1. How is the IS curve derived and what factors determine its slope? What happens to the slope of the IS curve if consumption is interest elastic?


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1 Chapte 7 Review Questions 1. How is the IS cuve deived and what factos detemine its slope? What happens to the slope of the IS cuve if consumption is inteest elastic? The IS cuve epesents equilibium in the goods maket (eal pat of the economy). Consumption is a linea function of disposable income. C = a + c ( T ) Investment is negatively elated to the inteest ate and detemined by a set of autonomous factos Θ. I ( ) = I,Θ Govenment spending and lump sum taxes ae exogenously detemined by the fiscal authoity (govenment). G = G T = T Equilibium in the goods maket is whee supply = demand, o output = expenditue. ( T ) + I( Θ) G = a + c, + a ct + I = 1 c (, Θ) + G Altenatively output equals the poduct of the multiplie ( k = 1 c) autonomous expenditues ( AE = a ct + I(, Θ) + G). 1 and the sum of = kae The IS cuve plots the elationship between equilibium output and inteest ates. An incease in inteest ates educes investment and autonomous expenditue, which leads to a multiplied eduction in output. ( Θ) Δ ΔAE ΔI = k = k, Δ Δ Δ
2 ( ) ΔI, Θ If Δ = φ then Δ Δ = φk The IS cuve plots an invese elationship between inteest ates and output. The gadient of the IS cuve is detemined by the multiplie and the inteest sensitivity of investment. 1 IS 1 Suppose consumption is inteest elastic due to the substitution and income effects of inteest ate changes (i.e. most people ae net boowes so an incease in inteest ates has both a negative income and substitution effect on cuent consumption.) C = a + c ( T ) γ Autonomous consumption, and hence autonomous expenditues, is now also detemined by inteest ates. Δ Δ ΔAE = k Δ = k ( φ + γ ) The slope of the IS cuve is now flatte because autonomous expenditues ae moe sensitive to inteest ate changes. This means a given change in inteest ates has a lage impact on equilibium output.
3 . How is the LM cuve deived and what factos detemine its slope? What happens to the LM cuve is thee is an incease in the cost of liquidating financial assets? The LM cuve epesents equilibium in the money maket, o whee demand and supply of money ae equal. The money supply is set by the monetay authoity. M s = M The demand fo money is a positive function of income (tansactions) and a negative function of inteest ates (cost of liquidity pefeence). M d = a b The LM cuve plots the combination of income and inteest ates whee: s M = M d M = a b = 1 b ( a M ) The slope of the LM cuve is Δ = Δ a b LM 1 1 The slope is detemined by two factos.
4 Paamete a is the income sensitivity of the demand fo money. As this inceases a given change in income leads to a lage incease in the demand fo money. The inteest ate will then have to ise by a lage amount in ode to estoe equilibium to the money maket. The LM cuve becomes steepe. Paamete b signifies the inteest sensitivity of money demand. This detemines the size of the inteest ate esponse equied to estoe money maket equilibium as income ises. As this paamete inceases the LM cuve becomes flatte, because fo any change in income the equied inteest ate change is smalle. 1 The fom of LM cuve we have used has abstacted fom the cost of liquidating assets. (This is explained in chapte 5). An incease in the cost of liquidating inceases aveage money holdings at each level of income. Theefoe, at each money supply equilibium inteest ates ae highe so the LM cuve shifts upwads. M LM ( c ) 4 LM ( c 1 ) 1 L ( 1, c, ) ( c ) L, 1, 1 L (, c, ) ( c ) L,, 1 1. Using the ISLM model, explain how the equilibium ate of inteest and level of output will espond to the following: a. Expectations of a futue incease in unemployment If consumption is fowadlooking, then an expected incease in futue unemployment will lead to a fall in cuent consumption and a leftwad shift in the IS cuve. At the cuent level of inteest ates thee is now a position of excess supply in the money maket, which leads to an incease in bond pices and a fall in inteest ates. The economy settles at a lowe inteest ate and level of income.
