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Unformatted text preview: Name:
Section:
T.A. Name: 180.101 ELEMENTS OF MACROECONOMICS
Fall, 2011 Problem Set #4 Prof. Louis J. Maccini Answer Key INSTRUCTIONS: Above, write your name, section number and T. A. name. Answer each
question in the space provided, or on the back of the same sheet. 1. Consider an economy in which tax collections are always $400 and in which the three
components of aggregate demand are as follows: GDP 1 Taxes Disp. Income C I I I G
$1,360 I $400 $960 $720 I $230 I $500
1,480 400 1,080 810 I 230 I 500
_ 1,600 400 1,200 , 900 230 I 500
1,720 400 1,320 990 230 I 500
1,840 I 400 1,440 1080 230 I 500 Find the equilibrium of this economy graphically. What is the marginal propensity to
consume? What is the multiplier? What would happen to equilibrium GDP if government
purchases were reduced by $60 and the price level remained unchanged? Using E=C+I+G we can calculate total planned expenditures for different levels of income. I GDP I c l 1 G E 
I $1,360 $720 $230 $500 _ $1,450 I
1,480 810 I 230 500 1,540 I
1,600 900 I 230 500 1,630 I
1,720 990 I 230 500 1,720 I
1,840 1080 I 230 500 1,810 I Graphically: E AC Equilibrium GDP is 1720 since Y=E. The marginal propensity is giVen by . Looking at the
(II: data table one can see that as It,“ increaSes from 960 to 1080, consumption increases ﬂow 720 to
90 3 810. Hence we have the marginal propensity to consume equals 15 = 1—56 = Z = 0.75 . The
multiplier is 1—17; = l g 75 = 4. If government purchases fell by 60, and the price level were unchanged, GDP would fall by 60x 4: 240 m 1480. ' "’1 T: HE 1' "ll .__....... 3 2. Consider an economy similar to that in the preceding question in which investment is also
$230, govarnment purchases are also $500 and the price level is also ﬁxed. But fences now
vary with income and, as a result, the consumption schedule looks lilce the following: Find the equilibrium graphically. What is the marginal propensity to consume? What is
the tax rate? Use your diagram to who the effect of a decrease of $60 in government
purchases. What is the multiplier? Compare this answer to your answer to Quastion 1
above. What do you conclude? As in the previous question we can calculate total planned eXpenditures: Graphically: \1 r. b E "1“? Icon me i l ll} li Eli Compared to question 1, the total expenditure line has a ﬂatter slope, but it still crosses
the 45degree line at a GDP of 1720. The marginal propensity to consume is still 0.75.
Now, however, the marginal tax rate is 1/3 (that is, when income rises by 3, taxes rise by l
1). Consequently the multiplier is given by: ~————1———— — ~———~—————  2 . A reduction in G of 60 will lower equilibrium GDP by 2 x 60 = 120 , to a new level of
1600. Comparison of the two questions shows that the introduction of a variable tax
lowers the multiplier. 3. Consider an economy described by the following set of equations:
C = 120 + 0.8K,“
I = 240
G = 480 TX = 200 + 0.25Y Y is real income or output, C is real consumption expenditure, I is real investment
expenditure, G is real government spending, Y dis is real disposable income and TX is real tax revenues. Find the equilibrium level of GDP. Next, ﬁnd the multipliers for
government purchases and for ﬁxed taxes. If full employment comes at Y=1,800,
What are some policies that would mOVe GDP to that level? Km =Y—TX
C=120+0.8(Y~TX)
C = 120+ 0.8(Y— 200— 0.2510 Y=C+I+G Y=120+0.8Y—~0.8><200~0.8><0.25Y+240+480
Y:120+0.8Y~160~—O.2Y+240+480 Y = 680 + 0.6Y (1—0.6)Y = 680
1 Y = —— 680
0.4 Y=17OO The multiplier for government expenditures equals: 1 l _ 1 J“ = 2.5 1—b(1—t):l—O.8x(l~—0.25) 1—0.6 0.4 The multiplier for fixed taxes equals: b 0.8 _ 0.8 3.53:4 _1——‘b(1t)=~1—0.8><(1—0.25): 1—0.6 : 0.4 To raise GDP by 100, a) raise G by 40, and the multiplier of 2.5 will do the rest,
or b) lower taxes by 50, and the multiplier of 2 will do the rest. 4. This question is a variant of the previous problem that approaches things in the
way that a ﬁscal planner might. In an economy whose consumption function and tax function are as given in question 3, with investment ﬁxed at 240, ﬁnd the
value of G that would make GDP equal to 1,800. There are two ways of answering this question:
1) Having done question 3, we know the equilibrium level of output is 1,7 00.
Therefore we need to increase G such that equilibrium output increases by
100. Since the multiplier for government expenditures is 2.5, G needs to increase by 100/ 2.5 = 40. Therefore the level of G that would make GDP
equal to 1,800 is 480+40=520. 2) We can assume that Y=1800 and solve for the level of G that satisﬁes the
equilibrium condition. We have: Y=120+0.8Y—160—0.2Y+240+G
Y: 200+O.6Y+G 041’ = 200+ G Using the fact that Y=l,800 we get: G==520 5. Suppose banks keep no excess reserves and no individuals or ﬁrms hold on to
cash. If someone suddenly discovers $12 million in buried treasure, explain what
will happen to the money supply if the required reserve ratio is 10 percent. How
does your answer change if the reserve ratio of 25 percent or 100 percent? The money multiplier is given by: 1/ 8 where g is the reserve ratio. Since we are
assuming that banks keep no excess reserves and no individuals or ﬁrms hold
cash the reserve ratio equals the required reserve ratio which is 10 percent.
Therefore the money multiplier equals 1/0.l = 10 . An initial increase of $12 million in reserves will lead to an increase in the money supply of
12 x 10 = 120 million dollars. If the reserve ratio is 25 percent the money multiplier is 1/ 0.25 = 4 and the
increase in money supply is 12 x 4 = 48 billion dollars. If the reserve ratio is 100
the money multiplier is 1/1 = 1 and the increase in money supply is 12 x1 = 12
billion dollars. ...
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This note was uploaded on 01/12/2012 for the course ECON AS.180.101 taught by Professor Maccini during the Fall '08 term at Johns Hopkins.
 Fall '08
 Maccini
 Macroeconomics

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