Chapters 10 and Imagine an economy that can be described with the following equations:

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1 Chaptes 10 and 11 Wanings: The Keynesian Coss/IS/LM model is a model that is pefect fo ceating extensions and then asking students to incopoate thei extensions in the model. A pefect example is to ask what happens when we assume taxes ae income based athe than lump-sum based (see poblem #5). A second type of question involves detemining the diffeence between a shift of the IS (o LM) cuve and a movement along the IS o LM cuve. My advice is that you change evey possible exogenous vaiable, and then show what happens in the Keynesian coss, IS/LM, and Money Supply/Demand cuves (see poblem #4). Students that can algebaically, intuitively, and gaphically answe questions such as that posed on p. 311 (#1 of poblems and applications) deseve an A on the final exam. B Level Questions 1. Imagine an economy that can be descibed with the following equations: C = (-T) I = G = 100 T = 100 a. Assuming = 10, what is this economy s equilibium level of income? AE = ( 100) (10) = so = b. The spending multiplie descibes how much moe GD (income) is ceated when spending inceases by one unit. In the example above, what is the spending multiplie? What does the spending multiplie depend upon? The spending multiplie is 5 it depends on any non-autonomous factos that change when changes (like the MC). c. Choose diffeent levels of and plot the IS cuve. What is the equation fo the IS cuve (Hint: ou should come up with a mathematical function that is a function of ). The IS cuve is given by the equation = This is found by equating AE with : ( 100) =. d. Now imagine that govenment spending ises fom 100 to 200. What has happened to the IS cuve? The new IS cuve is given by the equation = Thus, an incease in govenment spending does not change the slope of the IS cuve but does incease the intecept the IS cuve shifts up given a highe amount of govenment spending. e. How does the IS cuve depend upon the spending multiplie? Let me e-wite the poblem as: C = a + b( T) I = d - e G = G T = T Equilibium occus when a + b( T) + d e + G =. Solving fo gives bigge (close to 1) the IS cuve gets flatte. a + (b 1) bt + d + G e =. As b gets

2 2. Suppose an economy can be descibed by the following functions: Money Demand = M D = Money Supply = M S 1000 = a. Gaph the money supply/money demand diagam. Assume that = 100 and = 1. What is the equilibium inteest ate? M s 1020 The equilibium inteest ate occus when money supply equals money demand o when 1000 = In this case =.5. b. Now choose diffeent levels of. Gaph the LM cuve in this economy. What is the equation fo the LM cuve (Hint: It should be a function of and simila to pat b of #1). We know the LM cuve is detemined by the intesection of the money supply and money demand cuves. In this case that occus when 1000 = Simplifying this gives the LM cuve elationship: =.005. Note that the LM cuve epesents a positive elationship between inteest ates and income. c. Assume that the Fedeal Reseve aises the money supply to How does the LM cuve change? How much does it shift? What detemines the size of this shift? If the money supply ises fom 1000 to 1250, then the LM cuve is given by 1250 = In this case, 100 = o = If = 100 then = -2. In this case, with highe money supply, the LM cuve has shifted to the ight. This is displayed by the lowe intecept (-2.5) elative to the oiginal intecept (0). 3. Combine the LM and IS cuves of pat c of poblem #1 and pat b of poblem #2. a. What is the economy s equilibium level of inteest ate and income? Setting IS equal to LM gives = 3200 and = 16. b. What is the equation fo the aggegate demand cuve implied by these equations? (Hint: this is not a linea equation) To answe this, I stat be emembeing that the AD cuve plots the elationship between and. Since neithe the IS no the LM cuves that we found in poblems 1 and 2 incopoates, I need to stat at the beginning. Actually, should be in the LM cuve, but in poblem 2 we assumed = 1 so we don t see in the cuent LM cuve. To get a new LM cuve, I set money demand equal to money supply: = = ou see immediately the LM cuve found in pat 7 when = 1. M D Money

