The LM Curve

 

The Asset Market Equilibrium

Remember that:

M – Money supply which is policy determined

MD – Money Demand

 

 MD = P L(Y, r+πe)

 MD/P = L(Y, r+πe)

 

Money demand is determined by:

1.  The price level (proportionally)

2.  Real income

3.  Real interest rate

4.  Expected inflation

5.  Nominal interest rates (i= r+πe)

6.  Wealth

7.  Risk

8.  Liquidity (of non-monetary assets)

9.  Payment technologies

 

The relationship between MD and Y is determined by the income elasticity of demand:

 

ηy = %ΔMD / %ΔY

 

Or the percentage change in money demand resulting from a one percent change in real income.

 

0<ηy<1

 

Which means that money demand increases less than proportionally with increases in income.

 

Incidentally (nominal) interest elasticity of demand is:

 

ηi = %ΔMD / %Δr

and

ηi < 0

A 1% increase in interest rates will result in a decrease in money demand.

 

Deriving the LM curve:

 

 

·       When Y increases real money demand increases – i.e. the demand curve for money shifts up and to the right.

·       If the real interest rate did not change money demand would exceed money supplied.

·       Excess for money forces individuals to sell-off their non-money assets (such as bonds). **

·       The price of bonds decreases as the supply of bonds on the asset market increases.

·       As the price of bonds is inversely related to their rate of return the nominal interest rate increases.

·       With inflation held constant an increase in the nominal interest rate translates into an increase in the real interest rate.

·       Interest rates increase until the asset market is in equilibrium.

 

The LM curve maps out the level of the real interest with t he corresponding level of real income (Y) when the asset market is in equilibrium.

 

** remember that (Md – M)+(NMd-NM)=0

 

The LM curve is upward sloping as increases in Y (on the x-axis) lead to increases in money demand and increases in the interest rate need to clear the asset market.

 

 

Factors That Shift the LM Curve:

 

Anything the changes the equilibrium in the asset market (with output held constant) will shift the LM curve.

 

 

 

Example:

 

The Bank of Canada increases the money supply (using open market operations)

 

·       The M curve shifts right.

·       M > MD so individuals try to buy non-monetary assets to ride themselves of excess money holdings.

·       The price of non-monetary assets increase

·       Interest rates fall with output held constant.

·       The LM curve shifts down and to the right.

 

The nominal interest rate on money increases

·       Money demand increases.

·       Individuals sell non-monetary assets

·       Prices of non-monetary assets falls and returns increase

·       The LM curve shifts up as interest rates are higher with output held constant.

 

 

One more thing we need to know before we discuss the equilibium in the IS/LM – FE model:

 

How does the asset market equilibrium affect the price level (P)?

 

In equilibrium:

 

MD/P = L(Y,i) = M/P

 

So

 

P = M / L(Y,I)

 

Which says that the price level is equal to the ratio of real money supply to the real demand for money.

 

If we want to know about inflation ( π = ΔP/P ) we rearrange the terms in the equation above and get:

 

π = Δ M / M – Δ L(Y,i) / L(Y,i)

 

(see the appendix A-7 for extra help on growth rates)

 

or

 

π = ΔM / M - ηy ΔY / Y

 

Example:

 

Suppose that the money supply is constant (ΔM / M=0), that real income is growing at 3% per year and the income elasticity of money demand is .6. Inflation will be  equal to – 1.8%.

 

 

 

 

 

Consider the effects on the equilibrium position of the IS/LM model of:

 

A temporary adverse supply shock (labour market adjusts)

A future adverse supply shock (Goods market adjusts)

 

Notes:

 

1.  If the IS/LM model is not in equilibrium assume that the goods market and the asset market is in equilibrium and that the labour market is not (labour markets adjust the slowest while asset markets are quick to adust)

2.  If aggregate demand increases firms are willing to increase output (aggregate) temporarily.

Two examples from Macro Policy:

 

Fiscal policy:

What happened to the equilibrium when there is an increase in Government Spending?

1.  The savings curve shifts up and to the left as individuals reduce savings, and consumption.

2.  The interest rate that clears the goods market increases as firms compete for the supply of savings.

3.  The IS curve shifts up and to the right, as interest rates are now higher at every level of output.

4.  The short term equilibrium is now at the point where LM intersects with IS and output is above the full-employment level.

5.  Aggregate demand for goods is now greater than the aggregate (long term) supply, firms increase output and begin to increase prices.

6.  The LM curve shifts up and to the left as prices increase until the LM curve intersects the FE curve at the same point as the IS curve.

 

Monetary Expansion:

 

1.  The central bank uses expansionary monetary policy, increases the money supply.

2.  The LM curve shifts down and to the right, as discussed earlier.

3.  Aggregate demand for goods is now greater than the aggregate (long term) supply, firms increase output and begin to increase prices.

4.  The LM curve shifts up and to the left as prices increase until the LM curve intersects the FE curve at the same point as the IS curve.

 

The above effects will be same for a one time increase in the money supply and for any increase in the money supply which is greater than the trend in inflation.