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Question 1

In the tiny island of Papaya Republic they once again need your help. You have been called to actas a consultant to the government. The economy of Papaya Republic produces and consumespapayas and laptop computers only. In the following table you can find data for two different

years:

Year 2000 Year 2007

Price of a laptop $5,000 $6,000

Price of a papaya $10 $20

Number of laptops produced 100 120

Number of papayas produced 500,000 400,000

a) Using the Year 2000 as the base year, compute the following statistics for each year:Nominal GDP; Real GDP; Real GDP growth rate; the price deflator for GDP; and afixed-weight price index like the CPI assuming that the typical Papayan consumer buys125 papayas and 0.5 laptops every month. (4 pts.)

Nominal GDP(2000) = pL

00qL

00+ pP

00qP

00=5,000*100+10*500,000=$ 5,500,000

Nominal GDP(2007) = pL

07qL

07+ pP

07qP

07=6,000*120+20*400,000=$ 8,720,000

Real GDP(2000) = pL

00qL

00+ pP

00qP

00=5,000*100+10*500,000= 5,500,000

Real GDP(2007) = pL

00qL

07+ pP

00qP

07=5,000*120+10*400,000= 4,600,000

Real GDP Growth Rate=[4,600,0005,500,000]/ 5,500,000=-0.1636 -16.36%

GDP Deflator(2000) =100 %GDP Deflator(2007) = [Nominal GDP(2007)/ Real GDP(2007)]*100=

=[8,720,000/ 4,600,000]*100=189%

CPI(2000) =100

CPI(2007) ={[6,000*0.5+20*125]/[ 5,000*0.5+10*125]}*100=(5,500/3,750)*100=147%

b) What were the inflation rates according to the GDP Deflator and the CPI between year2000 and year 2007? (3 pts.)

Inflation Rate according to the GDP Deflator=89%

Inflation Rate according to the CPI=47%

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c) The Prime Minister is not happy with the figures on inflation you came up with. He asksyou to compute them in some other way. Check how your results change if the base yearnow becomes 2007. (4 pts.)

The Inflation Rate according to the CPI does not change if the base year changes.

Real GDP(2000) with base year 2007 =6,000*100+20*500,000= 10,600,000

Real GDP(2007) with base year 2007=6,000*120+20*400,000= 8,720,000

GDP Deflator(2000) with base year 2007=[5,500,000/ 10,600,000]*100=51.88

GDP Deflator(2007) with base year 2007= 100

Inflation Rate according to the GDP Deflator with base year 2007 93%

d) The Central Statistical office of Papaya had forgot to add data for 2003 to their tables (seebelow). Compute CPI and GDP deflator for the period 2000-03 maintaining 2000 as thebase year. Compute inflation with CPI for the period of 2000-03 and 2003-07. Inaddition, compute inflation with GDP deflator for the period of 2000-03 and 2003-07.Does it make a difference to compute inflation with CPI and with GDP deflator for thethe period of 2000-03 and 2003-07? (4 pts.)

Year 2000 Year 2003 Year 2007

Price of a laptop $5,000 $5,400 $6,000Price of a papaya $10 $15 $20

Number of laptopsproduced

100 90 120

Number of papayasproduced

500,000 600,000 400,000

Nominal GDP(2003) = pL03qL

03+ pP

03qP

03=5,400*90+15*600,000=$ 9,486,000

Real GDP(2003) with base year 2000 = pL

00qL

03+ pP

00qP

03 =

=5,000*90+10*600,000=6,450,000

GDP Deflator(2003) with base year 2000=[9,486,000/ 6,450,000]*100=147

CPI(2003) ={[5,400*0.5+15*125]/[ 5,000*0.5+10*125]}*100=(4,575/3,750)*100=122

Summarizing the information about the GDP Deflator for years 2000, 2003 and 2007

employing base year 2000:

GDP Deflator(2000) with base year 2000=100

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GDP Deflator(2003) with base year 2000=147 Inflation rate from 2000 to 2003=47%

GDP Deflator(2007) with base year 2000=189 Inflation rate from 2003 to 2007=28%

Summarizing the information about the CPI for years 2000, 2003 and 2007 employing

base year 2000:

CPI(2000) =100

CPI(2003)= 122Inflation rate from 2000 to 2003=22%CPI(2007) =147Inflation rate from 2003 to 2007=20%

From the above values we conclude that it does matter to use the CPI or the GDP

deflator in computing inflation rates. This conclusion does not change by taking into

account the new 2003 data information.

