What the model is for
IS-LM asks where output and the interest rate settle in the short run, while prices are fixed. It puts two markets on one diagram: the goods market, where planned spending must equal output, and the money market, where the demand for money must equal its supply. John Hicks drew it in 1937 as a reading of Keynes’s General Theory, and it has organised short-run macroeconomics teaching ever since.
The interest rate goes on the vertical axis and output on the horizontal. Every point on IS is a goods-market equilibrium; every point on LM is a money-market equilibrium. Only where they cross are both markets clearing at once.
Deriving the IS curve
Start from consumption C = 200 + c(Y − T) and investment I = 300 − 25r, with government spending G and taxes T set by policy. Output equals planned spending when Y = C + I + G, which rearranges to Y = (500 − cT + G − 25r)/(1 − c).
IS slopes down because a lower interest rate raises investment, and the multiplier turns that into more output. It is flatter when investment responds strongly to the interest rate, and flatter again when the marginal propensity to consume c is high, because each extra pound of investment then raises output by more.
Deriving the LM curve
People hold money for transactions, which rise with income, and hold less of it when the interest rate, the return on bonds, is high. In the explorer real money demand is 0.5Y − 50r, and it must equal the real money supply M/P. Solving for the interest rate gives r = (0.5Y − M/P)/50.
LM slopes up because higher income raises the demand for money, and with the supply fixed the interest rate has to rise to bring demand back down. A larger money supply shifts LM right; a higher price level shrinks M/P and shifts it left.
Fiscal policy and crowding out
With c = 0.75 the simple multiplier is 1/(1 − 0.75) = 4. Raise G by 50 and IS shifts right by 200 at the old interest rate. That is not where output ends up. Higher income raises the demand for money, the interest rate climbs from 3% to 4%, and investment falls from 225 to 200. Output rises from 2,300 to 2,400, by 100 rather than 200: the other 100 has been crowded out.
A tax cut works through consumption instead. Cutting T by 40 raises spending by c × 40 = 30 at every income, so IS shifts by 120, less than the same change in G would give, because part of the tax cut is saved. Exams like asking for exactly this comparison.
Monetary policy
Raise the real money supply from 1,000 to 1,100 and LM shifts right. At the old income there is now more money than people want to hold, so they buy bonds and the interest rate falls, from 3% to 2% in the explorer. Investment rises and output moves down along IS to 2,400.
The slopes decide which policy is stronger. When LM is very flat, as in a liquidity trap where interest rates can’t fall further, monetary expansion does little and fiscal policy crowds out almost nothing. When LM is very steep, fiscal policy mostly crowds out investment and money is the stronger lever.
IS-LM in a modern course
Central banks such as the Bank of England set an interest rate rather than the money supply, so many UK courses now teach IS-LM alongside a model with an interest-rate rule: David Romer’s IS-MP, or the IS-PC-MR model in Carlin and Soskice’s textbook. The IS curve and the multiplier logic carry straight over, and IS-LM remains the way most courses introduce crowding out and the policy mix.
IS-LM also builds the aggregate demand curve. Let the price level change and LM moves, tracing out a downward-sloping relationship between prices and output. The AD-AS page picks up from there.