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69

FIGURE 5.1 The AS-AD diagram

FIGURE 5.2 The IS-LM diagram



+ Ly. (5.2)

= -~>0, (5.3)

, denotes

lm L,

where L, and Ly denote the partial derivatives of !() and di /dY along the LM curve. Thus increases in the income elasticity of money demand, and decreases in the interest elasticity (in absolute value) make the LM curve steeper.

Implicitly, the IS-LM model treats all assets other than money as perfect substitutes. The market for these other assets is then suppressed by Wal-rass law. Specifically, total wealth in the economy equals the total value of all assets, and the total value of any individuals asset holdings must equal his or her total wealth; thus if the market for every asset but one clears, the market for the remaining asset must clear as well. In the IS-LM model there are only two assets (money and everything else), and so only one asset-market equilibrium condition is needed. Many important extensions of the

us to use the IS and LM curves to derive the AD curve. Although there are innumerable variations and extensions of the IS-LM model, here we consider a standard version.

The LM Curve

The LM curve shows the combinations of output and the interest rate that lead to equilibrium in the money market for a given price level. It is simplest to think of money as high-powered money-currency and reserves-issued by the government. Since high-powered money pays no nominal interest, the opportunity cost of holding it is the nominal interest rate. The demand for real money balances is therefore a decreasing function of the nominal interest rate. In addition, since the volume of transactions is greater when output is higher, the demand for real balances is increasing in output. The nominal money supply is set by the government. Putting all this together, the condition for the supply and demand of real balances to be equal at a given price level is

y = m,Y), Li <0, Ly >0. (5.1)

Since L(*) is decreasing in / and increasing in Y, the set of combinations of i and Y that satisfy (5.1) is upward-sloping. Formally, differentiating both sides of (5.1) with respect to ,



The /5 Curve

The IS curve shows the output-interest rate combinations such that planned and actual expenditures on output are equal. Planned real expenditure depends positively on real income, negatively on the real interest rate, positively on government purchases of goods and services, and negatively on taxes:

E = E{Y, i - 77- G, T), 0 < Ej < 1, < 0, Eg > 0, Ej < 0. (5.4)

tt is expected inflation, G is government purchases, and T is taxes; all of these are taken as given. The negative effect of the real interest rate on planned expenditure operates through firms investment decisions and consumers purchases of durable goods. Planned expenditure is assumed to increase less than one-for-one with income; that is, 0 < Ey < 1.

In textbook treatments, E is often expressed in terms of its component parts and strong assumptions are made about how the determinants of planned expenditure enter. A standard formulation is

E = ( - ) -h Id - tt") + G, (5.5)

where C(«) is consumption and /() is investment. The restrictions imposed in this specification may be highly umealistic. For example, there is considerable evidence that the real interest rate affects consumption, and almost overwhelming evidence that income influences investment. To give another example, if Ricardian equivalence holds (see Section 2.9), taxes have no effect on demand; more generally, there is little basis for assuming that income and taxes have equal and opposite effects on spending. Since the general formulation in (5.4) is only slightly more difficult, we will use it in what follows.

If one treats goods that a firm produces and then holds as inventories as purchased by the firm, then all output is purchased by someone. Thus

Two classic references are Tobin and Brainard (1963) and Tobin (1969). A large recent literature relaxes the assumption that assets held by banks, particularly their loans, are perfect substitutes for other interest-bearing assets. See Bernanke and Blinder (1988) and Kashyap and Stein (1994).

The IS curve is often described as showing equilibrium in the goods market. But since supply is ignored, this is not an accurate description.

"Properly speaking, expected inflation should be determined within the model rather than taken as given, since the path of the price level will be determined within the model. Taking it" as given here simplifies the discussion without altering the models main impUcations, however.

IS-LM model investigate the consequences of relaxing the assumption that all assets other than money are perfect substitutes.



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