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## IS-LM-model## IntroductionThe main difference between the cross model and the IS-LM model is that the nominal interest rate is exogenous in the cross model but endogenous in the IS-LM model. In this chapter we will explain how the nominal interest rate is determined in the IS-LM.
= r. This will allow us to talk about "the interest rate" without specifying whether we mean the nominal or real interest rates.R ## Aggregate demand## The investment function in the IS-LM modelInvestment was an exogenous variable in the cross model due to the fact that the interest rate was exogenous. Now that the interest rate is endogenous, investment will be endogenous. As for the classical model, investment depends negatively on the real interest rate but since in the IS-LM model, we can make investment a function of R: r = I I(R).## The consumption function in the IS-LM modelThe consumption function will be the same as in the cross model, consumption will depend positively on Y. In the classical model, consumption depends negatively on the real interest rate. You may allow consumption to depend negatively on interest rates in the IS-LM as well. You must then write depend on C only, Y = C(Y). We will also, for the same reason, model imports as a function of C only even though it may depend on Y as well.R ## Aggregate demand
Since investments depend on and Y In the cross model, we used the notation R. for aggregate demand. In the IS-LM model, we must instead use the notation YD(Y) R). We haveYD(Y, It does not make much of a difference if we allow to depend on Im as well, R will depend positively on YD and negatively on Y in any case.R It should also be clear that we can no longer determine GDP the way we did it in the cross model. We cannot successfully solve the equation as we have only one equation but two unknowns (Y and R). We need Y if we want to solve for both one more equation and R. This equation will come from the money market.Y ## The money market## Demand for money
As for any kind of goods, there is Instead, we define the We use the symbol the amount out of your wealth that you wish to hold as money. to the demand for money. In the IS-LM model, there is only one alternative to money and that is MD bonds.If your total wealth is 1.000 euro and you wish to keep 100 euro in cash or in an account connected to a debit or credit card and the rest in government bonds then your demand for money is precisely 100 euro. It is the amount that you want to have easily accessible for immediate payments. Note that having a low demand for money does money. Instead, it means that you prefer to hold most of your wealth in other types of assetswant ## Demand for money and the interest rateMoney has one important advantage and one important disadvantage compared to bonds: • than bonds. If most of your wealth is invested in bonds, you must first sell some of the bonds whenever you want to make a payment.liquid • At 0% interest, there would be no reason to hold bonds and the demand for money would be maximized. The higher the interest rate, the more you lose by holding money instead of bonds. Therefore, we would expect the demand for money to fall when ## Demand for money and GDPThe demand for money also depends on the GDP as GDP is closely related to national income. If you choose to hold a fixed proportion of your wealth as money, you will want to hold more money when As the demand for money depends on in the IS-LM model, we write R for the demand for money. Remember that it depends positively on MD(Y, R) and negatively on Y R.## Supply of money
The money supply is completely under the control of the central bank in all models in this book. Money supply is therefore an exogenous variable not affected by either interest rates or GDP. We denote the money supply by ## Equilibrium in the money market
This is our "missing equation" as discussed in section xx. It is now possible to determine all endogenous variables in the IS-LM model: We now have two equations and two unknown ( ## Money market diagramLet us begin by studying the money market when the is given, Ywill only depend (negatively) on MD and we can draw a diagram with supply and demand for money as functions of R.R
In the diagram above, R* is the interest rate in which the demand for money is exactly equal to the supply of money (again for a given Y). The IS-LM model, The justification for why • Say that • In this case, • People increase the amount of money they hold by selling bonds so there is an excess supply of bonds. • This excess supply of bonds will drive down the price of bonds. • When the price of bonds falls, interest rates increase. We discussed this negative relationship between the price of bonds and the interest rate in section 7.2.3. • The interest rate will increase until • The case of The money market diagram can be used to determine the equilibrium rate of interest |

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