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Question 2

The Papayan Central Bank has a fuzzy understanding of why it should really care about inflation.What are the real costs of inflation? Please remind them of the problems associated with inflationwhen:

a) Inflation is expected. (4 pts.)The real costs associated to expected inflation include, for example:

-Shoe-leather Costs: When inflation is high, currency and non-interest bearing checking

accounts are undesirable because they are constantly declining in purchasing power.

People will make extra trips to the bank in order to avoid holding money. These trips

involve real economic costs, and these costs would be avoided with stable prices.

-Menu Costs: If prices rise more rapidly, restaurants and other businesses must change

their menus and price lists more often. These menu cost changes also involve real

economic costs that could be avoided with more stable prices.

b) Inflation is unexpected. (4 pts.)The real costs associated to unexpected inflation include, for example:

-Tax distortions: This cost comes from the interaction between the tax system and

inflation. For instance, although the real rate of return on an asset is the real interest

rate (and not the nominal interest rate), income for the purpose of income taxation

includes nominal interest rate payments, not real interest rate payments.

Similarly occurs if income levels corresponding to different income-tax rates are not

increased systematically with inflation. As a result, people are pushed into higher taxbrackets as their nominal income (but not necessarily their real income) increases over

time due to inflation.

Another example could be the capital-gains tax. Taxes on capital gains are typically

based on the change in the assets dollar price between the time it was purchased and

the time it is sold. The method implies that the higher the rate of inflation, the higher

the tax.

-Redistributing Gains and Losses: When inflation hits, some people gain and some lose.

When inflation is higher than anticipated, significant sums can be redistributed from

creditors to debtors, including the government. Lenders may receive a low or even

negative real return. Homeowners gain because they can pay off their mortgages in less

valuable dollars.A similar logic applies to other nominal contracts, such as private pensions, that are not

indexed to the price level. A sudden burst of inflation drives the real value of such

pensions below what was anticipated, making recipients worse off and pension

providers better off.

-Fiscal Imbalances: When inflation hits, taxpayers gain from postponing paying taxes

(which are usually not indexed for inflation). By postponing tax payments, taxpayers

reduce government inlays temporarily and increase the necessity for the government of

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financing its spending in other ways (issuing debt or through monetization i.e.

printing money to pay for the goods & services it buys). The first way however makes

servicing the debt more expensive (lower prices of bonds and higher interest rates) and

hence monetization will be the only way after a while. But this will induce higher prices,

and hence higher inflation, worsening the inflationary spiral.

-Other: There is some evidence that higher inflation is associated with higher inflationvariability and hence more uncertainty about the rate of inflation, which may make

risk-averse households worse-off. Moreover some agents in the market may just not be

willing to bear certain inflation risks and gains from trade may be lost.

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Question 3

Consider the economy of the Papaya Republic.

1. The consumption function is given by C = 200 + 0.75(Y - T)2. The investment function is I = 20025r3. Government purchases and taxes are both 100

a) For this economy graph the IS curve for r ranging from 0 to 8. (3 pts.)Y=C+I+G

Y= 200+0.75*(Y-T) + 200-25*r +G

Rewriting the expression above with r as a function of Y, G and T:

r=16-0.03*T-0.01*Y+0.04*G

Taking into account G=T=100 we obtain the functional form for the IS curve:

r=17-0.01*Y

b) The money demand function in Papaya is (Md/P) = Y100r and the moneysupply is Ms= 1000 and the price level is 2. For this economy graph the LMcurve for r ranging from 0 to 8. (3 pts.)