5 LM 1 IS 1 b. Financial deegulation leading to the abolition of eseveasset atios A eduction in the eseve action asset atio inceases the money multiplie and leads to an incease in money supply at each level of high poweed money stock. The LM cuve will then shift downwads as the equilibium level of inteest ates is lowe at each level of output. The eduction in inteest ates leads to an incease in investment and a multiplied incease in income. Oveall inteest ates ae lowe and equilibium output is highe. LM 1 LM 1 1 c. A fall in copoate pofits This would be expected to lead to a fall in investment. This could be because of lowe intenal funds available to spend on investment pojects o lowe business optimism.
6 As a esult the IS cuve will shift inwads and equilibium output and inteest ates will fall. This can be epesented with the same diagam in pat a. d. A house pice boom An incease in house pices leads to an incease in asset wealth, and if it can be liquidated though motgage equity withdawal consumption will ise. The IS cuve will then shift outwads. At the existing level of inteest ates thee is now excess demand in the money maket. As a esult bonds ae sold, and falling bond pices push up inteest ates and cowds out some of the initial incease in output. Oveall, output and inteest ates ae highe. LM 1 IS 1 e. A pogam of investment in new ATMs This will lowe the cost of liquidating bank deposits, so would be expected to educe the demand fo money. Consequently, the LM cuve will shift downwads and put downwad pessue on inteest ates. This is because lowe money demand will lead to an incease in bond puchases and a ise in bond pices. As a esult of the lowe inteest ates investment will be stimulated and output will incease. The new equilibium position in the economy sees lowe inteest ates and highe output. The same diagam used in pat b applies. Suppose the cost of liquidating financial assets wee to incease. Theefoe aveage money holdings would ise and the money maket equilibium will yield highe inteest ates at each level of output. The LM cuve would shift upwads, the ise in inteest ates will lead to a contaction in investment. The new equilibium would esult in highe inteest ates and lowe output.
7 LM LM 1 1 IS 1 4. How is the effectiveness of monetay and fiscal policy affected by? a. The slopes of the IS and LM cuves The effectiveness of fiscal policy and the slope of the LM cuve A fiscal expansion consists of eithe a eduction in taxes o a ise in govenment spending. As a esult the IS cuve shifts hoizontally to the ight. As output inceases the money maket moves into a position of excess demand which foces the inteest ate up. The issue is how much the inteest ate must ise in ode to estoe equilibium as this detemines how much investment is cowded out and the oveall effect of policy on equilibium output. LM 1 1 LM IS IS 1 1
8 When the demand fo money is inteest inelastic, the inteest ate must ise consideably to emove excess money demand. As a esult the LM cuve is steep and the cowding out effect is stong. If though the demand fo money is elatively inteest elastic only a small ise in inteest ates ae equied to estoe equilibium in the money maket. Consequently the LM cuve is flatte and the cowding out effect is weake. In this case fiscal policy has a lage impact on equilibium output. The effectiveness of fiscal policy and the slope of the IS cuve An expansive fiscal policy leads to a ightwad shift in the IS cuve and an incease in equilibium inteest ates. The ise in inteest ates leads to some cowding out of investment which limits the impact of fiscal policy on equilibium output. If investment was elatively inteest inelastic the IS cuve would be steep. Theefoe, the ise in inteest ates would have small cowding out effects. If though investment was inteest elastic the IS cuve would be flatte. Theefoe cowding out is stonge and fiscal policy is less effective. IS1 IS LM LM 1 1 IS 1 1 The effectiveness of monetay policy and the slope of the IS cuve An expansion in the money supply leads to the pivate secto holding lage money balances than demanded at the pevailing inteest ate, the money maket is in a position of excess supply. Excess money holdings ae used to puchase bonds which foces bond pices upwads and inteest ates downwads. Because equilibium inteest ates ae now lowe at evey level of output the LM cuve shifts downwads. The impact of lowe inteest ates on investment depends on the inteest elasticity of investment. When investment is inteest elastic the IS cuve is elatively flat and
9 output expands stongly. When investment is inteest inelastic the IS cuve is steepe and the eduction in inteest ates is less influential on equilibium output. LM 1 LM 1 LM LM 1 1 IS IS 1 1 The effectiveness of monetay policy and the slope of the LM cuve LM 1 LM 1 1 LM 1 LM 1 1 Following an expansion in the money supply how is the excess supply in the money maket coected? When the demand fo money is inteest inelastic the LM cuve is steep. Hee, inteest ates must fall consideably to encouage the pivate secto to hold the exta money balances. A lage fall in inteest ates means that the LM cuve shifts downwads to a geate extent encouaging a lage incease in investment and equilibium output.
