Midterm Examination (100 pts)
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1 Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion whr ach addiional uni of inpu x brings abou a smallr incras in oupu han h las addd uni of x. 2. Lis h aldor (US 20 h Cnur) Growh facs (10 ps.) a. roughl consan ral pr capia oupu growh of 2% pr ar b. roughl consan ral wag growh of 2% pr ar c. consan ral inrs ra/ral rurn o capial d. consan capial shar of incom and labor shar of incom of 1/3 and 2/3 rspcivl. consan capial o GDP raio, invsmn o GDP raio and Consumpion o GDP raio 3. Dfin Toal Facor Producivi. (5 ps.) Effficinc in which a naion combins is inpu o produc goods and srvics, or alrnaivl, oupu pr uni of composi inpu. 4. Giv an xampl of an inangibl capial invsmn. Show wh such invsmns ar no includd in h Naional Incom and Produc Accouns. (10 ps) Exampls- raining of worrs in a nw sofwar, R&D xpndiurs, larning on h job. Schooling is an xampl, bu is acuall in h naional accouns, bu as a consumpion xpndiur. To s wh hs invsmns ar no includd in GDP, considr h cas of IBM ha pas a salar of $10,000 o Ms. X o ach IBM worrs a nw sofwar pacag. Clarl, h $10,000 salar of Ms. X couns in h Wags Incom cagor of NIPA. Bu i rsuls in an offsing nr ino h corpora profis of IBM, which is dfind as h rsidual of valu addd lss all h claims o valu addd. Par II. 40 Poins 1. Us a graph wih im masurd on h horizonal axis o compar h pah of an conom s pr capia oupu (logarihm) in boh h Solow Modl wih xognous chnological chang and h A modl bfor and afr h following changs. Assum ha prior o h chang, h conom is on is balancd growh pah quilibrium. a. An incras in h conom s savings ra. (5 ps.)
2 A Solow b. An arhqua ha dsros half h conom s capial soc. (5 ps.) A Solow
3 2. Us h Malhus Modl wihou chnological chang or capial. Show graphicall, how ach of h following changs affcs an conom s sad sa populaion and consumpion. a. a dcras in h birh ra (5 ps.) Birh ra c Dah ra c c ss N =AN α L 1 1-α
4 c. an incras in h soc of land (as in h cas of h Nhrlands which filld in som scions of h sa in h 16 h Cnur). (5 ps.) c ss N =AN α L 1 1-α N N 3. Maniw, Romr and Wil (1992) conclud ha diffrncs in savings ras accoun for mos of h diffrncs in inrnaional incom whras Hall and Jons (1999) conclud ha diffrncs in TFP accoun for mos of h diffrncs in inrnaional incoms. Explain how ach papr rachs is conclusion. (10 ps.) MRW (1992) solv for h balancd growh pah lvl of pr capia oupu in an augmnd Solow modl wih boh phsical capial and human capia. Pr capia oupu is a funcion of ach counr s phcial capial and human capial savings ra. Using cross scion daa, MRW sima h logarihm of pr capia oupu quaion. Thir prox for h phsical savings ra is h PWT invsmn ra and hir prox for h human capial savings ra is avrag ars of schooling of h populaion from Barro and L. Th find an R 2 of.75, hrb concluding ha diffrncs in savings ras accoun for 75 prcn of h oupu dispari across counris. HJ (1999) impu TFPs in a Cobb-Douglas producion funcion wih phsical capial and human capial adjusd labor hours. Th consruc capial socs for ach counr using h law of moin for capial and h im sris for invsmn. For human capial, h us Mincrian wag rgrssions ha sima h rurn o schooling. Th hn us hs rurns o compu h human capial soc for ach counr. Wih a capial shar of 1/3, h hn impu h Solow rsidual. Th conclud ha roughl 2/3rds of h oupu diffrncs ar TFP diffrncs. 4. Evalua h A modl as a modl of h voluion of inrnaional incom diffrncs ovr h las millnium. (10 ps.) Th A modl is no a good modl of h voluion of inrnaional incoms bcaus i prdics ha growh miracls ar quall lil in rich
5 counris as poor ons, and ha h ar quall lil now as h wr wo hundrd ars ago. Th A modl prdics ha an prmann chang in polic or savings ra will lad o a prmannl highr growh ra. If h US a som poin bcam li h Japans or li China oda, h modl prdics a prmanl highr ra of growh for h US conom. W hav nvr sn his happn- a growh miracl in a rich counr. Par III 30 Poins Considr h following growh modl wihou an populaion growh or chnological chang. Th imporan poin is ha hr ar wo forms of phsical capial: srucurs dnod b and quipmn dnod b E. Th modl quaions ar 1 1. N c = ( 1 s s ) 3. = A E N = (1 δ ) + s 4. E + 1 = (1 δ ) E + s a. Solv for h growh ras of h pr capia variabls, c,,,, and h rnal prics w, r and r. (10 ps.) Sp 1. Divid (2) b o conclud ha 1+g =1+g. No ha bcaus hr is no populaion growh, w (2) is jus + 1 = (1 δ ) + s Sp 2: Divid (4) b =E /N o conclud ha 1+g =1+g + 1 / = (1 δ ) + s / Sp 3. Ta h raio of da +1 and da of Eq. (3) = (5) Using h rsuls in Sps (1) and (2) wih Eq. (5), i follows ha ( ) ( ) 1+ g + g 1 + g = 1. (6) Hnc i follows from (6) ha h onl soluion is g =0. Sp 4. From (1), i follows ha g c =g. Sp 5. Th rnal prics and wag ras saisf: w = ( 1 ) N r = r = = E
6 I follows ha sinc,, and do no grow, ha nihr w, r, nor r grow. b. Rorganiz h following NIPA abls along h lins of h modl so as o arriv a a numbr for /GDP, E/GDP, C/GDP/ X /GDP and X /GDP whr X and X dno invsmns in ach p of capial (10 ps.) GDP $100 Consumpion $60 Invsmn Srucurs $5 Equipmn $10 Govrnmn Expndiurs Govrnmn Invsmn Srucurs $5 Equipmn$5 Govrnmn Consumpion $15 N Expors 0 Capial Socs and Land Priva Capial Srucurs $50 Equipmn $100 Land $5 Govrnmn Capial Srucurs $50 Equipmn $75 C/GDP= [$60 (Consumpion) + $15 (Govrnmn consumpion)]/100=.75 X /GDP=[$10 (Equip)+ $5 (Govrnmn Equipmn)]/100=.15 X /GDP=[$5 (srucurs) + $5 (Govrnmn Srucurs)]/100=.10 /GDP=[$50 (Priva Srucurs) +$5 (Land) + $50 (Govrnmn Srucurs)]/100=1.05 E/GDP=[$100 (Priva Equipmn) + $75 (Govrnmn Equipmn)]/100=1.75 c. Us h numbrs from par (b) oghr wih h obsrvaion ha h ral inrs ra in h conom is.05 o calibra h modl paramrs. (10 ps) Paramr Valu Sps
7 A 1.0 Normalizaion/Choic of Unis s.10 Obsrvaion of X /GDP as calculad in (b) s.15 Obsrvaion of X /GDP as calculad in (b).16 r =i+δ = =.155, = r =. 155x1.05 = r =i+δ = =.315, = r =. 312x1.75 =. 546 δ.105 δ.262 δ δ = s =. 10x1.05 =.105 = s =. 15x1.75 =..262 E
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