The Multiplier and Accelerator, Demand for and Supply of Money, and the IS-LM Model

This chapter brings the goods market and the money market together. It covers the multiplier and the accelerator, the competing theories of money demand, the determinants of money supply, and the IS-LM model that shows both markets clearing simultaneously; the next chapter covers inflation, business cycles, monetary-fiscal policy and the rational expectations critique.

1. The Multiplier and the Accelerator

The simple investment multiplier k = ΔY/ΔI = 1/(1−MPC) = 1/MPS shows that a rise in autonomous spending raises equilibrium income by a MAGNIFIED amount, because each round of new spending becomes someone else's income, part of which is re-spent. A higher MPC (lower MPS) means each round leaks less into saving, so the multiplier is larger; a multiplier of exactly 1 would mean no further rounds of spending at all (MPC = 0), which is why the multiplier is always strictly greater than 1 whenever 0 < MPC < 1. The accelerator principle, by contrast, links NET investment to the RATE OF CHANGE of output/demand, not its level: if capital-output ratio v is fixed, desired capital stock is K* = vY, so induced investment I = v(ΔY) — investment surges when output growth accelerates and can turn negative merely when output growth decelerates, even while output itself is still rising.

🎯 Why the multiplier and accelerator interact to amplify business cycles
The two mechanisms compound each other: an initial rise in autonomous spending raises income (multiplier), the rising income induces new investment through the accelerator, which itself is additional spending that the multiplier magnifies again — the Samuelson multiplier-accelerator interaction model formalises this feedback loop and, depending on the specific values of MPC and the accelerator coefficient v, can generate oscillating, damped, or explosive paths of income over time.

2. Demand for Money

Keynes's liquidity preference theory identifies three motives for holding money: the transactions motive (for day-to-day expenditure, rising with income), the precautionary motive (for unforeseen needs, also rising with income), and the speculative motive (holding money rather than bonds when the interest rate is expected to rise, since bond prices and interest rates move inversely) — the speculative motive makes money demand a DECREASING function of the interest rate. Total money demand is therefore Md = L1(Y) + L2(r), rising in income and falling in the interest rate. At very low interest rates, the speculative demand for money can become perfectly (infinitely) elastic — the LIQUIDITY TRAP — where everyone expects rates to rise (bond prices to fall) and prefers to hold cash, so monetary policy loses traction entirely.

ℹ️ The Baumol-Tobin and Friedman alternatives
The Baumol-Tobin inventory-theoretic model derives the transactions demand for money from an explicit cost-minimisation problem (weighing the interest forgone on idle balances against the cost of frequent trips to convert bonds to cash), predicting economies of scale in money holding. Milton Friedman's restatement of the quantity theory treats money as one asset among many in a broader portfolio, with money demand a stable function of permanent income and the returns on alternative assets — a very different foundation from Keynes's motive-based approach, but converging on money demand still depending on income and interest rates.

3. Supply of Money

Money supply is exogenously set (in the standard textbook model) as the product of the monetary base (high-powered money, H — currency plus commercial bank reserves) and the money multiplier: Ms = m × H. The money multiplier m = (1+cdr)/(cdr+rr), where cdr is the currency-deposit ratio (the public's preference for holding cash over deposits) and rr is the reserve-deposit ratio (the fraction of deposits banks hold as reserves, partly a statutory requirement and partly precautionary), is greater than 1 whenever rr < 1 — commercial banks 'create' money through repeated rounds of lending and re-depositing, exactly the credit-creation multiplier process. A rise in either the currency-deposit ratio or the reserve ratio SHRINKS the money multiplier and hence the money supply for a given monetary base.

  • Central bank tools that shift H — open market operations, the bank rate/repo rate, and reserve requirements are the classic levers, covered in depth in the Money and Banking unit.
  • Exogenous versus endogenous money supply — the textbook model treats Ms as centrally controlled; an alternative endogenous-money view (associated with post-Keynesian economics) holds that bank lending itself creates deposits on demand, making the money supply respond to the demand for credit rather than being fixed independently.

4. The IS-LM Model

The IS curve plots combinations of income (Y) and the interest rate (r) at which the GOODS market is in equilibrium — planned investment (a decreasing function of r) equals planned saving (an increasing function of Y) — and slopes DOWNWARD: a lower interest rate raises investment, which raises equilibrium income via the multiplier. The LM curve plots combinations of Y and r at which the MONEY market is in equilibrium — real money demand (rising in Y, falling in r) equals the (exogenously fixed) real money supply — and slopes UPWARD: higher income raises transactions money demand, which requires a higher interest rate to choke off speculative demand and keep total money demand equal to the fixed supply. The economy's simultaneous equilibrium in both markets is at the unique (Y, r) where the two curves intersect.

What shifts the IS curve and the LM curve
CurveShifts right when
ISAutonomous expenditure rises — government spending increases, taxes fall, or business optimism (the MEC schedule) improves; expansionary fiscal policy is precisely a rightward IS shift.
LMThe real money supply rises — an expansionary monetary policy action, holding the price level fixed; this lowers the interest rate needed to clear the money market at any given income.
🧠 Fiscal versus monetary policy potency depends on the slopes of IS and LM
A steep LM curve (money demand not very interest-sensitive) makes fiscal policy weak, because the rise in income from higher government spending pushes up the interest rate sharply, crowding out private investment — the CROWDING-OUT effect. A flat LM curve (the liquidity trap, where LM is horizontal) makes fiscal policy maximally potent (no crowding out at all) and monetary policy completely IMPOTENT, since a rightward LM shift in a horizontal region changes neither income nor the interest rate. NET has tested exactly this comparative-statics logic across all four combinations of steep/flat IS and LM.

