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### Lecture 18: The IS/LM Model (continued)

Based Primarily on Mankiw Chapters 10, 11

Review And Learning Objectives

- In the last lecture we derived the IS curve. In this lecture we will derive the LM curve and present the complete IS/LM model.
- IS/LM is the core macroeconomic model used to explain the short-run behaviour of the economy.
- We will explain how to derive the LM curve and look at what determines its slope and position.
- In the next lecture we will go on to consider how the IS/LM model can be used to understand the business cycle, and how it can answer questions about the effectiveness of fiscal and monetary policy.

The LM Curve (1)

- The LM curve shows all combinations of r and Y that are consistent with equilibrium in the money market.
- To understand this relationship, we need to begin by looking at a theory of interest rate determination called the theory of liquidity preference.
- This is part of Keynes’ General Theory. It is a theory of interest rate determination.
- To develop the theory we need to re-examine the supply of and demand for real money balances.

The Theory of Liquidity Preference

- We assume that the supply of real money balances (M/P) is fixed by the Central Bank.
- Money Supply = M*/P* where M* is determined by the Central Bank and P is fixed at P*. Remember IS/LM is a short-run model and so we assume that prices are fixed.
- This assumption means that the supply of real money balances does not depend on the interest rate r. Thus, when we plot the supply of real money balances against the interest rate we obtain a vertical supply curve.

Demand for Real Money Balances

- The theory of liquidity preference posits that the interest rate is one determinant of how much money people wish to hold.
- Why?
- Remember that the interest rate is the opportunity cost of holding money. It is what you forgo by holding assets as money rather than as interest-earning deposits.
- When the interest rate rises people will hold less of their wealth as money.
- The demand for real money balances is (M/P)d=L(r)
- This relationship is shown in the next slide.

What Equilibrates Supply and Demand?

- According to the theory of liquidity preference, the interest rate adjusts to equilibrate the money market.
- At the equilibrium interest rate, the quantity of real balances demanded equals the quantity supplied.
- If there is an excess supply or demand of/for real money balances then individuals try to adjust their portfolio of assets, and, in the process, alter the interest rate.
- The interest rate stops adjusting when the demand for real money balances equals the supply.

Comparative Statics

- Now that we have seen how the interest rate is determined, we can use the theory of liquidity preference to show how the interest rate responds to changes in the supply of money.
- Imagine that the ECB suddenly reduces the money supply. A fall in M reduces M*/P*, because we are assuming that P is fixed in the model. The supply of real balances shifts to the left, as in the next slide.
- The equilibrium interest rate rises from r1 to r2, and the quantity of real money balances demanded and supplied falls. The opposite would occur if there was an increase in the money supply.

Constructing the LM Curve (1)

- How does a change in the economy’s income, Y, affect the market for real money balances?
- Recall from earlier lectures that the level of income affects the demand for money.
- When income is high expenditure is high, so people engage in more transactions that require the use of money. Thus, greater income implies greater money demand.
- Our simple demand function need to be augmented to (M/P)d=L(r, Y). The quantity of real money balances is negatively related to the interest rate and positively related to income.

Constructing the LM Curve (2)

- If income increases, then the money demand curve shifts to the right. With a fixed supply of real money balances, the interest rate must rise from r1 to r2 to equilibrate the money market.
- See the next slide.

The LM Curve

- The LM curve plots this relationship between the level of income and the interest rate.
- The higher the level of income, the higher the demand for real money balances, and the higher the equilibrium interest rate.
- For this reason, the LM curve slopes upward, as in panel (b) of the previous slide.

Monetary Policy and the LM curve

- As we have just seen, the LM curve is drawn for a fixed supply of real money balances, M/P.
- If real balances change - because there has been a change in prices and/or because the Bank of England has altered the money supply - then the LM curve shifts.
- Suppose that the Bank of England reduces the money supply from M1 to M2, which causes the supply of real balances to fall from M1/P to M2/P. The level of income has remained constant but the equilibrium interest rate has risen. Therefore, the LM curve has shifted upward.

The Slope of the LM curve

- As important issue in macroeconomics is the slope of the LM curve.
- The slope of the LM curve depends upon (a) the income elasticity of money demand and (b) the interest elasticity of money demand.
- This should be intuitive given our construction of the LM curve.
- We can now use IS/LM to explain the short-run equilibrium of the economy.

The IS/LM Model

- We now have all the pieces of the IS/LM model.
- IS curve: Y = C(Y-T) + I(r) + G
- LM curve: M/P = L(r, Y)
- The model takes fiscal policy, G and T, monetary policy M, and the price level P as exogenous variables. Given these exogenous variables, the IS curve provides the combinations of r and Y that satisfy equilibrium in the goods market, and the LM curve provides the combinations of r and Y that satisfy equilibrium in the money market.
- The short-run equilibrium on the economy is the point at which the IS curve and the LM curve cross. So in the short-run both the goods market and the money market simultaneously determine r and Y.

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