Difficulty: Intermediate | Prerequisites: Goods market equilibrium (Keynesian cross), financial market equilibrium (money supply and demand), the multiplier.
The IS-LM model is the workhorse of short-run macroeconomics. It combines two markets you have already studied separately, the goods market and the financial market, into a single framework where output (Y) and the interest rate (i) are determined simultaneously. The key insight is that these markets do not operate in isolation: what happens in the financial market (changes in interest rates) feeds back into the goods market (through investment), and vice versa. This model, developed in the tradition of Keynes and Hicks, is the foundation for understanding how fiscal and monetary policy affect the economy in the short run.
The IS curve traces goods-market equilibria (higher interest rates reduce investment, so equilibrium output falls). The LM curve traces financial-market equilibria (higher output raises money demand, so the equilibrium interest rate rises). Where the two curves cross, both markets clear at once, and that intersection is what fiscal and monetary policy shift around.
Investment function, I(Y, i)
The relationship showing that investment depends positively on output (Y) and negatively on the interest rate (i). In simple terms, firms invest more when sales are strong and borrowing is cheap.
IS curve (Investment-Saving curve)
The set of all (Y, i) combinations at which the goods market is in equilibrium (Y = Z). It slopes downward: a higher interest rate means less investment, less aggregate demand, and therefore lower equilibrium output. Think of it as the "goods-market equilibrium line" in (Y, i) space.
LM curve (Liquidity-Money curve)
The set of all (Y, i) combinations at which the financial market is in equilibrium (money supply = money demand). It slopes upward: higher output raises money demand, which pushes the equilibrium interest rate up. Think of it as the "money-market equilibrium line" in (Y, i) space.
Real money supply (M/P)
Nominal money supply divided by the price level. In the short-run Keynesian model, prices are fixed, so changes in nominal money supply translate directly into changes in real money supply.
Real money demand, Y·L(i)
The demand for real money balances, which rises with income (Y) and falls with the interest rate (i). L(i) is a decreasing function of i because a higher interest rate raises the opportunity cost of holding money.
Fiscal policy
Government decisions about spending (G) and taxation (T). Expansionary fiscal policy means higher G or lower T. Restrictive fiscal policy means lower G or higher T.
Monetary policy
Central bank decisions about the money supply (M). Expansionary monetary policy increases M; restrictive (contractive) monetary policy decreases M.
Comparative statics
The method of comparing the old equilibrium to the new one after a parameter change, without tracing the path between them. In simple terms, you ask "where do we end up?" rather than "how do we get there?"
Policy mix
The simultaneous use of fiscal and monetary policy. For example, restrictive fiscal policy combined with expansionary monetary policy can reduce the interest rate while holding output steady.
Autonomous demand
The portion of aggregate demand that does not depend on current income: c₀ + I(0, i) + G − c₁T. For the goods market to function normally, this should be positive.
Crowding-in / crowding-out
Crowding-out: when government spending displaces private investment (e.g. higher G raises i, which reduces I). Crowding-in: the reverse, where a fiscal contraction frees up room for private investment.
The earlier assumption of fixed investment (I = Ī) is dropped. Investment now responds to two variables:
Expected sales, proxied by current output Y. Higher Y signals stronger demand, encouraging firms to invest. Positive relationship: I rises with Y.
The interest rate (i), which determines the cost of borrowing to finance investment. Higher i makes loans more expensive, discouraging investment. Negative relationship: I falls with i.
The investment function is written as I = I(Y, i), with (+, −) indicating the signs of the partial derivatives.
No specific functional form is assumed. The model works with the general shape.
Firms finance investment from three sources: internal profits, loan financing (where the interest rate matters), and issuing new equity (shares).
Empirical note: the negative relationship between investment and interest rates is theoretically standard but hard to confirm cleanly in the data. Scatter plots of the investment ratio (I/Y) or investment growth against interest rates show only a weak negative pattern.
With the new investment function, aggregate demand becomes:
Z = c₀ + c₁(Y − T̄) + I(Y, i) + Ḡ
Goods-market equilibrium requires Y = Z. For a given interest rate i, this pins down an equilibrium output Y.
Plotting all such (Y, i) pairs gives the IS curve.
The IS curve slopes downward:
A higher i reduces investment, which reduces aggregate demand, which (through the multiplier) reduces equilibrium Y.
A lower i does the reverse: more investment, more demand, higher equilibrium Y.
The IS curve is not a demand curve. It traces equilibria in the goods market, not quantities demanded at different prices.
