Problem Set 7 - Solutions

The Keynesian Model

The four main assumptions in the Keynesian Model are:

Prices are sticky. That is, they are not flexible as in the classical model. This is one of the most important assump-tions. The fact that prices are sticky introduces an important role for monetary policy: now the Fed can inducebooms and recessions when they change the amount of money supply in the economy. This assumption is quiterealistic; it is difficult that prices change instantaneously after a monetary policy shock. Empirical evidence sug-gests that it takes between 6 to 8 months for prices to adjust. There are various reasons: menu costs, competitivepressures, prices set in advance...

The money market is always in equilibrium: this assumption is again quite realistic. The money market can changevery fast. At least, faster than the output market: it is easier to change nominal interest rates (they can even changedaily in the bank system) than to change production.

Output is demand determined: this assumptionmight be themost controversial one. If demand determines output,this implies that during a boom, firms are producing more than they would like. In a classical economy, thiswould be impossible, since firms would make losses. In the Keynesian model, in order to support this assumption,we need to introduce monopolies (or monopolistic competition). However, it is true that in many sectors of theeconomy, there is no perfect competition (as in the classical world). So the introduction of monopolistic competitionis realistic.

Prices adjust at the following rate, DP = l(Yd Ys). The interpretation is straightforward: when the demand isbigger than the supply, there is a friction in the economy, and firms would like to increase the price level.

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Economics 3213

Answers to Problem Set 9:

Beauty and the Beast Prof. Xavier Sala-i-Martin

1. Beast

a. When the Fed prints more money, money supply increases, so that there is more moneyavailable in the economy. The Keynesian model assumes that (a) money market alwaysclears; and (b) prices cannot adjust instantaneously. If this is the case, the only way themoney market can clear is by increasing the money demand for the fixed level of prices(Diagram 1). If people choose to hold more money, interest rates must go down, so thatalternative interest-bearing assets are less attractive. If prices are fixed in the short-run, nominal and real interest rates are equal: R = r. Hence, both nominal and real interest ratesmust go down as a result of monetary expansion. By the same token, real and nominalinterest rates must go up if money supply is decreased.

b. Remember the formula for the money demand: . If prices are fixed in the

short run, we can replace the nominal interest rate with the real interest rate: . Now we can express r as a function of Y and plot this expression in Diagram 2 with Y and r

on the axes: . This liquidity-money (LM) curve represents all combinations ofoutput and real interest rate that clear the money market.

When the Fed increases the money supply and the price level is fixed in the short run, realinterest rate decreases (Diagram 2). The LM curve shifts clockwise (Diagram 3). Weassume that output is determined by demand in the short run. If firms are monopolistically competitive, i.e. there are many of them in each industry, but each product is slightlydifferent from others, each firm optimally charges a price higher than its marginal cost. Ifthe demand increases a little, each firm is still willing to supply this greater quantity becauseprice is still above marginal cost. Therefore, the short run equilibrium is found at theintersection of the LM curve and the aggregate demand curve. In the short run, output ishigher; real interest rate is lower; prices are fixed.

In the medium run, people demand more than firms are willing to sell at the lower interestrate. Prices start to go up (Diagram 2). The LM curve starts shifting back because peoplewant to carry more nominal money when prices are rising (Diagram 3). In the medium run,output is declining; real interest rates are rising; prices are rising. In the long run, output andthe real interest rate revert to the classical equilibrium at the intersection of aggregatesupply and aggregate demand. Only prices are higher.

c. The result in (b) is clearly different from the classical model. The key assumptions are theflexibility of prices in the classical model and price stickiness in the Keynesian model.When prices are flexible, everyone realizes that there is more money in the economy but thesame amount of real goods. Hence, prices go up instantaneously, and there are no realchanges. However, if prices are sticky in the short run, people can buy more for a while.Hence, real interest rates fall and real output increases. Money is neutral in the classical model and not neutral in the Keynesian model.

2. Lumiere

i. When the money supply decreases, the LM curve shifts counterclockwise (Diagram 4).

Remember that the LM curve is given by . When M decreases, r increases for any value of Y. If output is supply-determined, both real interest rate and real output increase. In the medium run, output supplied is greater than output demanded at the higherinterest rate. Prices start falling, and the LM curve starts shifting back. The initialequilibrium is reached in the long run.

ii. When money supply increases, the LM curve shifts clockwise. Both real interest rate andreal output decrease. In the long run, they revert to the classical equilibrium, while the pricelevel increases.

iii. Changes in money supply affect real interest rate and real output; therefore, money is notneutral when prices are sticky and output is supply-determined. However, money affects output in the wrong direction. In this model, expansionary monetary policy decreasesoutput, and contractionary policy increases output. This is clearly contradicted by empiricalevidence. In reality, when the Fed increases the money supply (equivalently, when the Fedlowers the interest rate), real output usually increases for some time. When the Feddecreases the money supply (raises the interest rate), real output typically decreases.

3. Gaston

i. If output is determined by the short side of the market, then at any particular real interest rate, the minimum of aggregate supply and demand determine the actual output: Y = min{Yd, Y s} (solid lines in Diagram 5).

When money supply decreases, the LM curve shifts counterclockwise (Diagram 5). For r >r*, the short-run equilibrium is determined by the intersection of the LM curve and theaggregate demand curve. Real interest rate increases, and real output decreases in the shortrun. In the medium run, demand is less than supply; hence, prices go down. Real interestrate and real output return to the classical equilibrium; prices are lower in the long run.

ii. When money supply increases, the LM curve shifts clockwise. For r < r*, the short-run equilibrium is determined by the intersection of the LM curve and the aggregate supplycurve. Real interest rate decreases, and real output decreases as well in the short run. In themedium run, demand is greater than supply; hence, prices go up. Real interest rate and realoutput return to the classical equilibrium; prices are higher in the long run.

iii. Money is still not neutral when prices are sticky and output is determined by the short sideof the market. However, money affects output in the right direction only when moneysupply is decreased. In this model, both expansionary and contractionary policies decreaseoutput. This is contradicted by empirical evidence because when the Fed increases themoney supply (equivalently, when the Fed lowers the interest rate), real output usuallyincreases for some time. To get consistent predictions in the Keynesian model, output mustbe demand-determined.

The cost of going to the bank

(a)

In the Classical Model, a change in y will only produce a change in the money market. Since the cost of going to thebank is smaller, people want to carry less money in their pockets. Then, the money demand curve will shift to the left inthe money market, thus producing an increase in the price level. The equilibrium level of consumption, output and thereal interest rate will remain unchanged. Changes in the money market are neutral in the output market.

(b)

In the Keynesian model, prices are fixed in the short run. Then, if the money demand curve shifts to the left, at the initialprice P, there is an excess of money supply in the economy. People will exchange money for bonds, thus reducing theinterest rate. In the real market, the LM curve will shift to the right, since for any level of income the interest rate isgoing to be lower (remember that the LM curve is given by r = yY2(M/P)2 . If output is demand determined, this willinduce a boom in the economy in the short run, so that output and consumption go up, and the real interest rate is lower.However, in the medium run prices can change, and since demand is higher than supply, the prices should start to go upslowly. This will also shift the LM curve slowly to the left. In the long run, we go back to the initial classical equilibriumbut with higher prices.

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