10 The low inteest esponsiveness of money demand gives a clue as to why monetay policy is effective in this situation. The emoval of excess supply equies an incease in money demand which comes mainly fom the tansactions pespective though a lage ise in income. If the demand fo money was pefectly inelastic, the LM cuve would be vetical. The only way the money maket equilibium can be estoed is fo output to ise sufficiently so that the demand fo money inceases to estoe balance. When the demand fo money is moe inteest elastic monetay policy is less effective in influencing equilibium output. Only a elatively small eduction in inteest ates is equied to eequilibate the money maket following an expansion in supply. Theefoe the LM cuve is flatte and only shifts downwads by a small magnitude. When the demand fo money is pefectly elastic the economy is often in a position known as the liquidity tap. Hee the inteest ate has fallen to such a low level that the pivate secto finds the compensation fom holding bonds is not sufficiently attactive to fogo the benefits of liquidity (holding money). An expansion in the money supply will have no impact on the inteest ate and the LM cuve, which is in this case is hoizontal, will fail to shift downwads. Monetay policy in this case would be completely ineffectual. b. A positive elationship between pices and the deviation of output fom its full employment level LM 1 LM LM LM IS IS (a) ˆ 1 (b) ˆ 1 The Neoclassical ISLM model assumes that thee is a full employment level of output ˆ such that pices espond in the same diection as the deviation of actual output to this level, P& = π ( ˆ ). Because pices ae no longe fixed then this has a long un implication fo monetay and fiscal policies. In panel (a) the case of a monetay policy expansion is shown. The LM cuve shifts downwads and equilibium inteest ates fall and output expands. Howeve, because
11 output is above its full employment level pices begin to ise. This has the consequence of educing the eal value of the money stock which pushed the economy back towads its oiginal equilibium. Theefoe, in the long un monetay policy is neutal. The money stock is highe, but as the pice level has isen the eal money supply and eal vaiables in the economy ae left unchanged. Panel (b) consides the case of a fiscal expansion. The IS cuve shifts ightwads and equilibium output ises above the full employment level. The subsequent incease in pices will lowe the stock of eal money shifting the LM cuve upwads and moving the economy back to equilibium. In tems of levels, pice adjustment means that fiscal policy is neutal in the long un, but not in tems of composition. Eithe govenment spending (if an incease in govenment spending) o consumption (if a cut in taxes) will be highe, but highe equilibium inteest ates will cowd out an equal amount of investment. The effectiveness of both policies depends on how quickly pices adjust, and whethe o not the policy has an impact on the full employment level of output. If pices adjust slowly, pehaps due to impefect competition factos in labou and poduct makets, output in the shot un can deviate fom its full employment level fo a consideable peiod of time. Hysteesis type effects might also lead to an outwad shift in the full employment level of output (inceased poductivity fom using peviously unemployed factos of poduction, highe paticipation due to geate job oppotunities) may make the effects of policy moe pemanent in the medium to long un. Moe advanced poblems 5. Conside the following: C = d d = T T = 100 I = G = 100 (M/P) d = M = 1000 P = 1 Whee C is consumption, d is disposable income, is income, T is the level of lump sum taxes, I is investment, is the inteest ate, G is govenment spending, (M/P) d is eal money demand, M is the money supply and P is the pice level.
