Topic 1 The IS LM Model Lecture Notes PDF

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IS–dl arnngutms By the end of this chapter, and having completed the Essential reading and activities, you should be able to: • • • • •

list and discuss the key equations of the IS–LM model describe the determinants of the intercept and the slope of both the IS and the LM curves calculate the equilibrium level of output and the interest rate in a closed economy with fixed wages and prices evaluate how any change in the variables and the parameters of the IS–LM model alters the equilibrium levels of output and the interest rate show how fiscal and monetary policies contribute to the determination of output and the interest rate in the short run, and their use as tools for macroeconomic stabilisation illustrate and explain the Keynesian view of short-run fluctuations in economic activity.

Essential readings: 1. Mankiw, N.G. Macroeconomics. (9th Edition) Chapters 3, 4 and 11. 2. Blanchard, O. and D.R. Johnson Macroeconomics. (2012) Chapters 2–5.

. Intrdutn •

The IS–LM model demonstrates the equilibrium relationship between interest rates and real output in the goods and the money market.

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The model focuses on the assessment of aggregate demand, in the short run, and in a closed economy.

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The model allows us to assess the factors that determine short-run fluctuations; and how macroeconomic policy can be employed to stabilise the economy in the short-run.

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The closed economy assumption means that the model is studied, without taking into account the effect of foreign trade on domestic aggregate demand.

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The short run is defined as the period of time during which the price level is fixed (no inflation)1. In the short run, say, one year, demand determines output.

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Therefore, the IS–LM model is useful in analysing the effects of stabilisation policy on real output and the real interest rate, but it cannot be employed to assess issues related to inflation, unemployment, and the exchange rate.

1 The

price level is a sluggish or sticky variable. It does not respond immediately to a macroeconomic disturbance. The adjustment of price builds up gradually, and it is fully completed after several years

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2. GdsarktSuly •

In a closed economy, output is equated with gross domestic product (GDP). Output has three equivalent definitions: (1) the value of final goods and services produced during a given period, (2) the sum of value added during a given period, and (3) the sum of labor and capital income and indirect taxes.

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The growth rate of real (nominal) GDP is the rate of change of real (nominal) GDP.

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Periods of positive GDP growth are called expansions; periods of negative growth, recessions.

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The economy has certain resources, most notably its labor and its stock of machines and factories (its capital stock).

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Firms in the economy use labor and capital as inputs to produce goods and services (GDP).

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We express the economy’s ability to produce goods and services from its resources as Y = F(K, L).

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This says simply that the amount of GDP an economy can produce depends on its capital stock K and its labor L.

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More capital or more labor allows the economy to produce more output.

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An example of a production function called Cobb–Douglas Production Function which is Y = K α L1−α

Exercise: what happens to output Y if we double the amounts of K and L?



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3. GdsarktDmand •

In a closed economy, demand for goods and services produced by the economy comes from consumption, investment, and government spending. 1) Consumption

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Consumption is the largest source of demand.

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Denoted as C, consumption is defined as the value of goods and services purchased by households and it follows the following functional form:

C = c0 + c1 (Y − T ) where c0 ≥ 0, 0 < c1 < 1

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–  indicates disposable income.

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c0 is the autonomous component of consumption. The value of c 0 depends also upon consumers’ spending habits and consumer confidence about current and future spending opportunities. It also measures the level of consumption affected by factors other than disposable income.

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c1 is the marginal propensity to consume (MPC). It measures the increase in consumption resulting from one unit increase in disposable income.

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Since 0 < c1 1. 1 − c1 (1 −τ 1 ) 1− c1 (1− τ 1 )

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Hence, an increase in a unit of the autonomous demand will result in increase in the equilibrium income by more than one unit.

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The balanced-budget fiscal multiplier refers to the ratio of the change in output to the change in government spending in the case where both government spending and taxes are changed by the same amount.

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Specifically, the balanced-budget fiscal multiplier is

∆Y following an increase in G and T ∆G

by ∆G and ∆T respectively where ∆G = ∆T .

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Exercise : Assuming τ 1 = 0 , check that the balanced-budget fiscal multiplier will equal to 1. If

0 < τ1 < 1, then the balanced-budget fiscal multiplier will be less than 1.

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Note a bigger the multiplier is associated with a flatter IS curve caused by a larger multiplier effect leading to a higher increase in equilibrium income for the same decrease in interest rate.

r

r0

A

B'

r1

B IS ' IS

Y0

Y1

Y2

Y

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7. Money, Bonds and the Financial Market •

Money which has no intrinsic value—such as dollar bills—is known as fiat money. It is money because the government says so.