Rewriting expression above assuming that in equilibrium Md/P = M

s/P:

r=0.01*Y- 0.01*(M/P)

Rearranging this expression and taking into account that Ms=1000 and P=2 we obtain the

functional form for the LM curve:

r=0.01*Y-5

c) Find the equilibrium interest rate r and the equilibrium level of income Y. (4 pts.)In equilibrium:IS = LM

17-0.01*Y = 0.01*Y-5 Y*=1100 r

*=6

r

IS

17 r =17-0.01*Y LMr =0.01*Y - 5

6

0500 1100 1700 Y

-5

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r

IS

17 r =17-0.01*Y LMr =0.01*Y - 6

5.5

0600 1150 1700 Y

-6

For those who used the new IS at point (d) the result can be similarly computed as:19-0.01*Y = 0.01*Y-6 Y

*=1250 r

*= 6.5

g) Derive and graph an equation for the aggregate demand curve. (5 pts.)In equilibrium:

IS = LM

16-0.03*T-0.01*Y+0.04*G = 0.01*Y- 0.01*(M/P)

Rewriting the equation above expressing Y as a function of T,G and (M/P) we obtain:

Y=800-1.5*T+2*G+0.5*(M/P)

Assuming that Ms=1000, G=T=100 we obtain the expression for the inverse of the AD curve:

Y=850 + (500/P)From this expression we conclude that the AD curve is a convex function in the (Y, P) space.

[Note: if you used the new IS and LM curve in solving for AD it is ok, as long as the

procedure is the one we show here].

P

AD

Y

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h) What happens to this AD curve if fiscal or monetary policy changes, as in parts(d) and (f)?(Note: Intuitive explanation is sufficient and no calculation isrequired) (5 pts.)

Recalling expression above from part g):

Y=800-1.5*T+2*G+0.5*(M/P)

We observe that, as G increases, Y increases for any given P. This means that increases in

government purchases generate a shift in the AD curve to the right.

We observe that, as M increases, Y increases for any given P. This means that increases in

the money supply also generate a shift in the AD curve to the right.

Therefore, as a result of fiscal or monetary policy changes, the AD curve shifts to the right.

Question 4

Suppose the government wants to raise investment but keep output constant. In the IS-LMmodel, what mix of monetary and fiscal policy will achieve this goal? In the early 1980s, theUS government increased government expenditures while the Fed pursued atight(contractionary) monetary policy. What effect should this policy mix have? (5 pts.)

By employing the IS-LM model we can see that the government can achieve its goal (of

rising investment but keeping the output constant) by means of combining a Monetary

Policy expansion with a Fiscal Policy contraction. This argument can be illustrated in

the following diagram:

LM0

LM1 (M1>M0)

r0

r1

IS0

IS1(G1

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In the goods market a reduction in G raises saving and raises equilibrium investment

(for every level of r, Sd is higher and hence the new equilibrium in the goods market is

at a higher Sd=Id). However by itself this would determine a lower output in the IS-LM

equilibrium (that is, if the LM does not move). We move the LM expanding monetary

policy up to the point at which Y* is the equilibrium output level.

The US experienced such sharp Monetary and Fiscal Policies in the early 1980s. Theeffects of the monetary contraction and the fiscal expansion were very much in line with

what the IS-LM model predicts (but notice that in this case its working in the opposite

direction: fiscal expansion and monetary contraction crowd out private investment).

Question 5

One of the smartest economists in the Papaya Republic comes to you and tells you: In theabsence of financial constraints and other capital market frictions, assuming permanentincome hypothesis holds and people have rational expectations, only unpredictable incomechanges may lead to changes in consumption stream of peopleShow that you can match her

intuition explaining why that is true (8 pts.)

Economists refer to Rational Expectations as a forward looking method of forming

expectations which can be interpreted as if people look to the future and do the best job

they can in predicting it. This is not the same as assuming that people know the future, but

rather that they use the information they have in the best possible way.

