EC201 Intermediate Macroeconomics. EC201 Intermediate Macroeconomics Problem set 8 Solution

Transcription

1 EC201 Intermediate Macroeconomics EC201 Intermediate Macroeconomics Prolem set 8 Solution 1) Suppose tat te stock of mone in a given econom is given te sum of currenc and demand for current accounts tat do not pa an interest rate (so tis represents te amount of mone tat people can old in a given period). Suppose a cange in government regulations tat allows anks to start paing interest on current accounts. a) How does tis cange in regulation affect te demand for mone? ) Wat appens to te velocit of mone? (Hint: Use te mone demand derived from te quantit teor. Assume tat te velocit is not constant ut independent on te interest rate). If te Central Bank keeps te mone suppl constant, wat will appen to output and prices in te sort run and in te long run? (Hint: Now use te aggregate demand derived from te quantit teor. Draw it in te same grap wit a orizontal and a vertical aggregate suppl). d) Sould te Central Bank keep te mone suppl constant in response to tis regulator cange? Solution a) Since te mone tat people old is given currenc plus current account tis regulation will make olding mone more attractive, since now people can otain interest income from a ver liquid asset like current accounts. Terefore, mone demand will increase. ) From te quantit teor of mone, mone demand is given : M = ky P 1 were k = V Since now te demand for real alances increases, ky must increase. However, since Y is still te same ten k must increase. Since k is negativel related to V, an increase in k must e done troug a decrease in te velocit of mone V. Te idea is: now people are olding more mone so mone circulate less frequentl. From te quantit teor te aggregate demand is given : MV P = Y If te mone suppl is kept constant, ten since V decreased wit te increase in te demand for mone, te aggregate demand must sift to te left (te AD decreases). Grapicall:

2 After te introduction of tis new regulation, if mone suppl is kept constant, ten te aggregate demand sifts to te left after te decrease in te velocit of mone. In te sort-run, wit fixed prices, tis implies tat real output decreases from point A to point B. As te time passes, prices ecome more flexile and te adjustment process will ring te econom from point B to point C tat is te new long-run equilirium. So te initial impact of tis regulation wen mone suppl does not cange is a recession, real output decreases. Since we are dealing wit te quantit teor of mone tere is no Kenesian effect in terms of reduction of te real interest rate. So ou ma tink intuitivel: in tis framework, wen people olds more mone, te spend less (to keep more mone in a current account and gaining te income from interest rate) and so real output decreases. As te prices decrease, te value of te mone alances increases since M is constant. Now people can u more goods wit te same amount of mone, so te spend more witout loosing te interest rate income (te need to witdraw less mone to u more goods tan efore), so te can spend more and real output increases until we reac te new long-run equilirium wit te same output as in A ut wit lower prices. d) If te central ank does not do anting te result is a recession at te eginning. If te Central Bank fears tat te recession can e ad it can eliminate te negative cange in te AD increasing te mone suppl. Tis is going to effective especiall if te cange in te regulation is predictale. Suppose te central ank knows wen te regulation will take place (tis is quite realisti and suppose tat te Central Bank can predict well te cange tat tis regulation will make in te velocit of mone (tis is less realisti, ten it can intervene at te time wen te regulation

3 takes place increasing te mone suppl in suc a wa to ring ack te econom from point B to A in a relativel sort time: 2) (Wealt Effect in IS-LM model) Consider te following version of te IS-LM model in log-linear form. Consumption = a + c( t) + d( m p) a > 0,0 < c < 1,0 < d < 1 Investment = f r f > 0, > 0 Government expenditure = g Taxes = t Mone demand = ( m p) = k r k > 0, > 0 Now consumption depends also on te real mone alances. In practice we are assuming tat mone is part of te wealt of ouseolds and ma affect teir consumption. Te term 0 < d < 1 can e called te Marginal Propensit to Consume wit respect to real mone alances. a) Derive te equilirium level of income and te real interest rate in te IS-LM model. Wat is te main effect on te equilirium of introducing wealt effects in te IS-LM model? ) Using a diagram to illustrate our answer explain te effects of an increase in mone suppl in tis IS-LM model; Using our answer in a) determine wat is te slope of te Aggregate Demand curve. How te introduction of wealt effects alters te slope of te AD curve compared to te case were tere are no wealt effects? d) Provide some comments aout te role of deflation wen wealt effect is considered; e) Consider in te same grap te vertical, te orizontal AS curve and te AD curve. Suppose to start at te long-run equilirium. Consider a positive sock on te AD curve. Explain te adjustment process to te new long-run equilirium in te case were tere are wealt effects and in te case were tere are not.