Key takeaways

  • The simple multiplier k = 1/(1−MPC) = 1/MPS is always greater than 1 for 0 < MPC < 1; the accelerator links induced investment to the RATE OF CHANGE of output (I = vΔY), and the two interact (Samuelson's model) to amplify cycles.
  • Keynesian money demand has three motives — transactions and precautionary (rising in income) and speculative (falling in the interest rate) — and at very low rates can become perfectly interest-elastic, the liquidity trap, where monetary policy loses traction.
  • Money supply Ms = m × H, where the money multiplier m = (1+cdr)/(cdr+rr) exceeds 1 whenever the reserve ratio is below 1 — the mechanism of bank credit creation.
  • The IS curve (goods-market equilibrium) slopes downward and the LM curve (money-market equilibrium) slopes upward; their intersection gives the unique income-interest rate pair clearing both markets simultaneously.
  • A steep LM makes fiscal policy weak through crowding out; a horizontal LM (liquidity trap) makes fiscal policy maximally potent and monetary policy completely impotent.

Practice questions (9)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. If MPC = 0.8, the value of the simple investment multiplier is:

    1. 5
    2. 0.8
    3. 1.8
    4. 0.2
    Show answer

    Answer: A — 5

    k = 1/(1−MPC) = 1/(1−0.8) = 1/0.2 = 5 — a common numerical item testing direct substitution into the multiplier formula.

  2. The accelerator principle links induced (net) investment to:

    1. The rate of change of output/demand, not its level
    2. The absolute level of output only
    3. The interest rate only
    4. The money supply only
    Show answer

    Answer: A — The rate of change of output/demand, not its level

    With a fixed capital-output ratio v, desired capital is K* = vY and induced investment is I = vΔY — investment depends on the CHANGE in output, so it can turn negative merely when output growth decelerates, even while output itself keeps rising.

  3. The speculative motive for holding money, in Keynes's liquidity preference theory, makes money demand:

    1. A decreasing function of the interest rate
    2. An increasing function of the interest rate
    3. Independent of the interest rate entirely
    4. A function of the price level only
    Show answer

    Answer: A — A decreasing function of the interest rate

    Since bond prices and interest rates move inversely, expecting rates to rise (bond prices to fall) makes holding money rather than bonds attractive — so speculative money demand rises as the current interest rate falls.

  4. In the liquidity trap, monetary policy loses effectiveness because:

    1. Speculative money demand becomes perfectly interest-elastic, so extra money is simply absorbed into idle balances without lowering the interest rate further
    2. The government stops issuing bonds
    3. MPC falls to zero
    4. Prices become perfectly flexible
    Show answer

    Answer: A — Speculative money demand becomes perfectly interest-elastic, so extra money is simply absorbed into idle balances without lowering the interest rate further

    At the trap, the LM curve is horizontal — everyone expects rates to rise (bond prices to fall) and prefers cash, so an increase in money supply cannot push the interest rate down any further and has no effect on income.

  5. If the currency-deposit ratio rises while the reserve-deposit ratio stays constant, the money multiplier:

    1. Falls, since a larger share of high-powered money is held as currency outside the banking system rather than as deposits available for re-lending
    2. Rises
    3. Stays exactly the same
    4. Becomes negative
    Show answer

    Answer: A — Falls, since a larger share of high-powered money is held as currency outside the banking system rather than as deposits available for re-lending

    In m = (1+cdr)/(cdr+rr), a rising cdr shrinks the multiplier — more cash held outside banks means less deposit base for the credit-creation process, cutting the number of re-lending rounds.

  6. The IS curve slopes downward because:

    1. A lower interest rate raises investment, which raises equilibrium income via the multiplier
    2. A lower interest rate raises money demand only
    3. Higher income requires a higher interest rate to clear the money market
    4. The government budget must always balance
    Show answer

    Answer: A — A lower interest rate raises investment, which raises equilibrium income via the multiplier

    The IS curve traces goods-market equilibrium; since investment is a decreasing function of the interest rate and the multiplier translates any change in investment into an amplified change in income, lower r maps to higher equilibrium Y — the negative slope. Option (c) actually describes why LM slopes upward, not IS.

  7. A very steep (near-vertical) LM curve makes expansionary fiscal policy relatively weak because:

    1. The rise in income sharply raises the interest rate, crowding out private investment
    2. It shifts the IS curve to the left
    3. Government spending has no multiplier effect at all
    4. The money supply automatically falls
    Show answer

    Answer: A — The rise in income sharply raises the interest rate, crowding out private investment

    A steep LM means money demand is not very interest-sensitive, so even a small rightward IS shift (from higher government spending) needs a large rise in the interest rate to keep the money market in equilibrium — that large interest-rate rise substantially crowds out private investment.

  8. Which of the following shift the LM curve to the right?

    1. An increase in the real money supply
    2. A fall in the reserve-deposit ratio, which raises the money multiplier and hence the money supply
    3. An open market purchase of bonds by the central bank
    4. An increase in government spending
    Show answer

    Answer: A — An increase in the real money supply; B — A fall in the reserve-deposit ratio, which raises the money multiplier and hence the money supply; C — An open market purchase of bonds by the central bank

    The first three all raise the money supply and shift LM rightward (lower interest rate needed at any given income); a rise in government spending is a fiscal action that shifts the IS curve, not the LM curve.

  9. Name the effect, central to IS-LM comparative statics, in which higher government spending raises the interest rate and thereby displaces (reduces) private investment.

    Numerical answer — type the value.

    Show answer

    Answer: crowding out

    Crowding out is the standard name: expansionary fiscal policy raises the interest rate along a given LM curve, and the resulting fall in interest-sensitive private investment offsets part of the multiplier's expansionary effect on income.