Macroeconomics I. Antonio Zabalza. University of Valencia 1. Class 5. The IS-LM model and Aggregate Demand

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1 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 1 Class 5. The IS-LM model and Aggegate Demand 1. Use the Keynesian coss to pedict the impact of: a) An incease in govenment puchases. b) An incease in taxes. c) An equal incease in govenment puchases and taxes. 2. In the Keynesian coss, assume that the consumption function is given by C= (-T) lanned investment is 100 ; govenment puchases and taxes ae both 100. a) Gaph planned expenditue as a function of income. b) What is the equilibium level of income? c) If govenment puchases incease to 125, what is the new equilibium income? d) What level of govenment puchases is needed to achieve an income of 1,600? 3. Suppose the tax system is T = T + t whee T is a fixed level of taxation and t is the maginal tax ate. a) How does this tax system change the way consumption esponds to changes in GD?

2 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 2 b) In the Keynesian coss, how does this tax system alte the govenment-puchases multiplie? c) In the IS-LM model, how does this tax system alte the slope of the IS cuve? 4. Conside the impact of an incease in thiftiness in the Keynesian coss. Suppose the consumption function is C = C + c ( T) whee C is autonomous consumption and c is the maginal popensity to consume. a) What happens to equilibium income when the society becomes moe thifty, as epesented by a decline in C? b) What happens to equilibium saving? c) Why do you suppose this esult is called the paadox of thift? d) Does this paadox aise in the classical model? Why o why not? 5. Suppose the money demand function is d ( M ) = 1, whee is the inteest ate in pecent. The money supply is 1,000 and the pice level is 2. a) Gaph the supply and demand fo eal money balances. b) What is the equilibium inteest ate?

3 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 3 c) Assume that the pice level is fixed. What happens to the equilibium inteest ate if the supply of money is aised fom 1,000 to 1,200? d) If the Fed wishes to aise the inteest ate to 7 pecent, what money supply should it set? 6. Use the IS-LM model to pedict the effects of each of the following shocks on income, the inteest ate, consumption and investment. In each case, explain what the Cental Bank should do to keep income at its initial level. a) Afte the invention of a new high-speed compute chip, many fims decide to upgade thei computes systems. b) A wave of cedit cad faud inceases the fequency with which people make tansactions in cash. c) A best selle titled Retie Rich convinces the public to incease the pecentage of thei income devoted to saving.

4 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 4 7. Conside the following economy: C = ( T) I = ( ) M = 100 M s = = 1,000 2 d G = T = 100 a) Gaph the IS cuve fo anging fom 0 to 8. b) Gaph the LM cuve, also fo anging fom 0 to 8. c) Find the equilibium inteest ate and the equilibium level of income. d) Suppose the govenment puchases ae inceased fom 100 to 150. How much does the IS cuve shift? What ae the new equilibium and? e) Suppose instead that the money supply is aised fom 1,000 to 1,200. How much does the LM cuve shift? What ae the new equilibium and? f) With the initial values fo monetay and fiscal policy, suppose that the pice level ises fom 2 to 4. What happens? What ae the new equilibium and?

5 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 5 g) Deive and gaph an equation fo the aggegate demand cuve. What happens to this aggegate demand cuve if fiscal o monetay policy changes as in questions d) and e)? 8. Explain why each of the following statements is tue. Discuss the impact of monetay and fiscal policy in each of these special cases and state how the shape of the aggegate demand cuve is affected. a) If investment does not depend on the inteest ate, the IS cuve is vetical. b) If money demand does not depend on the inteest ate, the LM cuve is vetical. c) If money demand does not depend on income, the LM cuve is hoizontal. d) If money demand is extemely sensitive to the inteest ate, the LM cuve is hoizontal. 9. Suppose the govenment wants to aise investment but keep output constant. In the IS-LM model, what mix of monetay and fiscal policy will achieve this goal? In the ealy 1980s the US govenment cut taxes and un a budget deficit while the Fed (the US Cental Bank) pusued a tight

6 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 6 monetay policy. What effect should this policy mix have? 10. The Cental Bank is consideing two altenative monetay policies: eithe holding the money supply constant and letting the inteest ate adjust; o adjusting the money supply to hold the inteest ate constant. In the IS-LM model, which policy will bette stabilize output unde the following conditions? a) All shocks to the economy aise fom exogenous changes in the demand fo goods and sevices. b) All shocks to the economy aise fom exogenous changes in the demand fo money. 11. Suppose that the demand fo eal money balances depends on disposable income; that is, d ( M ) = L [,( t) ] Using the IS-LM model, discuss whethe this change in the money demand function altes the following: a) The analysis of changes in govenment puchases. b) The analysis of changes in taxes.