Strictly speaking, Rational Expectations assumes that people act as if they have a little

algebraic model of the behavior of income over the business cycle in their heads and that

they use this model when guessing their future income. Nobody would actually use such a

model in their personal consumption planning. Nevertheless, the idea is that people may do

so indirectly by news appearing on the television or reading the newspaper, which

themselves reflect the forecasts of public and private forecasters who may use such a modelto get a view about future economic developments.

Therefore, if we assume that consumers obey the PIH theory when taking consumption

decisions and, in addition, have rational expectations, we will conclude that changes in their

consumption decisions do not take place unless they result from unpredictable changes in

current or expected future income.

Question 6

Fantastic news in the Papaya Republic the minister of finances tells you over the phone

We have discovered a large oil reservoir thats going to be available for centuries to comeand enough to supply oil at minimal cost for our national production. Describe himgraphically how the short run, labor market and the long run equilibrium will change inresponse to the news.

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Assume that workers in Papaya experience very low income effects. You may use the graphsbelow.

Short run here (4 pts.)

LRAS NsSRAS0

SRAS1

P0 0 W0/P0P1 1

AD1 NDAD0

*

0Y Y1

*

0N

NOTES

LRAS LM0LM1

r1 1r0 0

IS1

IS0

*

0Y Y1

-The cost of producing output for every pricelevel goes down. Hence, firms can supply moreoutput for every price level.-Both investment and consumption go up.Therefore, the AD curve increases and the IScurve shifts right.-Assume that prices decrease in the SR as a

result of these changes.

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Labor market here.(4 pts.)

NsLRAS Ns

SRAS0

SRAS1

2

1

P0 0 W0/P1 0P1 1 W0/P0

NDAD1 ND

AD0

*

0Y Y1

*

0N N2

*N1

NOTES

LRAS LM0LM1

r1 1r0 0

IS1

IS0

*

0Y Y1

-The labor market is affected in two ways.-Labor demand increases since its optimal forthe firms to demand more workers after thepermanent oil price decrease.-Labor supply may go up since (by assumption)the income effects are small and thesubstitution effects will be dominating theincome effects.

-Short run equilibrium in the labor market takesplace at point 1.

-The labor market new long run equilibrium atpoint 2 pins down a new full employment level

of laborN2*and hence a full employment level

of output that is no longer at point (0) but at a

higher level.

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Long run here (4 pts.)

NsLRAS SRAS0 Ns

SRAS2SRAS1

2W2/P2 1

P2 P0 0 2 W0/P1 0P1 1 W0/P0

ND

AD1 NDAD0

*

0Y Y2

*Y1*

0N N2

*N1

NOTES

LRAS LM0 LM2LM1

r2 2 1r1 0r0

IS1

IS0

*

0Y Y2

*Y1

-The labor market new long run equilibrium atpoint 2 pins down a new full employment level

of laborN2*

and hence a full employment levelof output that is no longer at point (0) but at ahigher level.

-The adjustment from the SR to the LR is dueto the self-correcting mechanism: workers areworking too much for the wages they arereceiving in nominal and real terms.-This will bid up nominal wages and SRAS

will shift to the long-run equilibrium at point 2.

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Question 7

Consider the effects of inflation on a graduated-rate income tax. In 1985, before the taxsimplification of 1986, the individual income tax system in the United States had many

different tax-rate brackets. A married couple paid individual income tax on labor incomein accordance with the following table:

Range ofTaxableIncome

3,540-5,719

5,720-7,919

7,920-12,389

12,390-16,649

16,650-21,019

21,020-25,599

25,600-31,119

31,120-36,629

36,630-47,669

47,670-62,449

62,450-89,089

89,090-113,859

113,860-169,019

169,020-

MarginalIncome

Tax Rate11 12 13 16 18 22 25 28 33 38 42 45 49 50

a) Compute average and marginal tax rates of a couple earning $13,000 in total. (4pts.)