3 Setting this LM cuve equal to the IS cuve of = gives an expession fo that is equal to: 10 1 = =. c. What happens to the aggegated demand cuve if govenment spending ises fom 100 to 200? Find the new equation and veify that the equation matches what you believe happens to the AD cuve. 1 Setting the LM cuve of b to the IS cuve of 1d gives an AD cuve of =. The AD cuve has shifted up (to the ight). d. Using the oiginal equations, what happens to the aggegate demand cuve if the Fedeal Reseve deceases the money supply fom 1000 to 750? Again, find the new equation and veify that the equation matches what you believe happens to the AD cuve. 7.5 A decease of the money supply shifts the LM cuve to the left. Its new equation is: LM cuve to the oiginal IS cuve gives an AD cuve of =. The AD cuve has shifted down =. Setting this

4 4. Cuently the Ameican economy is opeating with slow RGD gowth and little inflation. As a matte of fact, a numbe of pofessional foecastes have feaed the possibility of deflation in the futue. Imagine that afte a numbe of inteviews given though the New ok Times, these foecastes spead the impession that deflation will happen. On the plots below, diagam the impact on the economy of the expectations of futue deflation. Label the ode of the changes by placing the numbe 1 next to the fist change, the numbe 2 by the second, etc. AE 45 C+I+G M s LM M d IS M/ L LRAS SRAS AD The desciption fo the above gaphs is on pp of Mankiw. A Level Questions 5. Suppose an economy s consumes, investos, and govenment can be descibed by: C = ( T) I = G = 300 T = 300 a. What is the equation fo this economy s IS cuve? AE = C + I + G = ( 300) and AE = so:

5 = Solving fo gives the invese IS cuve of: = The IS cuve is given by =. b. If = 6, what is the equilibium level of output demanded? 2900 c. What happens to the IS cuve if govenment spending inceases by 100 fom 300 to 400? What happens to the aggegate demand cuve given the same change (assume the LM cuve is upwad sloping)? The new (invese) IS cuve is given by = The IS cuve shifts upwad. With an upwad sloping LM cuve, aggegate demand inceases by less than d. In the fomulation above, taxes ae allocated on a lump-sum basis. That is, egadless of an economy s income, taxes ae always a given numbe (like 300). et in many counties, taxes ae income based athe than lump-sum based (fo instance, in the U.S. we pay a faction of ou income athe than a lump sum in taxes). Let s imagine that fo evey dolla eaned, consumes pay a faction of thei income τ in taxes whee 0<τ<1. In othe wods, the consumption function is now C = (1 - τ) athe than C = ( T). If τ =.1931, what is this economy s equilibium level of output demanded (assume G = 300, = 6, and investment demand emains as befoe). AE = ( ) = Setting AE = gives = and solving fo gives e. How does the IS cuve s slope diffe unde a lump sum tax vesus an income tax? What implications does this have if the Fedeal Reseve wants to stimulate the economy though monetay policy? The equation fo the IS cuve in this case is given by setting AE = and letting vay: = ( ) =. Solving fo gives the invese of the IS cuve = The IS cuve is then Unde the lump sum taxes, the slope of the IS cuve was -.01, unde the income tax the slope gets steepe. Unde lump sum taxes, a decease in inteest ates causes investment to ise which encouages moe household spending. The total impact on income of this decease in inteest ates is elatively lage. Unde an income tax, the same decease in inteest ates cause the same incease in investment but, upon eceiving income, households must spend some of it on taxes so they spend elatively less on consumption leading to less of a multiplie and a smalle incease in income. f. How does the aggegate demand cuve diffe unde a lump sum tax vesus an income tax? The slope of the AD cuve is flatte when the IS cuve is flatte it is steepe when the IS cuve is steepe. Do poblems and applications #1-#5 on pp Do poblems and applications #1-#8 on pp Do poblems and applications #1 on p. 311.