IS and LM together

IS says which interest rates and incomes are consistent with the goods market; LM says which are consistent with the money market. Only one pair is consistent with both: where the curves cross. There, planned spending equals output and money demand equals money supply (CUET 2020, 2026). John Hicks set the model out in 1937 as a summary of Keynes’s General Theory; Alvin Hansen made it the textbook standard, which is why it is also called the Hicks–Hansen model.

Two assumptions stay in the background. The price level is fixed: IS–LM is a model of demand, in which firms supply whatever is demanded at the going price, so it implicitly assumes a horizontal aggregate supply curve (Hyderabad 2010; CUET 2020). And it is a short-run model: Lesson 6 lets prices move.

The method is always the same: write IS and LM as two equations in Y and r, then solve them together. The quickest route is usually to write both as “Y = …” and set them equal. Pick a real question below, check the working, then tap the diagram to throw the economy off equilibrium.

Use Lesson 2’s IS and Lesson 3’s LM and substitute the LM rate into IS:

DSE and JNU set this in letters. JNU 2013 gave IS and LM with parameters λ, b₁, m₀, m₁, m₂ and asked for the aggregate demand function and its slope: exactly this substitution, with the price level left in M/P. Lesson 6 does that step.

The two curves cut the diagram into four regions, and each point off equilibrium has one market out of balance on each side. Lessons 2 and 3 gave the rules:

Financial markets adjust in minutes; output takes months. So the economy first jumps to the LM curve, and then slides along it towards the equilibrium as output changes. That is the path the lab draws when you tap.

A shock shifts one curve; the new crossing is the new equilibrium. Lesson 5 studies policy in detail, but four results come up constantly:

• More money shifts LM right: the interest rate falls and income rises (Hyderabad 2010, 2020; JAM 2025; UGC NET 2024). The channel runs through bonds: people buy bonds with the extra money, bond prices rise, the rate falls, investment rises (UGC NET 2024).
• More spending (G, confidence, investment) shifts IS right: income and the interest rate both rise. Hyderabad 2010 turned it round: if output and interest rates are both rising, the cause must be IS shifting out.
• Two shocks at once: more money and a fall in consumer confidence both push the interest rate down, but pull output in opposite directions, so the effect on output is ambiguous (Hyderabad 2021).
• A liquidity trap caps income. JNU 2011 had I = 2,000 + 0.1Y − 8,000r and S = 1,000 + 0.2Y + 2,000r: IS is Y = 10,000 − 1,00,000r. With a trap at r = 0.01, the rate can’t go lower, so the highest income monetary policy can reach is 9,000.

So far there has been one interest rate. But investment depends on the real rate, r = i − π^e, while money demand depends on the nominal rate i, since that is what holding money costs. If the nominal rate changes but the real rate does not, money demand is affected and investment is not (DSE 2010).

Draw the model with the nominal rate on the axis. LM does not involve expected inflation, so it stays put (DSE 2011). IS, written as i = r + π^e, shifts up by the rise in π^e: at any nominal rate, the real rate is lower and investment higher. The new crossing has higher income and a higher nominal rate, but the nominal rate rises by less than π^e, so the real rate falls (DSE 2009; GATE 2023).