Employing the information in the table above, the marginal tax rate will be 16%. Theaverage tax rate will be 9.09% and can be computed as:

Average Tax Rate =

=[(5,719-3,540)*0.11+(7,919-5,720)*0.12+(12,389-7,920)*0.13+(13,000-12,390)*0.16]/13,000=

=[239.69+263.88+580.97+97.6]/13,000==[1182.14]/13,000= 9.09%

b) Suppose that each persons real income remains constant over time, so thatinflation steadily raises each persons nominal income. If the tax schedule shownin the table had remained unchanged, what would have happened over time toeach couples marginal tax rate? (4 pts.)

If each persons real income remains constant, so that the nominal income increases by

exactly the inflation rate, then people will be pushed into higher marginal income tax

brackets as their nominal income (but not their real income) increases over time with

inflation. This effect is known as the as the bracket creep.

c) What are the likely effects of this on labor supply according your analysis ofpoint b). Suppose there are no income effects. (4 pts.)

Assume from point b) that the bracket creep effect is present and there is absence of

income effects. Then, positive changes in the marginal tax rate (for given average tax rate)

will cut peoples after-tax wages (make leisure cheaper) and tend to discourage them from

working (by the substitution effect).

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d) Suppose now that the dollar bracket limits shown in the first row of the table areadjusted proportionately (or indexed) over time for changes in the real pricelevel. That is, if the price level rises by 5%, each dollar amount raises by 5%.What, then, is the effect of inflation on each couples marginal income tax rate?(This indexing provision applies in the United States since 1985.) (4 pts.)

If the government indexes the dollar bracket limits to the price level, then the marginal taxrate will not change in the case of people seeing their nominal income increase at the

inflation rate but their real income experiencing no change.

e) What are the likely effects of this on labor supply according your analysis ofpoint d). Suppose there are no income effects. (4 pts.)

In the absence of income effects, if the marginal tax rate does not change, peoples labor

supply will not be affected.

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Question 8

The following problem deals with indexed bonds.

a) Consider a one-year nominal bond that costs $1000. After one year the bond paysthe principal of $1000 plus an interest payment of $50. What is the one-yearnominal interest rate on the bond? What are the actual and expected one-year realinterest rates on the bond? Why is the nominal interest rate known but the realinterest rate uncertain? (As a notation for actual and expected inflation, use a and

e, respectively)(4 pts.)

The price of one-year bond today is the present value of the payment it promises in one

year. Given the information above, this present value relationship reduces to the following

expression:

1000=[1000+50]/(1+i); where i=current 1-year nominal interest rate.

Therefore the one-year nominal interest rate on the bond will be i=5%.

The actual one-year real interest rate on the bond will be: ra =ia

The expected one-year real interest rate on the bond is: re =i -e

The actual inflation rate a

t [Pt+1- Pt]/Pt(where, Pt denotes price level at time t) is uncertain

today and therefore the actual real interest rates for a one-year nominal bond will also be

uncertain.

b) Consider now a one-year indexed bond (such as the U.S. Treasurys TIPS TreasuryInflation-Protected Securities). Suppose that the bond costs $1000. One year later, thenominal principal of the bond is adjusted to be $1000*(1 + a), where ais the actualinflation rate over the year. Then the bond pays off the adjusted principal of $1000*(1 +

a) plus an interest payment of, say, 3% of the adjusted principal. What is the one-yearreal interest rate on the indexed bond? What are the one-year actual and expected

nominal interest rates on the indexed bond? Why is the real interest rate known butthe nominal interest rate uncertain? (4 pts.)

Given the information above, he actual one-year real interest rate on the bond will be:

ra =3%+ aa=3%

The actual one-year nominal interest rate on the bond will be: ia =3%+a

The expected one-year nominal interest rate on the bond is: ie =3%+e

The actual inflation rate a

t [Pt+1- Pt]/Pt(where, Pt denotes price level at time t) is uncertain

today and therefore the actual nominal interest rates for a one-year indexed bond will also

be uncertain.

c)

Now, consider an alternative indexed bond. Suppose that the bond costs $1000. One yearlater, the nominal principal of the bond is adjusted to be $1000*(1 + e), where eis theexpected inflation rate over the year. Then the bond pays off the adjusted principal of$1000*(1 + e) plus an interest payment of, say, 3% of the adjusted principal. What is the

one-year expected and actual real interest rate on the indexed bond? Why is the realinterest rate uncertain but the nominal interest rate known in this case? (4 pts.)