4 Solution a) Te IS curve is given : 1 1 r = a + f + g ct d [ ] + ( m p) Te LM curve is: k 1 r = ( m p) Te equilirium is given : c * d + = A + ( m p) k + (1 k + (1 r * k kd (1 = A + ( m p) k + (1 k + (1 =. Te equilirium values are now different compared te usual case wit d = 0 in te sensitivit wit respect to (m p) tat is now larger. Notice an important fact: wen d = 0 an increase in m will decrease te interest rate. However, ere it ma e possile tat interest rate increases wit an increase in m: were A [ a + f + g ct] * r kd (1 = m k + (1 Tat derivative can e greater tan zero if kd > (1-. ) Te idea is tat an increase in m now canges te LM ut also te IS: r LM 1 LM 2 a IS 1 IS 2

5 An increase in m sifts te IS to te rigt since troug te wealt effect consumption increases. On te oter and an increase in m sifts to te rigt also te LM curve. Te final effect on r can e positive or negative. In te previous grap we plotted te case were te effect was positive. Te effect on real output is alwas positive, ut igger tan in te case were tere are no wealt effects. So, te presence of wealt effects increases te effectiveness of monetar polic in affecting te equilirium value of. Te reason is tat now tere are two effects tat work at te same time: 1) Te Kenes effect: given te IS curve, an increase in m, sifts te LM curve and tis decreases r. Tis will increase I and so ; 2) Te Pigou effect (or wealt effect): an increase in m increases te wealt of ouseolds, consumption increases, te IS sifts to te rigt and so increases and r increases as well.. Te net effect on r is amiguous wile te effect on is positive and larger tan te effect witout wealt effect. Te aggregate demand is given te solution for derived previousl. However, we normall write te aggregate demand in te (p,) space so: p = k + (1 A + m d + d + Witout wealt effect it means d = 0, so te slope of te AD curve is: p k + ( 1 Wit wealt effect into te model te slope of te AD ecomes: p k + (1 c ) d + since d is positive, now te denominator is a larger numer, meaning tat slope is now smaller in asolute value. Tis implies tat te AD curve is now flatter tan in te case were tere are no wealt effects (ou can tink it in tis wa: now te same cange in output as less effect on p tan efore, impling tat te AD must e flatter tan efore). In te following grap we plot te aggregate demand wen wealt effect is asent (AD 1 ) and te one wen wealt effect is considered (AD 2 ).

6 p AD 2 AD 1 d) Since wit wealt effect te AD is flatter, te same cange in prices as now a igger effect on output. In particular, in tis case deflation is more effective in stailising output tan in te case witout wealt effect. We can see tis comparing te following derivatives: p d + k + ( 1 wit wealt effect p k + ( 1 witout wealt effect A decrease in p will ave a igger impact on in te first case tan in te second (te numerator is igger in te first case tan in te second). Deflation is now more powerful in stailising output (meaning increasing during a recession).

7 e) p AD 1 d p 1 AD p w c a AD w1 AD w In te grap we ave te aggregate demand curve wit wealt effects (AD w ) and te one witout (AD). Suppose te same positive sock in ot cases. Suppose we start at point a: 1) Wit wealt effect: AD w sifts to te rigt to AD w1. Te new sort-run equilirium is now point. Income is now larger tan te natural output. As prices start to ecome flexile, te ig demand puts pressure on p and so prices start to increase until we reac te new long run equilirium at c. 2) Wit no wealt effect: te AD is steeper. Suppose te same positive sock. Te AD sifts to te rigt te same amount as efore. However, now as te prices ecome flexile, te new long run equilirium will e at point d were te equilirium price level is now iger tan in case 1). As p increases te Kenes effect starts to work: p ( m p) r I Te main reason is: wit wealt effect, an increase in p decreases also consumption decreasing wealt. So tere are now two effects: Pigou + Kenes effect. Tis implies tat a small increase in p will ave a igger effect on, so will decrease in a faster wa now. Tis implies tat at te new equilirium te new price level is lower tan te price level we sould ave wit no wealt effect.