7 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 7 Answes 1. a) C b) C c) C; also = G = T. 2. a) E=C+I+G= (-100) E= E Slope=1 E= lanned expend. 350 Slope= ,300 1,400 b) E=; = ; =1,300 c)this effect can be solved using the multiplie. 1 = G = 4*25= 100 = + = 1, = 1,400

8 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 8 d) = (-100)+100+G 1,600= (1, )+100+G G= a) C = C + c ( T) whee T = T + t C = C + c ( T t ) + C = ( C ct) + c(1 t ) dc = c (1 t ) d It lowes the maginal popensity to consume fom c to c(1 t) b) GMultiplie 1 1 = = 1 MC 1- c(1- t) Since the MC has deceased, the denominato is highe and theefoe the multiplie is smalle. c) is now less esponsive to changes in G. Theefoe the slope of the IS cuve will be steepe in the, plane. Check this answe fo a specific example of the the IS cuve. See that if I = I (), the slope of the IS cuve is d I () 1 (1 ) o d c = = t d 1 c(1 t) d I ()

9 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 9 If t > 0 the last expession will be lage (IS steepe) in absolute tems. 4. a) Equilibium income is 1 c = ( C+ I + G) T 1 c 1 c d 1 1 = ; d = dc dc 1 c 1 c Theefoe, if dc < 0 d < 0 Income will go down by the extent of the decease in autonomous consumption times the multiplie. b) S = C G= C c ( T) G S = (1 c) C+ ct G ds d (1 c) = (1 c) 1= 1= 1 1= 0 dc dc (1 c) Theefoe, equilibium saving is not affected by the incease in thiftiness. c) Because saving does not incease despite that people consume less. d) No, because in that model income is fixed. Thee, as we saw in a pevious poblem, ds = dc

10 Macoeconomics I. Antonio Zabalza. Univesity of Valencia a) d M = 1, M = s M 1,000 = = d Money Supply 10 5 Money Demand 500 1,000 (M/) b) = (500) = 5 c) = (600) = 4 d) ( / ); s s = M ( M / ) = 300

11 Macoeconomics I. Antonio Zabalza. Univesity of Valencia a) LM IS IS,, C, I The final incease in investment is smalle that the initial shock due to the cowding out effect of the ise in the inteest ate. b) LM LM IS,, C, I c)

12 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 12 LM IS IS,, C, I 7.a) IS cuve = C + I + G = ( 100) (1 0.75) = = = 0 = 1,700 = 8 = ,700

13 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 13 s b) LM cuve M L (, ) = 1,000 = = = 0 = 500 = 8 = 1, ,300 c) IS = LM = =6; =1,100

14 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 14 d) This poduces a hoizontal shift to the ight in the IS cuve that equals the change in G times the multiplie. That is, 1 = G = 4*50= Theefoe, the new IS cuve is = 1, o = The new equilibium is = = 5+ 0,01 = 7; = 1,200 B 7 6 A 1,100 1,200 e) This poduces a downwad shift in the LM cuve. Daw the gaph. The new equilibium is given by,

15 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 15 = = = 5.5; = 1,150 f) The IS cuve stays the same. The LM cuve changes to 1,000 = = New equilibium, = = = 7.25; = 975 M I LM(=4) B LM (=2) A ,100 1,700

16 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 16 g) IS = 1, ,000 LM = 100 Eliminate. Fo instance, solve the fist equation fo ( = ) and substitute the esult on the second equation to get, 1, = + Then, solve fo = This is the Aggegate Demand cuve. To gaph this cuve note that So, the gaphical epesentation of this cuve is,

17 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 17 Aggegate Demand ,100 Keeping explicit G and M, the aggegate demand cuve can be witten as follows (Check that you undestand this): 1 M = G+ 2 It is easy to see that fo the initial values of G and M (100 and 1,000) this equation educes to 500 = which is the oiginal Aggegate Demand (AD) cuve.