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Why are people willing to give up valuable goods in exchange for intrinsically worthless pieces of paper?

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People hold money because it serves three useful functions: 1) Medium of Exchange: Money makes exchange easier. In an economy without money (a barter economy), people would spend a lot of time carrying out exchanges. 2) Store of Value: People will hold money only if they believe it will continue to have some value in the future, so money can operate as a medium of exchange only if it serves as a store of value as well. 3) Unit-of-Account: it is convenient to have a widely recognized measure for accounting and transactions using monetary units as the prices.

Research: Is Bitcoin a type of money?

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According to the Keynesian Liquidity Preference theory, financial market includes only two assets: money and bonds.

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Money is a liquid asset that can be used to purchase goods and services . However, it pays no interest.

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Bonds are financial assets that pay fixed amount of coupon payments at fixed intervals of time and face value upon maturity.

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Bonds are issued by the government and cannot be used for transactions.

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Assuming all bonds pay no coupon payment, individuals buy bonds at a price lower than the face value. The difference between the price and the face value of a bond is the gain/loss for the bond holder.

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Since the face value is fixed, the lower the price of bond the higher is the gain for the bond holder.

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The rate of return from investment in bonds, the nominal interest rate, is calculated by dividing the gain from bonds by the current price. Prepared by Dr Zhang Jianlin | Restricted materials for Singapore Institute of Management

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Let   indicates the face value of the bond and  is the current price of bonds, analytically, the relationship between the interest rate and the price of a bond is written as:

=

    −  = −1  

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An increase in the price of bond,, reduces the interest rate. The interest rate and the price of bonds are inversely related.

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An alternative method to find the price of a bond is by discounting the bond’s future payments.

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The equilibrium condition in the financial market states that the demand for money, Md, and bonds, Bd, must be equal to the supply of money, Ms, and bonds, B s: Md + Bd = Ms + Bs

 M d – Ms = Bs – Bd

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Since bonds and money are the only two assets available, equilibrium in money market automatically leads to equilibrium in bond market2 .

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For this reason, we ignore the bond market in what follows, and make use only of the money market equilibrium condition.

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This is an implication of Walras’ law, which states that if there are n markets and the first n–1 markets are in equilibrium, then also the n-th market is in equilibrium.

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8. Money Demand •

Suppose the financial markets include only two assets: money, which can be used to purchase goods and services and pays no interest; and bonds, which cannot be used for transactions, but pay a positive interest rate i.

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Financial wealth equals the sum of money and bonds.

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Money demand is then a portfolio decision, i.e., the amount of fixed wealth that the nonbank public desires to hold in money as opposed to bonds.

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The higher the output produced in the economy, the higher the level of transactions would need to be taken place, the more money is demanded.

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The interest rate can be regarded as the opportunity cost of holding money. The higher the interest rate, the higher is the cost of holding money, the lower the money demand.

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The demand for money, M d, is thus positively related to income and negatively related to the nominal interest rate. Analytically, real money demand is described as: !" = ℎ  + ℎ  − ℎ $ 

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Note the demand for money is a demand for real balances, implying that individuals are free from money illusion3.

i

%& , '

rather than nominal balances

i

L (Y 0 , i ) h2 L ( Y1 , i ) L ( Y0 , i ) M P

L( Y0 , i )h 2 M P

3

When individuals suffer from money illusion, they think of currency in nominal terms rather than taking into account its purchasing power.

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9. Money Supply •

The supply of money, MS, is assumed to be independent from the interest rate and it is directly controlled by the central bank.

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The central bank can change money supply through open market operations which are based upon the following simplifying assumptions: 1) The central bank has direct control over money supply through open market operations. 2) The government issues bonds on behalf of the central bank; the central bank does not directly issue bonds, but can only create money to buy bonds issued by the government. 3) Individuals are always willing to trade bonds at some price (i.e. bond demand from the private sector is unlimited).

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Consider a simplified central bank’s balance sheet in the following table. The central bank’s assets are represented by bonds, while the central bank’s liabilities are represented by the currency (money) held by the public.

Money expansion

Central Bank Balance Sheet Liabilities Assets Bonds Money Increase bond holding  Bond New money are created to buy price rises  additional bonds  Money supply Interest rate falls rises

Money contraction

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To increase the money supply, the central bank has to purchase new bonds from private sector. This increases both assets (through the additional bonds) and liabilities (through the new currency created and exchanged for bonds).

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When the central bank buys bonds from the private sector, the excess demand for bonds raises the price of bonds, in turn, it reduces the interest rate.

