Topic 4

Goods and Financial Markets: The IS-LM Model

1. Introduction + Review

  • Building on the Keynesian model by adding the financial market to the goods market.

  • Analyzing the joint effects of:

    • Fiscal policy

    • Monetary policy

  • Main Intuition: financial and goods markets affect each other.

    • interest rate (i) => Investment (I) => income (Y) => (i) => (Y) etc.

So far… The Keynesian goods market model:

  • Unique homogeneous good

  • Investment (I) fixed

  • No indirect taxes, subsidies, depreciation

  • NI= GNP

  • Closed economy

  • Y= GDP = GNP

  • All quantities are real (in constant prices)

  • Public budget balance: tY – G – TR

    • Income tax revenues T=t *Y

    • t = constant income tax

    • Public consumption G, transfers TR

    • TR=transfers

    • G = public expenditures

  • Next step: make Investment (I) endogenous, i.e. make it vary with relevant macro variables, such as the interest rate.

2. The goods market reloaded: the IS line

  • In Topic 2, the interest rate did NOT affect the demand for goods. The equilibrium condition was given by: Y = C(Y) + I + G

  • Assume investment depends negatively on the interest rate: I(i) = \overline{I} - b \cdot i, \overline{I}, b > 0

    • I(i) denotes the fact that Investment is a function of (i), the interest rate

    • Some business projects are not implemented when interest rates are high

  • Using the definitions of C and I, the equilibrium condition in the goods market becomes:
    Z = \overline{C} + c_1(Y - tY + TR) + \overline{I} - b \cdot i + G = Y

  • Higher interest rate (i) lowers aggregate demand Z,

  • and production Y since, in equilibrium Z=Y.

The Algebraic derivation of the IS line

  • Start from the goods market equilibrium (Z=Y):
    Y = \overline{C} + c_1(Y - tY + TR) + \overline{I} - b \cdot i + G

  • Denote the spending multiplier \alpha = \frac{1}{1-c_1(1-t)}

  • Solve for the interest rate (i) as a function of output Y: i = \frac{A}{b} - \frac{1}{\alpha b}Y

    • Where A = \overline{C} + c_1TR + \overline{I} + G

  • This is the IS line

Numerical example

  • Start from the goods market equilibrium:

    • Private consumption C = 80 + 0.8 Yd

    • Investment I = 180 – 10 i

    • Public consumption G = 200

    • Income tax rate t = 0.25

    • Transfers TR = 25

  • Solve for the interest rate (i) as a function of output Y

  • Graph the IS line

Derive the IS curve graphically

  • Given some value of the interest rate, i

    • (i is not determined in the goods markets directly)

  • Start in equilibrium in the goods market (Keynesian) model

  • Depict what happens when interest rate increases: i’>i

  • Equilibrium in the goods market implies:

    • an increase in the interest rate leads to a decrease in output (everything else constant):

    • This relation is represented by the downward-sloping IS curve.

The IS Relation – Summary

  • Shifters: G, t, TR, \overline{C}, \overline{I}

    • Changes in factors that decrease the demand for goods, given the interest rate, shift the IS curve to the left.

    • Changes in factors that increase the demand for goods, given the interest rate, shift the IS curve to the right.

Numerical example (2)

  • Start from the goods market equilibrium:

    • Private consumption C = 80 + 0.8 Yd

    • Investment I = 180 – 10 i

    • Public consumption G = 200

    • Income tax rate t = 0.25

    • Transfers TR = 25

  • Calculate and graph the IS line if the tax rate becomes t=0.40

3. The financial market: the LM line

Financial market:

  • Money demand increases in nominal income (Y), declines in nominal interest rate (i)

  • In real terms: real money demand depends on real income (Y) and the interest rate
    L = k \cdot Y - h \cdot i, k > 0, h > 0

  • Money supply controlled by central bank

    • does not vary with the interest rate

  • In real terms: real money supply: \frac{M}{P}

    • M=stock of money, P= the price level

Financial Markets and the LM Relation

  • The interest rate is determined by the equality of the supply of and the demand for money:
    k \cdot Y - h \cdot i = \frac{M}{P}

  • This is the LM relation:

  • Everything else equal, higher real income (Y) increases the demand for money

  • And thus, the equilibrium interest rate (i)

The Algebraic derivation of the LM line

  • Start from the financial market equilibrium:
    k \cdot Y - h \cdot i = \frac{M}{P}

  • Solve for the interest rate (i) as a function of real output Y :
    i = \frac{k}{h} \cdot Y - \frac{1}{h} \frac{M}{P}

  • The upward sloping relation between real output (Y, on the horizontal axis) and interest rate (i, on the vertical axis) is the LM line.

Numerical example (3)

  • Assume:

    • Price level P = 5

    • Real money demand L = 0.48 Y – 12 i

    • (Nominal) Money supply M = 1,920

  • Calculate and graph the LM line

Derive the LM curve graphically

  • Given some value of the real income (Y)

    • (Y is not determined in the financial markets directly)

  • Start in equilibrium in the financial market model (L=\frac{M}{P})

  • Depict what happens when real income increases: Y’>Y

  • Equilibrium in the financial market implies:

    • an increase in real income leads to an increase in the interest rate (given a real money supply):

    • This relation is represented by the upward-sloping LM curve.

The LM Relation - Summary

  • Shifters: M, P

    • An increase in real money supply \frac{M}{P}, at a given real income, shifts the LM line down.

    • A decrease in real money supply \frac{M}{P}, at a given real income, shifts the LM line up.

