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Unformatted text preview: Name:
Section:
T.A. Name: 180.1011 ELEMENTS OF MACROECONOMICS
Fall, 2011 Problem Set #3 Prof. Louis J. Maccini
Solutions 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. l. A decline in energy prices should reduce the average price level but otherwise leave the
economy unaffected. True, false, uncertain. Explain in depth. False. A decline in energy prices, that is, i Z), reduces the cost of production for business ﬁrms. Given prices, and assuming ordinary supply conditions, this shifts the aggregate
supply curve to the right. In an aggregate demand—aggregate supply framework, the new
equilibrium (See the diagram below) will be at a lower price level and a higher level of output
and income. A decline in energy prices is therefore a favorable supply shock. It not only lowers the price level but also raises output and income. 2. A country is at war, and the war is going badly. A politician argues that the fact that the
war is not going well has caused a “crisis of conﬁdence" among consumers and this will cause a
recession. Is this possible? If so, how? Use an aggregate demand~aggregate supply analysis to
answer the question. Explain intuitively what is going on. Yes, it is possible. A “crisis of conﬁdence" among consumers could cause consumers to
spend less on consumption goods. This would be represented by a decline in autonomous consumption spending, that is, a l C, which would shift the aggregate demand curve dowuwards
or to the left. See the diagram below. In an aggregate demandaggregate supply framework, the
new equilibrium would be at a loWer price level and a lower level of output and income. When
consumers spend less on goods and services, this reduces the aggregate level of planned
spending. Business ﬁrms respond to the reduction in planned spending by IDWering prices and
reducing the leVel of output. The latter implies that ﬁrms pay out less in income in the form of
wages and salaries, proﬁts, etc. Deﬁning a recession as a decline in output and income, then the
“crisis of confidence" can cause a recession. . clufh $66 M 2. Consider the following macroeconomic model of the economy operating under
“slack conditions”: Y=E
E=C+I+G C = 200 + (3/4)}3,’ K, =Y—TX+TR Ir TX = 240 + (1/3)Y TR=80
1:220
G=4OO where Y is real income or output, Bis aggregate real expenditure, C is real
consumption expenditure, I is real investment expenditure, G is real government spending, Y1”: is real dispdsable income, TX is real tax revenues, TR is real transfer payments. Expenditures are measured in billions of dollars, so that, e.g., autonomous
inVestment expenditures, is $220 billion. a. Provide a brief explanation of each of the relationships of the model. The ﬁrst equation is the equilibrium condition where equilibrium requires aggregate planned
spending to equal output or income. The second equation is a definition of aggregate planned spending which is the sum of planned
consumption, investment and government spending. The third equation is the consumption function which states that consumption rises with
disposable income where the marginal propensity to consume is “A. There is also an autonomous
level of consumption spending of $200 billion. The fourth equation deﬁnes disposable income to be national income less taxes plus transfer
payments. The ﬁfth equation states that taxes consist of an autonomous component, $240 billion, and income
taxes which are the product of the marginal tax rate, 1/3, and national income. The sixth equation speciﬁes that transfer payments are completely autonomous at $80 billion. The sixth and seventh equations specify respectively that investment expenditures are autonomous
at $220 billion and that government purchases are autonomous at $400 billion. 5 i. till' ll; b. Calculate the equilibrium level of income. Show your work, explain why it is
an equilibrium, and draw a graph that describes the equilibrium. Be sure to
label properly the relevant axes and curves. Substitute transfer payments and taxes into diSposable income, and then
substituting the latter into the consumption function, yields C=200+—3—[Y~240——1—Y+80]
4 3
3 1
=200—180+60+~(l~—~)Y
4 3 =80+[—3—][2—)Y =80+—1—Y
4 3 2 Then, in equilibrium, aggregate planned expenditure must equal income, or
Y = E = C + I + G
or, substituting for C, 1 and G, l l Y=E=80+EY+220+400=700+5Y or, solving for Y, Y(l——1)= 700
2 or 1Y=700
2 Ol‘ Y =(2)700 =14oo An equilibrium is achieved where aggregate planned expenditure equals income.
This occurs when the aggregate planned spending schedule intersects the
equilibrium schedule. See the diagram below. E. l: Ill. Ill c. Suppose that Congress is concerned about the cost of sending children to
college. It thus passes a bill that grants each family a $500 tax credit for each
child that is in college, no matter what the household’s income is. When
aggregated over all families that have children in college, this amounts to an
aggregate of $40 billion in tax credits. How can this policy be captured in the
abOVe model? Calculate the effect of this policy on real income. Draw a diagram
to illustrate your answer. And explain carefully what is going on. (i) The policy of granting $40 billion in tax credits to households with children in
college is in effect a tax out, which can be captured in the above model by a decline in autonomous taxes, that is, i, f}? , of $40 billion. (ii) One acceptable approach to calculating the effect on real income is to set TX = 200, which captures the decline in autonomous taxes from $240 billion to
$200 billion. Then, C=200+%[Y~200—%Y+80] 3 =110+(—3)[3)r=110+1r
4 3 2 Then, in equilibrium, = 200~150+60+%[l—1)Y Y=E=C+I+G or, substituting for C, I and G, Y=110+%Y+220+400 Y[l——l) = 730
2 lr=73o
2 01’ r=(2)730=1460 Hence, real income rises by $60 billion. HI I: A alternative acceptable approach is to state the multiplier for a change in
autonomous taxes, which is .— AY = [2
AT)? 1—b(1—t) which in the above model is .3: .3. .3.
i= 4 = 4 z—ﬂ—2— i (2):~~3—
ATX 3( 1] 3(2) 1 4
1—— —— 1” — 
4 3 4 3 2
Hence,
AY = JAE? = —3(—40) = 60 Thus, real income rises by $60 billion. NB: Either approach would be a complete answer to the calculation part of the
question.  1.5“ (iii) The diagram is U (iv) A tax credit of $40 billion is effectively a tax cut of $40 billion. This raises real
disposable income of households by $40 billion. This in turn causes hOllSGiloldStO
increase consumption by the marginal propensity to consume times the increase in
disposable income. Since the marginal propensity‘to consume is %, consumption
spending and thus aggregate planned spending in the primary stage of the multiplier
process rises by $30 billion. This causes business ﬁrms to raise output and income by
$30 billion. The increase in income in the primary stage of the multiplier process further
raises consumption spending in the secondary stages of the multiplier process, causing
ultimately a total increase in output and income of $60 billion. Hr ...
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 Fall '08
 Maccini
 Macroeconomics

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