# Problem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.

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1 Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When <0, people would hold only money and would never buy bonds, as t would actually cost them money to hold them. Suppose that the prce of the bond b today s 00. If s -5%, then n one year we would get only 95 as a payout: ayout n the future = b (+) = 00 (-0.05)=95 Nobody would buy the bond f he knew that he would receve less money n the future than the ntal outlay. The only reason to hold any of our wealth n bonds s that they pay a postve nterest rate. Note: In the realty bonds always pay a postve nterest rate and can not be negatve. The lowest nterest rate equals 0. If <0, nobody would buy bonds, everybody would lke to hold money. b) We are asked to show the relatonshp between the nterest rate and the money demand on a graph: 0 Mo M M D Money We can see now from the graph that money demand depends negatvely on the nterest rate. The money demand curve M D s drawn for a gven level of ncome Y and s downward-slopng. That means when s ncreasng, the demand for money s decreasng (ncrease n the opportunty cost of holdng money) and people want to put more of ther wealth nto bonds. Conversely, when s decreasng the demand for money s ncreasng and people prefer to keep cash.

2 c) Frst we are asked to derve the LM curve: Suppose, that for some reason output Y s decreasng from Y 0 to Y (Graph 2), so that money demand curve shfts to the left from M D to M D (Graph). But because money supply M S s fxed, the nterest rate decreases from 0 to n order to keep the money market n equlbrum. So we can see now, that a decrease n output leads to a decrease n the nterest rate and to a new equlbrum at pont. We have postve relatonshp between Y and, represented by our upward-slopng LM curve (Graph2). () Money Market Only (2) Both Money Market and Goods Market M S LM 0 0 M D M D M 0 M Y Y 0 Y But how wll LM curve look f the nterest rate s very close to zero? (See dagram below) Here we have frst the same case: Because of decreasng of Y from Y 0 to Y our money demand M D s decreasng causng a fall n the nterest rate form 0 to and new equlbrum at pont. Suppose now that output decreases even more from Y to Y 2. Money demand decreases and the M D curve shfts further to the left. But now the equlbrum on the Money Market s at pont wth = 0. When reaches zero people are now ndfferent f they hold money or bonds. Both money and bonds pay the same nterest rate, so they are wllng to hold more money and therefore fewer bonds. Even, f Y s decreasng below Y 2, people stll demand more money at the same nterest rate so that our LM curve s flat for ponts left of the equlbrum pont. Here has no mpact on Y. Because of =0, there s a lqudty trap.

3 M D M D M D M S LM M M Y 2 Y Y 0 Y (d) Expansonary monetary polcy: M S and the nterest rate s very close to zero Suppose, we are at pont wth output Y 0 and nterest rate 0 (whch s already very low) and central bank ncreases now M S to M S. In the frst step, f money supply s ncreasng, the nterest rate s decreasng to n order to brng money market back to equlbrum (Graph ). Because of decrease n, nvestment n the goods market s ncreasng and output ncreases to Y and the new equlbrum s (Graph 2). In the second step, the central bank ncreases M S further to M S. But at pont the nterest rate s already zero and people want to hold more money at the same. t =0 the LM curve s flat. The nterest rate does not change and nvestment does not change ether and output does not ncrease. Monetary polcy has fallen nto the Lqudty Trap. The ncrease n money supply can not ncrease output and economy remans at pont (Graph 2). () Money Market Only (2) Both Money Market and Goods Market M D M S M S M S IS LM LM LM 0 M 0 M M 2 M 0 Y 0 Y Y

4 (e) The queston: How effectve s expansonary monetary polcy at the nterest rate =0, we have already answered n pont (d): the polcy s not effectve because t falls nto the Lqudty Trap : an ncrease n M s has no effect on or on Y. Expansonary fscal polcy: G or T when the nterest rate s very close to zero If government spendng s ncreasng or taxes are decreasng, the IS curve (representng goods market) shfts to the rght and causes an ncrease n output from Y 0 to Y (Note: we have here no crowdng-out effect because LM s flat). If we have a further ncrease n G or decrease n T, the IS curve shfts further to the rght. Output ncreases further from Y to Y 2 and fnally we can get the economy out of lqudty trap. IS IS IS LM 0 Y 0 Y Y Y 2 Comparson: Expansonary monetary polcy and LM curve s flat If LM curve s flat, the expansonary monetary polcy s not effectve. If M S s ncreasng, the nterest rate s not ncreasng because nterest elastcty of M D s nfnte, n other words M D s very senstve to nterest rate whch does not change. No ncrease n causes no ncrease n nvestment, and therefore no ncrease n output. In the presence of lqudty trap LM curve s also flat for the same =0 and the polcy causes no ncrease n output, so that the polcy s not effectve. Comparson: Expansonary fscal polcy and LM curve s flat If the LM curve s flat, the expansonary fscal polcy s always effectve. If government spendng s ncreasng or taxes are decreasng, the IS curve shfts to the rght and causes an ncrease n output. Because the money demand s nfntely elastc, the nterest rate does not change and there s no decrease n nvestment and no crowdng-out effect at all. In the presence of the lqudty trap LM curve s also flat for the same =0 and the polcy causes an ncrease n output, so that t s effectve. Concluson: If the nterest rate does not change, the nterventon n the goods market through the expansonary fscal polcy, s effectve, but the nterventon n the money market, through the expansonary monetary polcy, s not effectve!

