Problem Set 1 Answers. a. The computer is a final good produced and sold in Hence, 2006 GDP increases by $2,000.

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1 Social Analysis 10 Spring 2006 Problem Se 1 Answers Quesion 1 a. The compuer is a final good produced and sold in Hence, 2006 GDP increases by $2,000. b. The bread is a final good sold in GDP increases by $2. c. The flour is an inermediae good a good used in he producion of some oher good. Hence, GDP does no change as a resul of his ransacion. d. The basic value of he book is $10. Tha is how much you would have had o pay for i if you had bough i direcly from he suden who sold i o he Coop. If hey bough i new, is value had obviously depreciaed during heir ownership. Tha, in iself, would no affec GDP. The fac ha now he Coop can sell he book for $50, however, almos cerainly does no mean ha he book s value appreciaed afer he Coop bough i. Raher, i indicaes ha he Coop provided a service o is cusomers. I cenralized he process of buying and selling used exs, and provided a convenien way for consumers of used books o purchase wha hey wan. Wha is he value of his service? $40 he difference beween wha he Coop paid and he final sales price. Hence, 2006 GDP increased by $40. e. Given ha he card was already in he hands of a privae collecor, i consiues a used good (arguably now an asse) previously produced and sold. Hence, his ransacion would have no impac on GDP. 1

2 Quesion 2 a. Nominal GDP in year is calculaed as: P Q + P Q + L+ P where P i Q i i = 1, N Q..., N, is he price of good i in year is he quaniy of good i produced in year N (for each of he N goods in he economy) In his case, N = 3 (here are 3 goods in he economy). Hence, nominal GDP in 20 equals: P RB RB TP TP + P Q + P Q = $25x100 + $1x500 + $2x1000 TShirs TShirs Q = By a similar calculaion, nominal GDP in 2005 is found o be $7,100. b. Real GDP in year, using year b as a base, is calculaed as: Pb Q + Pb Q + L+ P where P i b i = 1,..., N b is he price of good i in year b (he base Q i Q is he quaniy of good i produced in year N, year) N (for each of he N goods in he economy) So, he calculaion for real GDP in 2005, using 20 as a base, is: $5,000 TShirs TShirs RB RB TP TP P Q05 + P Q05 + P Q05 = $25x110 + $1x500 + $2x900 = $5,050 The calculaion of 20 real GDP, using 20 as he base year, is jus he calculaion for 20 nominal GDP. Thus, 20 real GDP is $5,000. c. To calculae he percenage change, or growh rae, beween 20 and 2005, we simply ake Y 05 Y Y $5050 $5000 = $5000 =

3 where Y sands for real GDP in 20, and Y 05 sands for real GDP in So real GDP grew by 0.01 or 1% from 20 o d. For his exercise, he base year has been swiched. Now, he real GDP calculaion for 2005 is simply he calculaion of 2005 nominal GDP, which is $7,100. The calculaion of 20 real GDP, using 2005 as a base, is: TShirs TShirs RB RB TP TP P05 Q + P05 Q + P05 Q = $25x100 + $1.50x500 + $4x1000 = $7,250 Noice how sensiive hese calculaions are o wha year is chosen as he base. e. The calculaion is now: Y 05 Y Y $7,100 $7,250 = $7,250 = 0.02 Because he base year on which are calculaions are based has changed, we ge a very differen picure of he performance of he economy beween 20 and f. The GDP deflaor is calculaed as: Nominal GDP in year Real GDP in year. Thus, he deflaor for 20 is: Nominal GDP in 20 / Real GDP in 20 (using 20 as a base) = $5,000/$5,000 = 1 (This will always be he case when calculaing he deflaor for he base year, i.e., he deflaor will always be 1.) The GDP deflaor for 2005 is: Nominal GDP in 2005 / Real GDP in 2005 (using 20 as a base) = $7,100/$5,050 = 1.4 g. The percenage change in prices beween 20 and 2005 can be calculaed jus like any oher percenage change: PGDP05 PGDP PGDP = =

4 where PGDP sands for he GDP deflaor in 20 and PGDP 05 sands for he GDP deflaor in Hence, prices changed by abou 40% from 20 o Quesion 3 a. I will ake (70/2.27) = years o he Unied Saes, (70/2.51) = years o India, (70/1.08) = 64.81years o Argenina. Because Nigeria has a negaive real per capia growh rae, is income will never double! Acually, i will half in years. b. Firs, U.S. per capia GDP is growing a an average rae of 2.27%. Hence, any counry which sars from a lower GDP per capia, and has a growh rae of 2.27% or less, will never be able o cach up o he US. This means ha Argenina and Nigeria will never cach up o he US if we assume ha real per capia growh raes do no change. India will insead cach up. Le s consider India. To see how long i will ake o India o cach up o he U.S., we can use he formula provided in he hin: ln y() = ln y(0) + g, where y(0) is real GDP per capia in Firs consider he US. Subsiuing in he equaion he values of he US given in he able we obain: ln y US () = ln Now, consider India. Subsiuing in he equaion he values of India given in he able we obain: ln y India () = ln We wan o find how many years () i will ake for U.S. and India real per capia GDP o converge. We mus keep in mind ha U.S. per capia GDP is coninuing o grow, jus no as fas as in India. We simply need o se he equaion for he U.S. equal o he equaion for India: ln = ln Solving he equaions for : ln ln = = ( ) 4

