Problem Set 5 Answers

Transcription

1 Economcs 330 Menze D. Chnn Fall 2006 Socal Scences 7418 Unversty of Wsconsn-Madson Problem Set 5 Answers Due n lecture on Wednesday, December 13 th. No late submssons wll be accepted. Make sure your name s on your problem set, as well as the name of your (ocal) TA. 1. In a world wth currency holdngs and where banks hold excess reserves, f reserve requrements on checkable deposts were set at zero, the amount of multple depost expanson would go on ndefntely. Is ths statement true, false, or uncertan? Explan. False. There would stll be leakage nto currency and excess reserves that would lmt the ncrease n depost expanson. We can also see ths n Equaton (4) because the denomnator wll not equal zero f r = 0; therefore, the money multpler wll not be nfnte. 2. Why mght the procyclcal behavor of nterest rates (rsng durng busness cycle expansons and fallng durng recessons) lead to procyclcal movements n the money supply? The rse n nterest rates n a boom ncreases the cost of holdng excess reserves and the ncentves to borrow from the Fed. Therefore, e falls, whch ncreases the amount of reserves avalable to support checkable deposts, whch rases the monetary base. The result s a hgher money supply durng a boom. Smlarly, when nterest rates fall durng a recesson, the money supply also has a tendency to fall because e rses. 3. The only way that the Fed can aect the level of borrowed reserves s by adjustng the dscount rate. Is ths statement true, false, or uncertan? Explan your answer, usng graphs f helpful. False. The Fed also can aect the level of borrowed reserves by drectly lmtng the amount of dscount loans an ndvdual bank can have. (Although the text mentons that for the overall economy, t wll be hard to control borrowed reserves w/o resort to changng the dscount rate.) 4. If the Fed has an nterest-rate target, why wll an ncrease n the demand for reserves lead to a rse n the money supply? An ncrease n the demand for reserves wll rase the federal funds target. In order to prevent ths, the Fed wll buy bonds, thereby ncreasng the amount of nonborrowed reserves, whch shfts the supply curve for reserves to the rght, thereby keepng the fed funds rate from rsng. The open market purchase wll then cause the monetary base and the money supply to rse. 5. Suppose the Fed targets the Fed Funds rate by usng ths rule: = π ( π π ) ( y y r, ) Where r, s the equlbrum real Fed Funds rate, π s the nflaton rate, π s the target nflaton rate, y s log real GDP, and y s log potental GDP. Hence, ( π π ) s the nflaton gap and 1

2 ( y y ) s the output gap. If the nflaton gap rses from 0 to 2 percent (0.02), but the output gap falls by 1 percent (0.01), what should happen to the target Fed Funds rate? Show your work. Take the total derental of the Taylor rule: = π ( π π ) ( y y ) r, = π ( π π ) ( y y The answer depends on whether the nflaton gap rses because ( π π ) = 0. 02, wth π = 0.0, or because π = In the former case, = 0.5 (0.02) ( 0.01) = In the latter case (whch s more lkely), = ( 0.01) = ) 6. What are the key advantages and dsadvantages of the monetary strategy used n the Unted States under Alan Greenspan, n whch the nomnal anchor s only mplct? Ths strategy has the followng advantages: 1) t enables monetary polcy to focus on domestc consderatons; 2) t does not rely on a stable money-nflaton relatonshp; 3) t has had a demonstrated success, producng low nflaton wth the longest busness cycle expanson snce World War II. However, t has the followng dsadvantages: 1) t has a lack of transparency; 2) t s strongly dependent on the preferences, sklls, and trustworthness of ndvduals n the central bank and the government; and 3) t has some nconsstences wth democratc prncples because the central bank s not hghly accountable. 7. Usng data from the 2006 Economc Report of the Presdent. 7.1 Calculate velocty for the last fve complete years. P M1 M2 V1 V Is velocty constant? No. 7.3 What mplcatons does your fndng have for the dea of targetng monetary aggregates? Targetng the monetary aggregates only makes sense f the relatonshp between money and the goal (ncome stablzaton) s stable. The lack of stablty of velocty casts ths n doubt. 8. Queston 8 refers to the materal n Chapters (8/e) [Chapters /e], and/or Economcs 302. Show the eects of the followng n an IS-LM dagram. 2

3 8.1 Decrease n money supply. LM(M 1,P 0 ) Increase n autonomous consumpton ( a n the consumpton functon)

4 8.3 Increase n lump sum taxes. 0 1 IS(a 0,T 1,I 0, G 0 ) Increase n the autonomous component of mports (n other words, a decrease n the autonomous component of net exports). 0 1 IS(a 0,T 1,I 0, G 0, autonomous mports 1 ) IS(a 0,T 0,I 0, G 0, autonomous mports

5 9. Consder the model n Chapter 22 (8/e) [Chapter 25 7/e]: 9.1 Usng an AD-AS dagram, carefully ndcatng the curve shfts, show what happens n the short run when housng nvestment confdence decreases (say n perod 1). P AS(cost, P 0 ) P 0 P 1 AD(M 0,a 0, T 0,I 0, G 0 ) AD(M 0,a 0, T 0,I 1, G 0 ) n 9.2 On another graph, ndcate what happens over tme to the nterest rate, the prce level and output as the economy moves to medum run equlbrum. P AS(cost0,P0) AS(cost0,P1) AS(cost0,P2) ASfnal P 0 P 1 P 2 AD(M 0,a 0, T 0,I 0, G 0 ) AD(M 0,a 0, T 0,I 1, G 0 ) n 5

6 9.3 Explan why the economy takes ths path (referrng to the graphs, and equatons). Indcate where output and the prce level end up. In perod 2, the expected prce level s the prce level n the prevous perod,.e., P 1 (whch s less than P 0 ). The AS schedule shfts down and out n the top graph. In the bottom graph, the decrease n the prce level ncreases the real money stock, thereby shftng out the LM curve. Interest rates fall, and hence nvestment and output rses to 2 (greater than 1 ). As long as output s less than potental GDP, prces keep on fallng, the expected prce level keeps on beng revsed downward. Lower and lower prce levels contnue to expand the real money stock (all these ntermedate steps are not shown above). Ths process stops when = n, so the economy ends up at Fnal, Fnal, P Fnal. Note that n the end, the economy has returned to ts pre-shock level of output, but the prce level and nterest rates are lower. Snce output s the same as ntally, but consumpton s lower, t must be the case that somethng else s at a hgher level. The fact that nterest rates are lower gves us the hnt that nvestment s crowded n dollar for dollar for the decrease n consumpton. 9.4 Suppose n perod 1, the Fed ncreases the money supply to counter the nvestment declne. What eect would ths have n perod 1? In subsequent perods (Use a separate graph)? P AS(cost, P 0 ) P 0 P 1 AD(M 0,a 0, T 0,I 0, G 0 )= AD(M 1,a 0, T 0,I 1, G 0 ) AD(M 0,a 0, T 0,I 1, G 0 ) n \e330ps5a_f06 6 December 2006 The ntal nvestment declne shfts n the AD curve so ncome falls. Expansonary monetary polcy shfts the AD back out to where t started from. Output and the prce level can stay at the ntal levels forever, n the absence of further shocks. 6