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Resources › IS–LM to AD–AS › 3. LM curve
IS–LM to AD–AS · Lesson 3 of 10

The LM curve: the money market

Lesson 1 built the demand for money; the central bank fixes the supply. When income rises, people want more money for transactions, and with the supply fixed only a higher interest rate can talk them out of it. Plot those pairs and you have LM, the other half of the model.

← IS–LM to AD–AS moduleLesson 3 of 10 · about 35 minutes
1Money demand2IS curve3LM curve4IS–LM5Policy6AD–AS7Phillips curve8Expectations9Open economy10Hard problems
A question to hold on to
In a two-sector model, C = 60 + 0.80y, I = 116 − 2i, money demand L = 0.20y − 5i and the money supply M = 120. What is the equation of the LM curve?
CUET-PG Economics, 2026Solved at the end ↓
In this guide
Lesson · about 35 minutes
  1. The money market
  2. Deriving LM, one income at a time
  3. The equation of the LM curve
  4. What makes LM steep or flat
  5. Vertical, horizontal, and a central bank that pegs the rate
  6. What shifts LM
  7. The opening question, solved
  8. The lesson on one screen
  9. Check yourself
  10. Past papers, by level
01
The idea

The money market

The central bank decides how many rupees exist, M. With the price level fixed for now, that fixes real balances M/P: the supply of money is a vertical line. Demand is Lesson 1’s liquidity preference, L = kY − hr: more income means more transactions, a higher interest rate means a higher cost of holding money. The interest rate adjusts until people are content to hold exactly the money there is.

How does it adjust? If people hold more money than they want, they buy bonds with the surplus. Bond prices rise, and since PB = C/r the interest rate falls, until the extra money is wanted. A shortage of money works the other way: people sell bonds and the rate rises.

Money-market equilibrium
PM​=kY−hr
m = M/P is real balances. k: how much money demand rises with income. h: how much it falls with the interest rate.

The LM curve is every combination of income and the interest rate at which this holds: the locus where the quantity of money demanded equals the quantity supplied (CUET 2019). Since money and bonds are the two assets, it is also where the asset market as a whole is in equilibrium (CUET 2022). Its name comes from Liquidity preference equal to the Money supply.

02
Interactive

Deriving LM, one income at a time

Pick an income. Money demand is a downward line in the money market; where it meets the fixed supply is the interest rate. Now raise income: demand shifts right, and with supply fixed the rate must rise. Each (Y, r) pair is a point on LM, which slopes upward. Then try h = 0, and the liquidity-trap box.

1. The money market at Y = 1,20020040060080010005101520M/Pr %supply mdemand L
2. The LM curve: each Y and the r that clears money5001000150020005101520Yr %LM
The chain

Y = 1,200 → money demand at each rate is 600 − 20r → it equals 400 at r = (600 − 400) ÷ 20 = 10%.

The equation and its slope

LM: r = (0.5Y − 400) ÷ 20. Slope dr/dY = k/h = 0.025: steeper when money demand responds more to income, flatter when it responds more to the interest rate. More money, m, shifts LM right.

Pause and predict
Income rises and the money supply is unchanged. To keep the money market in equilibrium, the interest rate must
03
The algebra

The equation of the LM curve

The LM curve
r=hkY−M/P​orY=kM/P+hr​
Solve the money-market condition for r, or for Y. The consumption and investment functions play no part.
JNU 2021 · foundation
Money demand is 0.5Y − 50r and the money supply is ₹1,000 crore. Find the LM equation.
  1. 1
    Set demand equal to supply.
    1,000 = 0.5Y − 50r.
  2. 2
    Solve for Y.
    Y = 2,000 + 100r.
Answer
Y = 2,000 + 100r.
CUET 2023 · standard
Money demand is L = 0.25Y and real money supply is 500. What does the LM curve look like?
  1. 1
    Set L = M/P.
    0.25Y = 500, so Y = 2,000.
  2. 2
    No r in it.
    Whatever the interest rate, only Y = 2,000 clears the money market.
Answer
A vertical LM curve at Y = 2,000: the quantity theory’s LM.

UGC NET 2023 asked which equation could represent the money market: 300 = 2Y − 1.5i, money supply on one side and a demand that rises with Y and falls with i on the other. Its companion asked which description of LM is wrong: the one calling it combinations of investment and the interest rate.

04
The shape

What makes LM steep or flat

One more unit of income raises money demand by k. To choke that off, the interest rate has to rise by k/h. So LM is steeper when money demand responds strongly to income, and flatter when it responds strongly to the interest rate (JNU 2021; DSE 2006, 2017).