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To reduce the money supply, the central bank sells bonds for existing currency. This operation reduces assets (through the sale of bonds) and liabilities (through the reduction of currency held by the general public).

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As a result of excess supply the bond price falls, the interest rate increases, and money demand decreases.

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Analytically, real money supply is written as: !( ! =    Prepared by Dr Zhang Jianlin | Restricted materials for Singapore Institute of Management

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where M is the level of nominal money supply chosen by the central bank. •

Graphically, this is shown below:

i

M0 P

M P

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Another method to control money supply is adjusting the discount rate.

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A third method is adjusting banks' reserve requirements.

10.The LM Curve •

The LM curve comprises combinations of the interest rate and income, where the money market is in equilibrium. It is plotted in the income-interest rate space.

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Analytically, the LM curve is computed by combining the equations for money demand and money supply and then solve for the interest rate as a function of income. This yield the following equation: ∗

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=

1 ! ℎ )ℎ  − * + ∗ ℎ$ ℎ$ 

Graphically this is shown below:

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i

i

M0 P

i1

L (Y1 ,i )

i0

L (Y0, i ) Y0

•

Y1

M P

Y

M Assuming that the quantity of money supply is fixed at  0  P0 income/output is at Y0, the equilibrium level of interest is i0 .

S

  . At point A when 

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Following an increase in income/output to Y1 , demand for money increases to L(i, Y 1).

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At point C where interest rate still remains at i0, there will be an excess demand for money.

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Some people will want to sell their bonds and convert them into cash which result in an excess supply of bonds and lowers the price of bonds.

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As price of bonds is inversely related to interest rate, a lower bonds price means that interest rate is now higher.

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An alternative understanding is to look at the borrowing and lending activities in the money market. At point C, there are more borrowers than lenders. To attract lending, borrowers need to increase interest rate paid to lenders.

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Subsequently, equilibrium interest rate will rise to i1 (point B in the above diagrams). Prepared by Dr Zhang Jianlin | Restricted materials for Singapore Institute of Management

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This shows that there is a direct relationship between the levels of national income and interest rates. This yields equilibrium in the money market.

Exercise: Derive the LM equation ( ∗ = money supply functions.

•

 +,

%

-ℎ − ' . +

+ ∗ ) +,

by combining the money demand and the

An increase in money supply shifts the LM curve down resulting to a lower equilibrium interest rate.

i

i

LM

M0 P

M1 P

0

i0

L (Y0 , i )

Y

0

Y

M P

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An increase in money demand shifts the LM curve up resulting to a higher equilibrium interest rate.

i

i

M0 P

LM0

i0

L ' ( Y 0, i) L( Y0 , i)

Y0

•

M P

Y

The slope of the LM curve depends on the sensitivity of money demand to income and the interest rate, as measured by the co-efficient h1/h2.

Exercise: What would happen to the LM curve when holders of bonds believe there is a risk of a future default in bonds?

i

i

LM

M0 P

0

i0

L (Y0 , i )

Y0

Y

M P

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•

The more money demand is sensitive to income, relative to the interest rate, the steeper the LM curve.

i

i

M0 P

LM i1

L (Y 1,i )

i0

L (Y0 , i ) Y0

Y1

M P

Y

Exercise: what would happen to the LM curve if money demand does not depend on income?

i

i

M0 P

i0

L( Y0 , i)

Y

M P

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The more money demand is sensitive to the interest rate, h2 is larger, the flatter is the LM curve. Prepared by Dr Zhang Jianlin | Restricted materials for Singapore Institute of Management

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i

i

L( Y0 ,i )h 2

M0 L (Y1 ,i )h2 P

i2

LM h 2 i1 i0

L( Y1, i )h 2 L (Y0 , i ) h2 Y0

11.

Y1

Y

M P

The Liquidity Trap

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Suppose the equilibrium interest rates are at or close to zero, bonds offer no better return than money (and the risk of capital losses were interest rates to rise again).

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However, money still has the advantage of being the most liquid asset.

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In such a situation, money demand function becoming perfectly elastic with respect to interest rates (horizontal).

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A perfect elastic money demand also means that agents are prepared to hold an arbitrarily large amount of money without any further decrease in the interest rate. In such a situation, the economy is in the liquidity trap.

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i

L (Y2 , i ) L (Y1 , i) L( Y , i) 0

M0 P

i

LM

i0

i0 Y2

Y1

Y0

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Assume the economy is in the liquidity trap for some output-interest rate combination. Now suppose that inco...