Workbook For Chapter 5 Of Blanchard Macroeconomics. Part B

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1 Workbook For Chapter 5 Of Blanchard Macroeconomcs. Part B Problem 3 The response of nvestment to fscal polcy. Usng the IS- graph, show the effects on output and the nterest rate of a decrease n government spendng. Can you tell what happens to nvestment? Why? Explan what happens to Investment and why. Now, consder the followng IS- model. G and T are gven. C = c I = b c ( T ) + b b M / P = d d a. Solve for equlbrum output. =. b. Solve for the equlbrum nterest rate. =. (Hnt: equlbrum output determnes money demand.)

2 c. Solve for the level of nvestment by pluggng n equlbrum output from part (a) and the nterest rate that s consstent wth ths level of output from part (b). I =. (Wrte ths as I = a constant term + a term that depends on + a term that depends on M/P. In your answer, the term that depends on ought to have two parts, one that stands for the sales effect on nvestment and another that reflects the nterest rate effect on nvestment and monetary parameters). d. Now we ll derve the effect of G on I. Frst, what s the effect of G on equlbrum? (See part a). / G =. Second, what s the effect of on I? (see part c) I/ =. Because G affects I through, I/ G = ( / G) x ( I/ ). I/ G =. Remember that c 1 < 0. Look carefully at the numerator and the denomnator of the formula you just derved. How can you make sure that ths rato wll be negatve?. e. Now we are gong to explan the condton you just derved n (d), usng for your explanaton the meanng of each of the parameters and how they are related. Frst, recall that a fall n G affects I drectly through and ndrectly (through and then through ). What happens to when G decreases? How does ths affect Investment? What does ths change n do to? So what ends up happenng to when G decreases? How does ths affect Investment? So, for I to rse when G falls, the drect effect must be (smaller/larger) than the drect effect. Now let s thnk about the parameters. What effect does b 1 represent? What effect does b 2 d 1 /d 2 represent? Note that ths last effect contans two terms: () d 1 /d 2, whch s the slope of, whch gves the

3 effect of a one unt change n on, and () b 2, whch gves the effect of a one unt change n on. Interpret your answer to (d) s ths lght.. Addtonal Exercse wth IS - Consder the followng model of a closed economy, where we have the followng demands of consumpton and nvestment: C = c 0 + c 1 D I = b 0 -b 2 where s GDP, C s consumpton, D s dsposable ncome, s the nterest rate, I s gross domestc nvestment. Assume Taxes are fxed at T 0, and assume government spendng (G=g 0 ) to be exogenous. It s helpful to defne a autonomous expendture, A, as: A = c 0 + b 0 + g 0 c 1 T Money supply s fxed (M s = M). Money demand s gven by: M d = m 0 + m 1 m 2 1. Wrte down the equaton of the IS curve, solvng t for. Remember substtute all the exogenous expendture terms for A. Replace D = T. =. What does the IS curve represent?. The slope of the IS equaton s. 2. Wrte down the equaton of the curve, solvng t for. =. What does the curve represent?. The slope of the equaton s. 3. Solve for equlbrum output n ths economy by combnng the IS and equatons (usng the fact that the nterest rates that are consstent wth equlbrum n both markets must be equal n IS- equlbrum). N =

4 Lets call ths a normal year (you ll understand why below). Call ths level of output you have solved for N. Usng algebra or economcs, what happens to N after an ncrease n the money supply, M?. Let s examne the mechansm by whch ths happens. A mnute after M rses, the money market fnds tself n dsequlbrum. To restore equlbrum, the must fall. The reason s that now there s more money n the economy, and ndvduals must be encouraged to hold money rather than, whch s the other asset we consder as a repostory of wealth. Ths causes an ncrease n, whch s a component of aggregate expendture, whch leads to the change n N reported above. Would your answer be dfferent f m 0 changed?. Notce that m 0 s the exogenous component of money demand, just lke M s the exogenous component of money supply. Ths means that exogenous ncreases n money demand wll cause equlbrum output to. Ths economy faces a problem: every few years consumers become very scared of the possblty of war and accumulate money stocks, so that ncreases. ou can wrte the new level as (m 0 + m 0 ). 4. Solve for the equlbrum wth a war scare. W = We call ths output level W because of the war scare. Compare ths result wth N. Whch one do you thnk s larger? Usng basc rules of arthmetc (such as addton, subtracton, and fractons) we calculate the dfference N - W.