What shifts the IS curve:
Taxes (T) increase: disposable income falls, consumption falls, demand falls at every i. The IS curve shifts left.
Government spending (G) increases: demand rises at every i. The IS curve shifts right.
Autonomous consumption (c₀) rises: demand rises at every i. The IS curve shifts right.
Movement along the IS curve: caused by a change in i (which changes investment and thus equilibrium Y).
Movement of the IS curve: caused by a change in G, T, or c₀ (which changes demand at every i).
Financial-market equilibrium requires real money supply = real money demand:
M̄/P = Y · L(i)
The money supply M̄ is set by the central bank. Prices are fixed in the short run (P = P̄), so there is no difference between nominal and real in this model.
In an (M/P, i) diagram, the supply curve is a vertical line and the demand curve slopes downward (higher i reduces money demand). Their intersection determines the equilibrium interest rate.
Plotting all (Y, i) pairs that satisfy this equilibrium gives the LM curve.
The LM curve slopes upward:
Higher Y raises money demand. With fixed money supply, the equilibrium interest rate must rise to restore balance.
The LM curve is not a supply curve. It traces equilibria in the financial market.
What shifts the LM curve:
Money supply (M) increases ("money is printed"): at every Y, the equilibrium i is lower. The LM curve shifts right.
Price level (P) rises: real money supply (M̄/P) falls. At every Y, the equilibrium i is higher. The LM curve shifts left.
The IS curve shifts left. The LM curve does not move (T does not appear in the money market).
New equilibrium: both Y and i fall.
The dynamic sequence:
Government raises T, lowering disposable income (Y_D).
Households cut consumption (C), aggregate income Y drops.
Lower Y shifts the money demand curve left, so i falls.
Investors face conflicting signals: lower i encourages investment, but lower Y discourages it. Consumers also spend less as Y_D has dropped. On balance, aggregate demand falls further.
Steps 3 and 4 repeat until the new equilibrium is reached.
Critique: contractive fiscal policy may generate additional private investment demand (crowding-in), as firms fill the gap left by reduced government activity. This effect is not captured in the basic model.
The IS curve shifts right. The LM curve does not move.
New equilibrium: both Y and i rise.
The logic is the mirror image of a tax increase.
The LM curve shifts right. The IS curve does not move (M does not appear in the goods market model).
New equilibrium: i falls and Y rises.
The dynamic sequence:
The central bank increases M, raising M/P. The interest rate drops sharply (Y has not moved yet).
Firms increase investment I(Y, i) in response to the lower i. Aggregate demand Y rises.
Higher Y increases money demand, pushing i back up, but not as far as it fell.
Higher aggregate demand Y boosts consumption and further investment.
Steps 3 and 4 repeat to the new equilibrium.
If market participants anticipate the new equilibrium, the economy may move along the IS curve directly rather than following the curved path described above. Expectations matter.
A government and central bank acting together can shift both curves at once.
Classic example: restrictive fiscal policy (IS shifts left) combined with expansionary monetary policy (LM shifts right) can hold output Y constant while lowering the interest rate i.
Limitation: a lower interest rate at the same output level may generate inflation in the medium run, when prices are no longer fixed. The central bank, legally obliged to control inflation, may refuse to cooperate.
Historical cases from Blanchard:
US in the 1990s: restrictive fiscal + expansionary monetary policy produced a balanced budget and strong growth.
Germany during reunification: expansionary fiscal + restrictive monetary policy produced a recession.
Investment function:
I = I(Y,\, i) \qquad (+,\, -)Goods-market demand (with endogenous investment):
Z = c_0 + c_1(Y - \bar{T}) + I(Y,\, i) + \bar{G}Goods-market equilibrium (IS relation):
Y = ZReal money supply:
\frac{M^s}{P} = \frac{\bar{M}}{P}Real money demand:
\frac{M^d}{P} = Y \cdot L(i)Financial-market equilibrium (LM relation):
\frac{\bar{M}}{P} = Y \cdot L(i)Autonomous demand:
c_0 + I(0,\, i) + \bar{G} - c_1 \bar{T}Central banks use interest rate adjustments to influence output and employment, which is the monetary policy channel of the IS-LM model in action. When a central bank cuts rates (shifting the LM curve right), the model predicts higher investment and higher output, which is broadly what policymakers intend during recessions.
Fiscal stimulus packages (higher G or lower T) work through the IS curve. The debate over whether governments should respond to downturns with spending increases or tax cuts maps directly onto the question of which shift of the IS curve is more effective.