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We could design the indexed bonds to be adjusted to the expected inflation rate einstead.

In this case, the real interest rate would be uncertain but not the nominal interest rate.

ra =3%+ ea

ia =3%+e

Nominal and real interest rates cannot be both uncertain in case of a one-year nominal

bond as in this example. It can be so, for example, in the case of equities or stocks.

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Question 9

Consider the following FOMC meeting statement released April 18, 2001

The Federal Open Market Committee decided today to lower its target for the federal fundsrate by 50 basis points to 4-1/2 percent. In a related action, the Board of Governors approved a50 basis point reduction in the discount rate to 4 percent.The FOMC has reviewed prospects for the economy in light of the information that has becomeavailable since its March meeting. A significant reduction in excess inventories seems welladvanced. Consumption and housing expenditures have held up reasonably well, though activity

in these areas has flattened recently. Although measured productivity probably weakened in thefirst quarter, the impressive underlying rate of increase that developed in recent years appears tobe largely intact.

Nonetheless, capital investment has continued to soften and the persistent erosion in current and

expected profitability, in combination with rising uncertainty about the business outlook, seemspoised to dampen capital spending going forward. This potential restraint, together with the

possible effects of earlier reductions in equity wealth on consumption and the risk of slowergrowth abroad, threatens to keep the pace of economic activity unacceptably weak. As aconsequence, the Committee agreed that an adjustment in the stance of policy is warranted

during this extended intermeeting period.The Committee continues to believe that against the background of its long-run goals of price

stability and sustainable economic growth and of the information currently available, the risks

are weighted mainly toward conditions that may generate economic weakness in the foreseeablefuture.

a) What is the likely effect of the policy action described in the statement on money supply?(5 pts.)

A monetary expansion. By lowering the fed funds rate target, the Fed is releasing liquidity

in the economy (in this case reserves that then through the money multiplier become

deposits). This monetary expansion, if unanticipated, will boost AD and possibly bring the

economy closer to Y*.

b) Discuss the orientation of the statement: how concerned seems the Fed in this statementabout inflation relative to output stabilization? Explain briefly why. (5 pts.)

The Fed seems mostly concerned about weakness in the economy (Y < Y*, full-employment)

and unemployment above its natural level. In its balance of risk in fact says that the risksare weighted mainly toward conditions that may generate economic weakness in the foreseeable

future.

c) Interpret for the layman the expression A significant reduction in excess inventoriesseems well advanced.And give it an interpretation in terms of forecasting the futurestate of the U.S. economy. (5 pts.)

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Inventories are stocks of goods that firms accumulate either in expectation of future

increases of demand or because of sudden drops in demand (hence they are excess

inventories). In this case the discussion is about inventories that were accumulated during

the recession and now are being sold. This can be a good sign if interpreted as a

strengthening of demand (but only if production is still strong).

d) What are the reserves of private banks held in the Federal Reserve? Does the FederalReserve pay an interest on them? What is the Fed funds rate? (4 pts.)

It is the interest rate that private banks apply each other to their overnight lending of

reserves (the fed funds). These reserves do not pay interest themselves, but have a price

determined by supply and demand of fed funds (because private banks may have different

needs in terms of reserves in different periodsthey may hold excess reserves or willing to

borrow some reserves to extend their deposits). The market price that arises in equilibrium

in that market is the fed funds rate.

e) Interpret why in the sentence: This potential restraint, together with the possible effectsof earlier reductions in equity wealth on consumption and the risk of slower growthabroad, threatens to keep the pace of economic activity unacceptably weak. Reductionsin equity wealth and slower growth abroad may play a role in keeping the pace ofeconomic activity weak. (5 pts.)

The Fed seems to be afraid of a negative income effect on private consumption, C, (PVLR

goes down because wealththe value of equity people heldhas fallen) and a transmission

of slower business cycle abroad to the US economy through a reduction in the quantityt of

American exports (NX).