18 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 18 Now, if thee is an incease in govenment expenditue to 150, we find that the new AD cuve is 500 = 950+ That is, the new AD cuve will be asymptotic to =950. The AD will shift in a paallel fashion to the ight by 100. Aggegate Demand ,075 1,200 If money supply goes to 1,200, then the AD cuve is 600 = 850 +

19 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 19 The asymptotic values of the cuve do not change, but the slope does and the esult is that fo the inteest ate values consideed hee, the effect is a ightwad shift of the AD cuve ,000 1, To solve this poblem, the best appoach is to wok with an explicit fomal epesentation of the IS-LM model and AD cuve, such as the one consideed in the Appendix to Chapte 11 of Mankiw.

20 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 20 To emind ouselves, C = a+ b ( T) I = c d L (, ) = e f abcde,,,, and ae all positive paametes. IS cuve: a+ c 1 b d = + G T 1 b 1 b 1 b 1 b LM cuve e 1 M = f f Aggegate Demand cuve za ( + c) z zb d M = + G T+ 1 b 1 b 1 b (1 b) f + de/(1 b) Whee, z = f [ f + de/(1 b) ] a) Investment does not depend on (d=0) If d=0, z=1 [ ] IS a+ c 1 b = + G T; theefoe IS vetical 1 b 1 b 1 b

21 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 21 a+ c 1 b AD = + G T 1 b 1 b 1 b Theefoe AD vetical. AD does not eact to monetay policy. Only to fiscal policy. b) Money demand does not depend on (f=0) If f=0, z=0 Multiply both sides LM by f = e M if f = 0, = 1M e f Theefoe LM is vetical ( does not depend on ). 1 M AD =. The AD cuve is a ectangula e hypebola, fo a given M. AD does not eact to fiscal policy. Only to monetay policy. c) Money demand does not depend on (e=0) If e=0, z=1

22 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 22 1 M LM =. Theefoe LM is hoizontal; does f not depend on. AD a+ c 1 b d M = + G T + 1 b 1 b 1 b (1 b) f Theefoe, AD shifts to fiscal policy accoding to full multiplies. Fiscal policy is vey effective. d) Money demand is vey sensitive to If f vey lage, z 1 LM is hoizontal. This can be seen fom the fomula of LM. a+ c 1 b AD = + G T. Theefoe AD is 1 b 1 b 1 b vetical. does not depend on. Fiscal policy fully effective.

23 Macoeconomics I. Antonio Zabalza. Univesity of Valencia a) Expansive monetay policy ( M ) to lowe inteest ate and aise investment, and contactionay fiscal policy ( T ) to lowe consumption and compensate the effect of the expansive monetay policy on output. This will lowe the inteest ate, incease investment, decease consumption and geneate public suplus. LM A LM B IS IS In the US the policy followed in the ealy 80 s was exactly the opposite: tight monetay policy Shift upwads of the LM cuve), which meant a substantial incease in the ate of inteest and theefoe a fall in investment, and a lax fiscal policy

24 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 24 (shift ightwads of the IS cuve), by educing taxes, which aised consumption and geneated a public deficit. LM B LM A IS IS 10. a) Shocks come fom the IS cuve. Then bette to hold constant M and let adjust. LM B A A IS IS

25 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 25 By holding M constant the Cental Bank stees the economy fom A to B. Wheeas if it had followed an accommodating monetay policy to keep the inteest ate constant, it would have led the economy to A, with a much lage oscillation in output. b) Shocks come fom the LM cuve. Then bette to counteact these shocks by a monetay policy that maintains constant the inteest ate. LM A, B LM A IS 11. If the demand fo money depends on disposable income, the LM cuve takes the following fom: e e 1 M = T f f f This means that movements in taxes will not only move the IS cuve, but also the LM cuve.

26 Macoeconomics I. Antonio Zabalza. Univesity of Valencia 26 a) The effects of, say, aising govenment expenditue will, as in the basic model, move only the IS cuve to the ight. b) The effects of loweing taxes will move both the IS cuve (to the ight) and the LM cuve (upwads). This leads to an incease in the inteest ate, and may lead to a fall in income (o in any case, a smalle incease than in the basic model) LM B LM A A IS IS