going price, so short-run supply is horizontal and spending decides output. With prices fixed, expected inflation is zero and the nominal and real interest rates coincide, which lets one rate appear in both halves of the model. The goods-market half starts from the Keynesian cross.
Planned spending is consumption, which depends on disposable income, plus investment and government purchases. Equilibrium is where planned spending equals output; if firms produce more than is bought, unplanned inventories accumulate and production falls.
Because each round of spending becomes someone's income, a change in government purchases moves income by a multiple, one over one minus the marginal propensity to consume, while a tax change works through a smaller multiplier since only part of it is spent.
Letting the interest rate vary turns the cross into the IS curve: a lower rate raises investment, lifts planned spending and increases output, so IS slopes downward in a diagram with the rate on the vertical axis and output on the horizontal. The money-market half comes from the theory of liquidity preference. The central bank fixes the money supply and prices are fixed, so real balances are given.
Money demand falls with the interest rate and rises with income, because more activity needs more money for transactions. Higher income therefore requires a higher rate to keep money demand equal to the fixed supply, which is why the LM curve slopes upward. Short-run equilibrium is the single pair of interest rate and output at which both markets clear. The model's value lies in its experiments.
Pessimism among firms or households shifts IS left, lowering output and the interest rate. Policy has three levers, government purchases, taxes and the money supply, and each can offset such a shock, but the fiscal route raises the interest rate while the monetary route lowers it, which changes who gains.
The chapter also separates ordinary cycles from crises, when shocks are large or financial and the standard lever may run out.
What this chapter covers
- 01
Fixed prices and the short run
- 02
The Keynesian cross and the multiplier
- 03
Deriving the IS curve
- 04
Liquidity preference and the LM curve
- 05
Solving for short-run equilibrium
- 06
Shocks, policy levers and crises
Worked example · free
Solve an IS-LM economy for the interest rate and output
- 2Build IS: Y = 80 + 0.75Y minus 150 + 300 minus 25r + 250, so 0.25Y = 480 minus 25r and Y = 1,920 minus 100r.
- 2Build LM: 920 = Y minus 100r, so Y = 920 + 100r.
- 2Equate: 1,920 minus 100r = 920 + 100r gives r = 5.
- 1Substitute back: Y = 920 + 500 = 1,420.
Key terms
- Keynesian Cross
- A diagram of planned spending against income whose crossing with the 45-degree line gives equilibrium output at a fixed interest rate.
- IS Curve
- The combinations of interest rate and output at which the goods market clears; it slopes down because lower rates raise investment.
- LM Curve
- The combinations of interest rate and output at which money demand equals the fixed real money supply; it slopes up.
- Liquidity Preference
- The theory that the interest rate adjusts to balance real money supply with money demand, which rises with income and falls with the rate.
The IS-LM Model: Output and Interest Rates FAQ
Why does a fiscal expansion raise output by less in IS-LM than in the Keynesian cross?
The cross holds the interest rate fixed. In IS-LM, higher income raises money demand, the rate climbs along the LM curve, and investment falls, which offsets part of the multiplier effect of the extra government spending.
Does a fall in the interest rate shift the IS curve?
No. The interest rate is on the diagram's axis, so a change in it is a movement along IS. The curve shifts only when something held fixed in its derivation changes, such as government purchases, taxes or business confidence.
How can monetary and fiscal expansion both raise output but move rates differently?
Fiscal expansion shifts IS right, so output and the rate rise together. Monetary expansion shifts LM right, so output rises while the rate falls. Rate-sensitive sectors such as investment and housing fare better under the monetary route.
Exam move
For every IS-LM question, draw the two curves before reading the options, move exactly one curve, and write the directions of r and Y beside the new crossing. Then do three algebra drills a week in which you build both curves from equations, since the same four steps cover every numerical item.
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