Students often think the IS curve is a demand curve. It is not. It traces equilibrium points in the goods market, not quantities demanded at various prices.
Students often think the LM curve is a supply curve. Same error, different market. It traces equilibrium points in the financial market.
A common mistake is to say that a change in the interest rate "shifts" the IS curve. A change in i causes movement along the IS curve. Only changes in exogenous variables (G, T, c₀) shift the IS curve itself.
Students sometimes forget that the policy mix has limits. The model assumes fixed prices, so it cannot capture the inflationary consequences of holding output constant at a lower interest rate. In the medium run, prices adjust and the neat policy-mix result breaks down.
⚠️ Know the direction of every shift: which curve moves, which way, and what happens to Y and i at the new equilibrium. This is the most commonly tested skill in IS-LM questions.
⚠️ Be able to distinguish movement along a curve from a shift of the curve. A change in i moves you along IS; a change in G, T, or c₀ shifts IS. A change in Y moves you along LM; a change in M or P shifts LM.
⚠️ The dynamic adjustment stories (the step-by-step sequences for tax increases or money supply increases) are frequently tested as short-answer or essay questions.
⚠️ Understand the policy mix: how combining fiscal and monetary instruments can achieve a target (e.g. same Y, lower i) and why it may not work in the medium run.
⚠️ The empirical weakness of the investment-interest rate relationship is a fair exam topic. Be ready to explain why theory predicts a negative relationship that data shows only weakly.
True or false: the IS curve slopes upward in (Y, i) space.
Fill in the blank: an increase in government spending shifts the IS curve to the ____.
True or false: an increase in the money supply shifts the LM curve to the left.
Fill in the blank: at the IS-LM equilibrium, both the ____ market and the ____ market are in equilibrium simultaneously.
True or false: if the government raises taxes, the new IS-LM equilibrium has a higher interest rate.
Answers: 1. False (it slopes downward). 2. Right. 3. False (it shifts right). 4. Goods, financial. 5. False (both Y and i fall).
Q: In the IS-LM model, what happens to equilibrium output (Y) and the interest rate (i) when the government increases spending (G), holding everything else constant?
A: The IS curve shifts right. The LM curve does not move. The new equilibrium has higher Y and higher i.
Q: Explain the step-by-step dynamic adjustment when the central bank increases the money supply.
A: The central bank raises M, increasing M/P. The interest rate falls sharply (Y has not adjusted yet). The lower i stimulates investment, raising aggregate demand and Y. As Y rises, money demand increases, pushing i partly back up. Higher Y further increases consumption and investment. This process repeats until the new equilibrium is reached, with lower i and higher Y than before.
Q: Why does the IS curve slope downward?
A: A higher interest rate raises the cost of borrowing, reducing investment I(Y, i). Lower investment means lower aggregate demand, which through the multiplier leads to lower equilibrium output Y. So higher i corresponds to lower Y, giving a downward slope.
Q: A government wants to reduce its budget deficit without lowering output. Using the IS-LM model, explain how a policy mix could achieve this.
A: The government raises T or cuts G (restrictive fiscal policy), shifting the IS curve left. This would normally reduce Y. To offset this, the central bank simultaneously increases the money supply (expansionary monetary policy), shifting the LM curve right. With careful coordination, Y can remain unchanged while the interest rate falls and the deficit shrinks.
Q: What is the difference between a movement along the IS curve and a shift of the IS curve?
A: A movement along the IS curve is caused by a change in the interest rate i, which alters investment and therefore equilibrium Y. A shift of the IS curve is caused by a change in an exogenous variable (G, T, or c₀) that alters aggregate demand at every level of i.
This material builds directly on the goods-market model (Keynesian cross, the multiplier) and the financial-market model (money supply and demand). The IS-LM framework is later extended to include the labor market, forming the AS-AD model. The labor-market chapter (wages, prices, natural unemployment) provides the supply side that IS-LM lacks.
The policy-mix discussion connects to debates about central bank independence, inflation targeting, and the coordination problems between fiscal and monetary authorities.
IS-LM model, IS curve, LM curve, investment function, goods market equilibrium, financial market equilibrium, Keynesian cross, money market, real money supply, real money demand, fiscal policy, monetary policy, expansionary policy, restrictive policy, contractionary policy, comparative statics, dynamics, policy mix, crowding out, crowding in, autonomous demand, multiplier, interest rate, output, income, Hicks, Keynes, Blanchard macroeconomics