12 a. Calculate the IS and LM cuves and find the equilibium level of inteest ates and income. What is the level of investment in equilibium? The IS cuve: = C + I + G ( 100) = * + ( 1 0.4) = = The LM cuve: 1000 = = + Equilibium is whee IS = LM = 5000 = = 1 1 = 0. I ( 0.) 180 = * = ( 0.) = * = 1066 (fom the IS cuve) o 1 ( 0.) = 1 + * = 1066 (fom the LM cuve) b. Concened that the cuent level of investment is too low the govenment announces an expansionay fiscal policy and inceases govenment spending by 00. Find the new equilibium values of output, inteest ates. By how much has investment been cowded out? Govenment spending inceases to 00 giving the new IS cuve:
13 = Equilibium is whee IS = LM = = Equilibium inteest ates ae = = 0.5 Investment in equilibium is: I ( 0.5) 146 = * = Equilibium output: ( 0.5) = * = (fom the IS cuve) o ( 0.5) = + * = (fom the LM cuve) Following the fiscal expansion thee is an incease in output and inteest ates, but investment is cowded out. c. The level of income in b is the full employment level. What might be expected to happen if the govenment doesn t incease govenment spending by 00 as in b? If output is below the full employment, < ˆ then pices would be expected to fall P, but by how much? The full employment level is taken fom pat b. ˆ = What is equilibium inteest ate at ˆ = ? Fom the IS cuve,
14 1 = = ( ) 1666 = ˆ = Fom the LM schedule, the eal money supply equied to delive inteest ates of 15.% is: M P ( ) *( 0.15) 000 = * = Theefoe, the pice level needs to fall to: 1000 = 000 P = P 1 As a esult of lowe inteest ates investment expands : I ( 0.15) 46 = * = 6. Suppose the govenment changes the tax system away fom lump sum taxes to a popotional income tax. Tax evenue is now equal to t whee t is the maginal tax ate. a. Wite down the new consumption function and deive the IS cuve Consumption is still a linea function of disposable income d = ( 1 t) C = a + c( 1 t) Substituting into the IS cuve using a simila fom fo investment and govenment spending ( 1 t) + I( Θ) G = a + c, +
15 ( 1 c( 1 t) ) = a + + I(, Θ) G + a + I = 1 (, Θ) + c( 1 t) G b. Use the ISLM diagam to show how changes in maginal tax ate affect the equilibium level of output? Changes in the tax ate lead to pivots in the IS cuve. Fo a given level of autonomous expenditue, the multiplie effect on output would be geate when the tax ate is lowe. This leads to pivots because if inteest ates ae high autonomous expenditues (investment) ae lowe, so the effect of the tax ate cut on output is smalle. Likewise, as inteest ate falls the ise in autonomous expenditues has a geate effect the highe the multiplie (lowe the tax ate). 0 LM 1 IS 1 ( 1, Θ) + c( 1 t ) a + I G 1 =, 1 1 ( 1, Θ) + c( 1 t ) a + I G =, t 1 > t 1 At the inteest ate 1, a cut in taxes would lead to a pivot in the IS cuve and output inceases to. Howeve, the money maket is now in a position of excess demand, hence inteest ates ise, investment is cowded out and the economy moves to a new level of equilibium output at.
16 7. The economy is chaacteised by the following set of elations: C = d d = t t = 1/6 I = G = 100 M d = 9000 M = 00 Whee C is consumption, d is disposable income, is income, t is the tax ate, I is investment, is the inteest ate, G is govenment spending, M d is money demand and M is money supply. a. Deive the IS and LM schedules The IS cuve, = C + I + G: ( 1 ) = * 6 ( 1 ) = = The LM cuve, M = M d : = = b. Calculate the equilibium level of income () and inteest ate () in the economy. Equilibium income and inteest ates ae whee the IS and LM cuves intesect epesenting a geneal equilibium of the goods and money makets = = 7500
17 The equilibium inteest ate is = = 0.1 o 10% The equilibium level of output is ( 0.1) 600 = * = fom the IS cuve ( 0.1) 600 = * = fom the LM cuve c. At the equilibium in (i) the economy is below its full employment level of output * = 750. By how much does the govenment have to incease its expenditue in ode to each this level of income? What is the budget deficit/suplus at this point? What is the new equilibium ate of inteest and how much is investment cowded out? If ˆ = 750 then what is the equilibium inteest ate? Fom the LM cuve: ( 750) = * = 9000 = = 0.1 Given this inteest ate, what level of G will geneate ˆ = 750? Fom the IS cuve 1 ( 750 ( 750) ) * ( 0. ) + G 750 = * 6 1 G = Hence the equied incease in govenment spending is ΔG = = 8. The budget deficit is the diffeence between govenment spending and tax evenues, G  T then T = 1 *( 750) = 15 If = Govenment deficit ( G T ) = = 58. At the new equilibium inteest ate I = *(0.1) = 1