5 Queston 2 roblem Set 3 The equlbrum condton for the Labour Market s gven by followng equaton: F n ( u, z) = + µ a) We are asked to draw the prce settng equaton and wage settng equaton on the graph: Real wage W/ Equlbrum wage rate W = + µ rce-settng relaton (S) Wage-Settng relaton (WS) u n Unemployment rate u Natural rate of unemployment Dervaton of Wage-Settng Equaton (Worker/Labour Sde): ssumpton: s a gven actual prce level Nomnal wage: W = F( u, z) If we dvde both sdes of the equaton by, we get: W = F ( u, z), whch s the WS equaton (, + ) Here, W s real wage (nomnal wage dvded by a gven prce level ), whch tells us how many goods an employee can buy wth her nomnal wage; u s the unemployment rate and z s an exogenous varable that denotes other factors (e.g. unemployment

6 benefts, employment protecton, mnmum wages) whch determne the real wage gven and u. Summary: The WS equaton characterzes wage determnaton n the Labour Market. It s drawn on the graph as the downward-slopng curve and t shows a negatve relatonshp between the unemployment rate and the real wage. Ths means; the hgher the unemployment rate, the less barganng power employees have and so the lower the real wage that wll be chosen by wage setters. There s a postve relaton between parameter z and the real wage. If z s ncreasng, the barganng power of employees s ncreasng and the real wage s ncreasng as well. Dervaton of rce-settng Equaton (Frm Sde): ssumptons: The goods market s not perfectly compettve and frms set prces hgher than Margnal Costs (MC) Labour s the only factor of producton and MC=W = ( + µ )MC = ( + µ )W Here, µ s the markup on the prce over costs. rce exceeds the margnal cost W by a factor equal +µ. (Note: If goods market s perfectly compettve: µ= 0 and p=mc=w.) If we dvde now both sdes of the equaton by and then by (+µ), we get: W =, whch s the S equaton + Summary: The S equaton characterzes prce determnaton n the Labour Market. It shows the negatve relatonshp between the real wage and the markup set by the frms. The hgher the markup, the lower the real wage wll be. The S relaton s drawn on the graph as the horzontal lne. The real wage mpled by the prce settng relaton does not depend on the unemployment rate. For example f the unemployment rate ncreases, the real wage mpled by prce settng relaton does not change. (b) We are asked to show equlbrum parameters. The equlbrum s gven at pont. Here the WS relaton equals the S relaton: F( u n, z) = + µ The equlbrum real wage s and the equlbrum unemployment rate s un, + µ whch s called the natural rate of unemployment. In other words, u n s the

7 unemployment rate such that the real wage W chosen n the wage settng s equal to the real wage W mpled by the prce settng. (c) We are asked, what wll happen to u n, f the government ncreases the employment protecton, denoted as z n the WS equaton. n example of employment protecton: Employers have to gve a long perod of notce when dsmssng a worker. W/ + µ S WS WS u n u n u If at a gven and a gven u n, employment protecton (represented by z) ncreases, the employees have more barganng power because they are less afrad of the possblty of beng made unemployed. s the barganng power of employees ncreases, they wll demand an ncrease n ther real wages. The WS curve shfts up. But the frms are wllng to pay only the real wage whch s not bgger than ncrease from u n to u n to keep the real wage at the level gven by. The unemployment rate has to + µ. The economy + µ moves rght along the S lne from to, a new equlbrum n the Labour Market, where the equlbrum real wage has not changed, unemployment rate s u n where u n > u n., and the new equlbrum + µ

8 Summary: n ncrease n employment protecton causes an ncrease n the natural rate of unemployment, but has no effect on the real wage. (d) Now we are asked, what wll happen to u n, f parlament adopts a stronger anttrust law, whch ams to ncrease the market competton. Ths s captured n the parameter µ n the S equaton. n example of anttrust law: European Unon lberalzaton of the goods market that reduces the monopoly power of the exstng frms sellng n the EU. W/ + µ ' + µ S S WS u n u n u Because of ncreased competton n the market, the market power of frms s decreasng and so leads to a decrease n ther markup µ. decrease n markup shfts the S lne up gven u n and gven, so that the real wage set by frms ncreases from to. + µ + µ ' Ths ncrease n the real wage causes the natural rate of unemployment to decreasng from u n to u n. The economy moves left along the WS curve from to, a new equlbrum n the Labour Market, where the new equlbrum real wage s > and the new equlbrum unemployment rate s u n < u n. + µ ' + µ Summary: n ncrease n market competton caused by stronger anttrust legslaton ncreases the real wage and decreases the natural rate of unemployment.

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