5 N W m0 m2 = 1 c1 m + b m The monetary shock the relaton between and M d N - W = slope of IS curve + slope of curve I m gvng you the answer, but show the algebrac work necessary to get to ths result. Be careful wth sgns when addng and subtractng. Look at your answer carefully. Gven what you know about the parameters (postve or negatve? larger than one?) what can you say about the sgn of ths dfference? Is N - W > 0?. 5. The war scare does not affect the equaton and geometrc postons of the IS curve. Why?. On the other hand, the war scare does affect the curve. Wrte down the war scare curve: Do any of the ntercept parameters change (these are the parameters that would cause a shft of the curve)?. Do any of the slope parameters change? (these are the parameters that multply a term; recall you solved the curve for and the curve s graphed on - space). Show the changes geometrcally: normal IS normal Make sure your answers here are consstent wth what you found n questons 3 and 4.

6 Maybe you can now see why havng the equatons, as opposed to just the graphs, s very useful. Suppose that we have defnte numbers for each of the parameters n the C, I, and M d functons. We may have gotten these numbers from econometrc estmates, usng actual data and regresson analyss. Wth those numbers, we can make forecasts of how the war scare wll affect output and of what the approprate polcy response should be. 6. Would a larger ncome-expendture multpler ncrease or dmnsh the dfference between the two equlbrum output levels? Let s go back to the IS curve and fnd the multpler. Wrte down the IS curve agan, but ths tme solve t for =. It s clear that the (ncome-expendture) multpler s. Now that you know ths, what happens to N W?. (Hnt: look at the formula for N W n Queston 4). Now, ths s very nce and mathematcal, but what s the economc ntuton? We can get some of that ntuton by lookng at what happens to the IS and curves. A larger (ncome-expendture) multpler, obvously, does nothng to the curve. Why?. How does t change the IS curve? (Look at the IS curve n Queston 1, where t s solved for ). Does the ntercept change, shftng the curve? If so, up or down?. Does the slope change? If so, s the curve now flatter or steeper?. (Thoroughly unnecessary hnt: a smaller absolute value of the slope mples a flatter curve, and vce-versa). Then, what happens durng the war scare? Use the graphs below to compare two stuatons, one wth a small multpler and one wth a large multpler, by drawng the approprate IS curves on each graph. In each graph I ve drawn two curves. (Usng your answer from Queston 5, determne whch one s the normal and whch one s the war scare.)

7 Wth the graphs, you can see that the fall n output s much larger f the multpler s (large/small). The reason should be pretty obvous. Descrbe that reason n terms of what the war scare does to money demand, nterest rates, and nvestment, and then what happens to output for dfferent multplers:. 7. Would t help to stablze the economy to have a proportonal tax rate t nstead of the lump-sum tax T 0? Re-wrte the C functon, but now nstead of D wrte -t. C =. Now re-wrte the IS functon = Is the proportonal-tax IS curve steeper or flatter than the lump-sum tax one?. Is the multpler larger or smaller?. Now what happens durng the war scare? Use the graphs below to compare two stuatons, one wth a proportonal taxes and another wth lump-sum taxes, by drawng the approprate IS curves on each graph (label the curves normal and war scare approprately ). Whch knd of tax gves a bgger output change durng the war scare? Ths wll gve you the ntuton to fgure out what a proportonal tax does to N W. ou can get the answer easly by pluggng n the new slope of the IS curve nto the formula for N W that we found n Queston 4. N W =

8 Is the whole rato smaller or larger?. Ths means that, wth proportonal taxes, war scares wll cause output to devate from the normal level by (less/more). Why does ths make sense? Suppose there s a war scare. Gven the (by now well-known effects on money demand and nterest rates, we know what happens to output. Ths change n output causes T = t to. What effect does ths have on consumpton and on equlbrum output?. (Hnt: f the exogenous effect of the monetary shock and the endogenous effect of the change n tax revenue offset each other, the latter wll compensate for the former. Fscal contractons wll moderate booms, and fscal stmul wll moderate recessons. But f the exogenous M d effect and the endogenous t effects work together, N W wll be exacerbated.) Now assume that the government decdes not to change the tax structure (t stays wth the old T = T 0 ) but t decdes to change the way t sets ts spendng every year. In partcular t decdes that government spendng wll move accordng to: G = g0 g1 The man mplcaton s that when output falls, government spendng wll rse. 8. The slope of the curve does not change. Why?. Derve the new IS curve. = What happened to the slope? To the multpler?. Agan, use these graphs to draw what happens when the new government expendture polcy s nsttuted. 9. Does the new fscal polcy have any effect on the stablty of output? Explan.

9 . Notce that ths polcy s automatc : t doesn t requre the government to know anythng, to estmate anythng, or to pass any new laws. Most of the lags and uncertantes assocated wth fscal polcy become rrelevant. (By the way, ths last queston was n the frst test n an MIT macroeconomcs course several years ago. It was an n-class, closed book test. It ddn t have any step-by-step nstructons, just plan questons. These nne questons were just one-thrd of the test. And t was a Prncples of Macroeconomcs course.) Dr. Gabrel Martnez Academc 2056 gmartnez@avemara.edu (239)