5 So, if he raes of growh of real GDP per capia lised in he able persis from 2000 on, India caches up wih he U.S. in around years. Quesion 4 The equaion o keep in mind here is he growh raes form of he macro producion funcion: % Y = % A + α % K + (1 α) % L a. A reducion of he average work week would decrease % L, and hence % Y. b. A decrease in he capial gains ax rae would increase he incenive o save. Savings ranslae ino financial capial, which in urn becomes real capial, K. So, % K increases, in urn increasing % Y. c. Developmen of new, higher-yield varieies of grain represens an increase in oal facor produciviy, % A. This ranslaes direcly ino an increase in % Y. Quesion 5 Y %Δ a. Growh in per capia GDP, L, is given by % Y % L. In his case, ha comes ou o be 4.2 (.55) = 4.75%. b = 0.78% c. Many facors besides he savings rae come ino play in he growh process. Firs, growh depends no only on he level of growh in he capial sock (which is wha is mos direcly affeced by savings), bu also on growh in oal facor produciviy, TFP. Boswana could have had a higher growh rae in TFP han Zambia over his period. Likewise, he labor force may have grown. Second, he savings rae is someimes no as imporan as he uses o which he invesmen ha flows from savings is pu. Some counries squander heir financial capial, for example on real esae speculaion or loans o dubious, bu poliically wellconneced, businessmen. A counry wih more efficien capial markes, which channel naional savings o is mos producive uses, can achieve a higher growh rae han oher counries wih a comparable savings raes, bu less efficien capial markes. 5

6 Third, a counry can mainain a higher rae of invesmen han is savings would indicae hrough he inflow of foreign capial. We will sudy his laer on in he semeser. Lasly, a counry wih beer insiuions will almos cerainly be able o achieve a higher rae of growh han a counry wih poor insiuions, regardless of he savings rae. I is in his dimension ha, by all accouns, Boswana has excelled. Graced wih a measure of poliical sabiliy, well-defined and respeced propery righs, and a reasonably efficien and hones public adminisraion, Boswana illusraes how a counry which ges he insiuional facors more or less righ can overcome oher obsacles o susain a high rae of growh. Quesion 6 a. A ceeris paribus decrease in governmen expendiures will improve he governmen budge (i.e.: if we sar wih a balance budge, he governmen will run a budge surplus afer he decrease in G). Public saving increases, hence naional saving increases as well. This can be represened wih a shif o he righ of he supply of loanable funds. The demand curve for loanable funds does no shif because a change in he governmen budge will no affec he amoun agens wan o borrow a each ineres rae. The new equilibrium is a E 2. As you can see he ineres rae is lower and he equilibrium quaniy of loanable funds demanded and supplied is higher. The lower ineres rae leads o higher invesmen. The increase in invesmen due o he fall in governmen spending is called crowding in and i is represened by he movemen along he demand curve from Q 1 o Q 2. 6

7 Ineres rae S 1 S 2 i 1 E 1 i 2 E 2 D Q 1 Q 2 Loanable Funds b. Here we have o consider 2 experimens a he same ime: he invesmen ax credi and he increase in he budge defici. Boh are separaely discussed in your exbook. We now pu hem ogeher. i) The invesmen ax credi leads o an increase in privae invesmen which can be represened wih a shif o he righ of he demand of loanable funds. The supply curve for loanable funds does no shif because he ax credi has no effec on he amoun agens save a each ineres rae. This change leads o higher ineres rae and higher quaniy of loanable funds. ii) The increase in he governmen budge defici implies a decrease of public saving (i.e.: (T - G) falls). Naional saving goes down for any level of he ineres rae. This can be represened wih a shif o he lef of he supply of loanable funds. The demand curve for 7

8 loanable funds does no shif because a change in he governmen budge will no affec he amoun agens wan o borrow a each ineres rae. This change leads o higher ineres rae and lower quaniy of loanable funds. Noe ha he increase in ineres rae induces privae savings o go up (implicily we're assuming ha Y, T, and G don' respond o r --he ineres rae-- bu consumpion does and when r goes up, consumpion goes down, so (Y - T - C) goes up when r goes up). However, his is represened by a movemen along he curve and no by a shif of he curve. i) + ii) The equilibrium ineres rae definiely increases. Wheher he amoun of loanable funds demanded and supplied increases or decreases depends by he magniude of he wo effecs. In he graph below, he equilibrium is consisen wih Q 2 > Q 1. Ineres rae S 2 S 1 i 2 E 2 i 1 E 1 D 2 D 1 Q 1 Q 2 Loanable Funds 8