18 Thee is actually disinvestment, implying at these inteest ates the existing capital stock is above its optimal level. d. Suppose the govenment decides against a fiscal expansion and decides to implement a monetay expansion. What incease in the money supply would be equied to each the taget * = 750. What is the govenment deficit/suplus at that point? A monetay expansion to achieve = 750 Given the oiginal IS cuve, what inteest ate is equied to meet the taget? 750 = = = 0.05 What money supply will achieve this inteest ate? Fom the LM cuve: M ( 750) 9000 * ( 0.05) 1050 = * = Hence the equied incease in the money supply is ΔM = = 750 The govenment deficit: G = 100 and T = 1 ( 750) = 15 ( G T ) = = 5 6 A suplus! Although govenment spending hasn t changed tax evenues have isen due to the highe level of equilibium output. Incidentally, lowe inteest ates mean that investment is highe at I = =. ( ) 50 e. The govenment s fiscal ules imply that it must un a balanced budget. What combination of fiscal policy (inceasing G) and monetay policy (inceasing M) would enable it to each the full employment level of output whilst maintaining the balanced budget? What combination of monetay and fiscal policy will achieve the full employment level of output and maintain a balanced fiscal budget? At = 750 T = then ( 750) 15 1 = 6
19 Hence, balanced budget equies G = 15 implying ΔG = = 5 Substituting this into the IS cuve: ( ( 750) ) = * = 75 = = This is the inteest ate that is simultaneously consistent with G = T and = 750. Fom the LM cuve: M ( 750) 9000 * ( 0.075) 85 = * = Hence, the change in the money supply equied to achieve the inteest ate that satisfied full employment and a balanced budget is ΔM = = What policies could the govenment use to keep income at its pevious level following: a. an incease in cedit cad faud Cedit cads ae a way of dawing on cuent accounts. As a esult of inceasing faud the demand fo money (liquidity pefeence) ises at each income level. The LM cuve shifts upwads as the domestic inteest ates ae highe at each level of output. Theefoe the economy moves fom equilibium a to equilibium b, and output falls fom 1 to. Thee ae two ways in which this could be offset. One would be an expansive monetay policy to lowe equilibium inteest ates and evese the shift in the LM cuve. This would move the economy back to point a. Hee cedit cad faud inceases the demand fo money, so an expansion in the money supply means that the pivate secto can hold exta money balances without having to sell bonds which would foce up inteest ates. Altenatively, thee could be an expansion in the IS cuve though pehaps a ise in govenment spending o a tax cut. This will move the economy to point c. This fiscal expansion diectly offsets the output effect of the cedit cad faud.
20 LM LM 1 1 c b a IS 1 b. An incease in the maginal popensity to save LM 1 LM a 1 b c IS IS 1 This is the same as a fall in the maginal popensity to consume, which ceates an inwad pivot in the IS cuve fom IS 1 to IS. This is because the multiplie effect of the autonomous expenditues is educed by geate leakages fom savings. As a esult the economy moves fom point a to point b and output falls. To evese this, the govenment could unleash a fiscal expansion and shift the IS cuve to IS, o move the economy to point c though an expansionay monetay
21 policy. In doing so they must howeve note that the multiplie is now lowe because of the highe saving popensity. An altenative would be to ty and diectly offset the impact of the highe saving popensity and pevent the IS cuve fom pivoting. If thee ae popotional income taxes then the IS cuve may take the following fom. a + I + G = 1 c(1 t) Following a fall in the popensity to consume, c, the IS cuve can be pevented fom pivoting if the multiplie is left unchanged. This could be achieved though a compensating fall in the tax ate t. Although households save a lage popotion of thei disposable income, a tax cut will incease the level of disposable income leaving consumption unchanged. 10. Using the ISLM model, suggest a suitable policy mix to achieve the following: a. an incease in income whilst keeping inteest ates constant LM 1 LM b 1 a c IS 1 This could be achieved by a fiscal expansion (eithe a ise in govenment spending o a eduction in taxes) with the inteest ate accommodated by an expansion in monetay policy. The fiscal expansion will shift the IS cuve to the ight. The incease in output will lead to an incease in the demand fo money fo tansactions puposes. To achieve this, the pivate secto will sell bonds, loweing bond pices and focing up inteest ates. Theefoe the economy moves fom point a to point c. In ode to pevent this,