The slope of LM
dYdr​​LM​=hk​
In general, differentiating M/P = L(Y, r) gives dY/dr = −L_r/L_y along LM (CUET 2023); with L = kY − hr that is h/k, or dr/dY = k/h.
Pause and predict
ATMs and digital payments spread, and money demand becomes less sensitive to the interest rate. The LM curve (Hyderabad 2020)
An endogenous money supply

Suppose the money supply itself rises with the interest rate: banks lend more when rates are high. Then as income rises and pushes r up, extra money appears and the rate rises less. LM is flatter than with a fixed supply (DSE 2008; JNU 2020), and fiscal policy becomes more effective (DSE 2013).

05
The limits

Vertical, horizontal, and a central bank that pegs the rate

Vertical (h = 0): the classical case. If money demand ignores the interest rate, as in the quantity theory, only one income clears the money market, Y = (M/P)/k. The classical LM must be vertical (JNU 2021).

Horizontal (h → ∞): the liquidity trap. At a floor rate people will hold any amount of money, so income can rise without the rate rising. LM is flat at the floor (CUET 2023): monetary policy cannot push it lower.

A third case is common in recent papers. If the central bank sets the interest rate and supplies whatever money is demanded at that rate, the money supply becomes endogenous, and LM is simply a horizontal line at the chosen rate (CUET 2024; UGC NET 2023). That is how most central banks, including the RBI with its repo rate, actually run policy today.

06
The movers

What shifts LM

At a given interest rate, LM moves whenever the income that clears the money market changes:

  • More money shifts LM right (down): more income is needed to absorb it at each rate (Hyderabad 2012, 2014; JAM 2023).
  • A higher price level lowers real balances M/P and shifts LM left (up); a lower price level shifts it right (DSE 2005). Lesson 6 turns this into the AD curve.
  • A rise in money demand at each income and rate (say, more precautionary holding) shifts LM left.

A point to the right of LM has too much income for its interest rate: people want more money than there is, an excess demand for money. To the left, an excess supply of money.

The size of the shift
ΔY​r fixed​=kΔ(M/P)​
Horizontal shift at a given r when real balances change by Δm.
07
Solving the opening question

The opening question, solved

CUET 2026 · standard
C = 60 + 0.80y, I = 116 − 2i, L = 0.20y − 5i and M = 120. Find the LM equation.
  1. 1
    Ignore C and I.
    They belong to the IS curve. LM uses only the money market.
  2. 2
    Set L = M.
    120 = 0.20y − 5i.
  3. 3
    Solve for i.
    5i = 0.20y − 120, so i = 0.04y − 24.
Answer
i = 0.04y − 24. The options with 0.10y come from solving the goods market instead.
Watch out for

The mistakes examiners are fishing for

  • Using the goods market. Consumption and investment functions in an LM question are there to tempt you.
  • Flat against steep. High interest sensitivity of money demand makes LM flatter; high income sensitivity makes it steeper.
  • Nominal against real money. LM shifts with M/P, so a rise in prices has the same effect as a cut in the money supply.
  • Direction of a money-supply shift. More money: LM moves right, which is also down.
08
Revise

The lesson on one screen

The lesson on one screen
Money market
M/P = kY − hr. The rate clears it, through bond prices.
LM
Pairs (Y, r) where money demand = money supply. Slopes up.
Equation
r = (kY − M/P)/h.
Slope
k/h. Flatter with larger h; steeper with larger k or smaller h.
Extremes
h = 0: vertical (classical). Liquidity trap or a pegged rate: horizontal.
Shifts
M up or P down → right by Δ(M/P)/k. Money demand up → left.
Off the curve
Right of LM: excess demand for money. Left: excess supply.
09
Practice

Check yourself

0 of 6 correct so far

Compute

LM equation
M = 600, P = 2 and money demand is 0.25Y − 10r. What interest rate clears the money market when Y = 1,600?
Slope
Money demand is 0.4Y − 80r. What is the slope dr/dY of LM?
Shift
With k = 0.5, real money supply rises by 40. How far does LM shift to the right?

Quick questions

1A positively sloped LM curve is relatively flat when the interest elasticity of money demand is
2If the central bank fixes the interest rate and supplies whatever money is demanded, LM is
3The LM curve shifts right if
10
Real questions

Past papers, by level

Foundation

Definitions, directions of shifts and one-step problems. Most CUET, UGC NET and Hyderabad questions sit here.

4 questionsPractise →

Standard

Solving models, comparing slopes and multi-step reasoning, up to the hardest JNU, JAM and GATE questions.

14 questionsPractise →

Delhi School level

This topic’s hardest questions, from the DSE entrance, are worked through in Lesson 10: IS–LM in letters.

31 questionsLesson 10 →
All 18 past-paper questions for this lesson, easiest first: practise the full set →

✦These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.

← Lesson 2The IS curve: the goods marketLesson 4 →IS and LM together

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