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 ) $Y^<em>$ and the interest rate $(i^</em>)$ 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 $Y^<em>$ and $i^</em>$

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

| | | | |
| 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).