22 policymakes must incease the money stock sufficiently so that the pivate secto can satisfy thei liquidity pefeence without selling bonds. This will shift the LM cuve downwads and the economy will move to point c. Output expands futhe, because the subsequent fall in inteest ates eveses the cowding out effects of the initial fiscal expansion on investment. b. a decline in the fiscal deficit while keeping output constant LM 1 LM 1 a b c IS 1 To close a fiscal deficit will equie eithe an incease in taxes o a eduction in govenment spending. Eithe of these will shift the IS cuve inwads. Howeve, to pevent this fom educing output the govenment will need to unleash a monetay expansion and shift the LM cuve downwads. This example demonstates why coodinating monetay and fiscal policies might be offe advantages when an economy needs to coect a fiscal deficit. The fiscal etenchment will educe out and move the economy fom point a to point b. Theefoe, unless monetay policy is simultaneously loosened, moving the economy to point c, output will fall. This might be a consideation when choosing to delegate monetay policy to an independent cental bank because monetay and fiscal policies ae now opeated by sepaate bodies coodinating them to such extent may become difficult. In this case the fiscal authoity may be discouaged fom attempting to deal with a deficit in the fist place if it knows that an offsetting monetay policy stance isn t necessaily fothcoming. c. an incease in the shae of investment in GDP See the answe to pat b. Hee a fiscal etenchment and a monetay expansion keeps output at the same level, but lowes the pevailing domestic inteest ate in
23 equilibium. As a esult investment expands and epesents a highe popotion of GDP. If the fiscal contaction was a ise in taxes, household consumption will be lowe, o altenatively the fiscal contaction epesented a fall in govenment spending as a popotion of output. 11. It is agued that the following equation is a moe accuate desciption of investment behaviou: I = I + β Investment is equal to a fixed quantity I and positively elated to income. a. What factos might justify this fom of investment function? Fist, this functional fom suggests that investment is insensitive to inteest ates. This is not an unconventional thought. Fist, inteest ates may not epesent the tue cost of capital which also needs to take into consideation elements such as depeciation and capital gains. It is also widely consideed that inteest sensitivity is low in its own ight, and changes in output ae much moe significant. Fo example, if the economy is expected to ente into a sevee ecession fims may be unwilling to undetake lage investment pojects egadless of how low cuent ates of inteest actually ae. Vicevesa, if the economy is expanding stongly fims may be willing to undetake investment pojects even if the inteest ate is ising. Thee ae vaious easons as to why investment might be positively elated to income. It is widely acknowledged that indicatos of business optimism and confidence ae impotant dives of investment, and these in themselves tend to be pocyclical. Also, q valuations of investment pojects ae likely to ise if the economy is pefoming well, and this is an indicato that the economy will continue to pefom well in the futue. Finally, it might be agued that because financial makets ae impefect due to asymmetic infomation, the availability of cedit may be a moe impotant facto than the cost of cedit. When cuent output is stong, it would be expected that fims will have geate pofitability and can theefoe finance moe investment pojects fom intenal funds. b. Using this new investment equation, constuct an IS cuve. What happens to the size of the multiplie? Substituting the new investment equation into the typical fom gives: ( ) = a+ c T + I + β + G
24 ( 1 c β ) = a ct + I G + a ct + I + G = 1 c β = kae whee 1 k = and AE = a ct + I + G 1 c β Note, that because investment now esponds positively to output movements the multiplie in the economy is much geate. Changes in autonomous expenditue than geneate output movements will now have feedbacks though both consumption and investment. c. Using the new IS cuve, examine the effects of fiscal policy on equilibium output. Fiscal policy is vey effective, fo two easons. Fist, the multiplie is lage, so fo a given fiscal expansion the ightwad shift in the IS cuve is much geate. Second, because investment is inteest insensitive thee is no cowding out effect. So, oveall fiscal policy can have a significant impact on the economy. In fact, in this case fiscal policy actually cowds in, athe than cowds out, investment expenditues. IS LM 1 1
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