Numerical example (4)

  • Assume:

    • Price level P = 5

    • Real money demand L = 0.48 Y – 12 i

    • (Nominal) Money supply M = 1,920

  • Calculate and graph the LM line when M=2400

4. Equilibrium of the economy in the short run: the IS-LM model

Putting the IS and the LM Relations Together

  • Equilibrium in the goods market implies: i↑ => Y↓ (the IS line)

  • Equilibrium in financial markets implies: Y ↑ => i ↑ (the LM line)

  • Only at point A, which is on both curves, are both goods and financial markets in equilibrium.

  • This gives the output (and income ) Y^ and the interest rate (i^) that will prevail in the short-run

The Algebraic derivation of the IS-LM model

  • Write the IS equation: i = \frac{A}{b} - \frac{1}{\alpha b}Y

  • Write the LM equation: i = \frac{k}{h} \cdot Y - \frac{1}{h} \frac{M}{P}

  • Solve for Y and i

  • Given values for A, t, \alpha, k, h, M, P

  • At equilibrium :
    Y^* = \frac{\alpha h}{\alpha b k + h}A + \frac{\alpha b}{\alpha b k + h}\frac{M}{P}
    i^* = \frac{\alpha k}{\alpha b k + h}A - \frac{1}{\alpha b k + h}\frac{M}{P}

Numerical example (5)

  • Private consumption C = 80 + 0.8 Yd

  • Investment I = 180 – 10 i

  • Public consumption G = 200

  • Income tax rate t = 0.25

  • Transfers TR = 25

  • Price level P = 5

  • Real money demand L = 0.48 Y – 12 i

  • (Nominal) Money supply M = 1,920

  • Find the equilibrium Y^ and i^

5. Policy analysis: expansionary fiscal policy

  • Fiscal contraction, or fiscal consolidation, refers to fiscal policy that reduces the budget deficit.

  • An increase in the deficit is called a fiscal expansion.

  • Fiscal policies affect the IS curve, not the LM curve.

Expansionary fiscal policy

  • The effects of an increase in public spending

  • An increase in G shifts the IS curve to the right and leads to an increase in the equilibrium level of output and the equilibrium interest rate

  • Effects:

    • Increase in income Y

    • Increase interest rate i

    • C=?

    • I=?

    • PBD=?

Expansionary fiscal policy: the crowding out effect

  • The increase in Y is moderated by the increase in interest rates

  • As IS shifts right, Y increases, there is a move up the LM line

  • The increase in i hurts private investment

  • This is the crowding-out effect
    Y = C + I + G

6. Policy analysis: expansionary monetary policy

  • Monetary contraction, or monetary tightening, refers to a decrease in the money supply.

  • An increase in the money supply is called monetary expansion.

  • Monetary policy does not affect the IS curve, only the LM curve. For example, an increase in the money supply shifts the LM curve down.

Expansionary monetary Policy

  • The effects of a monetary expansion

  • A monetary expansion leads to higher output and a lower interest rate

  • Effects:

    • Increase income Y

    • Lowers interest rate i

    • C=?

    • I=?

    • PBD=?

7. Policy analysis: the liquidity trap

  • The combination of:

    • very low (zero) short-term nominal interest rates

    • Low inflation rate or deflation

    • Low economic growth or recession

  • Conventional monetary policy cannot increase output in the short-run

  • Expansionary fiscal policy more appropriate

8. The policy mix

  • The combination of monetary and fiscal polices is known as the monetary-fiscal policy mix, or simply, the policy mix.

  • Sometimes, the right mix is to use fiscal and monetary policy in the same direction.

  • Sometimes, the right mix is to use the two policies in opposite directions

The policy mix

  • Expansionary fiscal + expansionary monetary policies

    • Increases income without increasing interest rates

    • Public budget deficits are met by expansionary monetary policies

    • Typical downside: increased inflation

  • Expansionary fiscal + contractionary monetary policies

    • Controls inflation

    • Strong increase in interest rates

    • Strong crowding out effects

The policy mix Table 1 The Effects of Fiscal and Monetary Policy

Policy

Tool (instrument)

Effect on the money supply

Ultimate effect

Expansionary

• Reduce the reserve ratio • Reduce reference interest rate • Purchase bonds in Open market operations

M

GDP (eventually inflation)

Contractionary

• Increase the reserve ratio • Increase reference interest rate • Sell bonds in Open market operations

M

GDP (eventually disinflation)

| | | | |
| The policy mix Table 1 | | | |

| | | | |
| | IS | LM | Movement in Output | Movement in Interest Rate | |
| Increase in tax rate | Left | None | Down | Down |
| Decrease in tax rate | Right | None | Up | Up |
| Increase in spending | Right | None | Up | Up |
| Decrease in spending | Left | None | Down | Down |
| Increase in money | None | Down | Up | Down |
| Decrease in money | None | Up | Down | Up |

9. Conclusions

  • IS-LM describes well the short-run evolution of the economy

  • Prices change little in the short-run

  • Survey of Eurozone companies (2019)

Frequency of Price Changes over one year (UK)

  • 0 (6%)

  • 1 (37%)

  • More than 12 (6%)

  • 5-12 (8%)

  • 3-5 (17%)

  • 2 (26%)

  • Frequency of price changes over one year. The majority of firms change prices twice a year or less. Source: Hall, Walsh and Yates. How Do U.K. Companies Set Prices?. Bank of England Working Paper 67 (1997).