Midterm Exam. Tuesday, September hour, 15 minutes
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1 Ecoomcs of Growh, ECON560 Sa Fracsco Sae Uvers Mchael Bar Fall 203 Mderm Exam Tuesda, Sepember 24 hour, 5 mues Name: Isrucos. Ths s closed boo, closed oes exam. 2. No calculaors of a d are allowed. 3. Show all he calculaos. 4. If ou eed more space, use he bac of he page. 5. Full label all graphs. Good uc
2 . (5 pos). The ex fgure shows he aural log of real GDP per capa wo coures, A ad B, over he 40 ear perod a. Based o he fgure (crcle he correc aswer),. Cour A s growg faser ha cour B before 990. Boh coures grow a he same rae before 990. Boh coures grow a he same rae afer 990 v. Cour A s real GDP per capa s growg a accelerag rae before 990. b. Based o he fgure, he approxmae aual growh rae of GDP per capa, cour A, over he ere perod s (crcle he correc aswer),. %. 2.5%. 4% v. 5% c. Based o our aswer o par b, ad gve ha populao cour A grows a % per ear, fd he approxmae aual growh rae of real GDP cour A. RGDP RGDP POP POP 2.5% RGDP % RGDP 3.5%
3 2. (0 pos). Suppose ha Apple compa produces oupu accordg o produco fuco Y A, where A s producv ad s he umber of worers. Over he las ear, Apple expereced a 3% crease producv, ad a 0.5% crease he umber of worers. a. Wha s he approxmae chage Apple s oupu? Y ˆ Aˆ ˆ 3% 0.5% 3.5% b. Usg he rule of 70, how log wll ae for Apple s oupu o double, f las ear s growh raes were o coue? ears 3.5 2
4 3. (0 pos). The followg able provdes made up daa o oupu per worer wo coures, whch produce wo goods ol: cars ad meals. Aume ha cars are raded goods whle meals are o raded. Cars produced Meals produced Cour A 2 20 Cour B 3 5 Josh ad sa are IMF ecoomss ha sud he cro cour come dspar he world. Usg he mare exchage rae, Josh foud ha cour A s GDP per worer s 5 mes ha of cour B. oog a hese umbers ad he above able, sa poed ou ha Josh s resuls do mae sese, ad ha he should have used he PPP exchage rae sead of he mare exchage rae. Brefl expla usg he umbers provded above, wh sa foud Josh s resuls flawed, ad how usg he PPP exchage rae ma mprove he cro cour comparso. Based o he oupu per worer daa he able, cour A s oupu per worer s ol 4 mes ha of cour B, so Josh s fdg ha hs rao s 5, s exaggeraed. Poor coures, such as B, ed o have cheaper o-raded goods, ad he PPP exchage rae aes ha o accou. The mare exchage rae o he oher had, s based o prces of raded goods ol, ad herefore eds o udervalue he sadard of lvg poor coures. 3
5 4. (0 pos). Suppose ha oupu s produced wh he Cobb-Douglas produco fucoy AK, 0, where Y s oupu, K s capal pu ad s labor pu. a. Prove ha he Cobb-Douglas produco fuco exhbs cosa reurs o scale. e 0. The, A ( K) ( ) A K AK b. Prove ha f pus are pad her margal producs, he a fraco of oupu s pad o capal ad a fraco of oupu s pad o labor. Pame o capal: AK Pame o labor: K AK Y ( ) AK ( ) AK ( ) Y 4
6 5. (20 pos). Suppose ha he aggregae GDP ca be modeled wh he Cobb- Douglas produco fuco: Y A K, 0, where Y s he oal GDP, A s he Toal Facor Producv, K s he oal capal ad s he umber of worers. a. Derve he equao of oupu per worer ( ) as a fuco of capal per worer ( ). Y AK A b. Derve he equao of oupu per capa ( worers populao s / N. N ), whe he fraco of N Y N Y A 5
7 c. The ex able shows daa for wo coures: U.S. ( ) ad Sra ( ). The varables ad deoe GDP per capa U.S. ad Sra respecvel. A A 2? 3 Based o he above able, f he ol dfferece bewee he wo coures was producv, wha would be he rao of U.S. o Sra GDP per capa? A A d. If he capal share s 2, he U.S. capal per worer s mes greaer ha he Sra capal per worer. Crcle he correc aswer v. 2 6
8 6. (5 pos). Cosder he Solow model dscued cla, ad descrbed as follows. Oupu s produced accordg o Y A K, 0. Capal evolves accordg o K K ( ) I, where s he deprecao rae ad I s aggregae vesme. People save a fraco s of her come. Ths fraco s exogeous. Thus, he oal savg ad oal vesme hs ecoom are S I sy. The populao of worers grows a a cosa rae of, whch s exogeous hs model. Thus, ( ). a. Solve for he sead sae capal per worer, oupu per worer, ad cosumpo per worer (.e. derve he expreos for,, c ). Dervg he law of moo of capal per worer: K K ( ) sak ( ) ( ) sa Usg he defo of a sead sae: ( ) ( ) ( ) sa sa c A sa sa ( s) sa 7
9 b. Derve he golde rule savg rae, s GR (he savg rae whch maxmzes he sead sae cosumpo per worer). We sar b dervg he opmal capal per worer: maxc s A A s.. ( ) sa The cosra meas ha deed he capal per worer s a s sead sae level. Pluggg he cosra o he obecve, gves: sa max c A ( ) The frs order codo s: AGR ( ) 0 A ( ) GR A GR Comparg hs o he sead sae capal per worer, from he prevous seco, sa, mples ha he golde rule savg rae s: s GR c. Hgher savg rae he Solow model leads o hgher sead sae cosumpo per worer. True/false, crcle he correc aswer ad provde a bref proof. Hgher savg rae has wo opposg effecs o cosumpo: () hgher oupu per worer, ad () lower cosumpo rae: c ( s ) I s o obvous whch effec s sroger, bu s obvous ha f savg rae approaches 00%, cosumpo becomes zero, so he saeme s false. 8
10 9 7. (0 pos). I hs queso use he cro-cour accoug formula, based o he sead sae of he Solow model. s s A A a. Accordg o hs model, f he ol dfferece bewee he wo coures was he savg rae, wha would have bee he rao of GDP per capa he wo coures? s s b. Accordg o hs model, f he ol dfferece bewee he wo coures was he populao growh rae, wha would have bee he rao of GDP per capa he wo coures?
11 8. (0 pos). Suppose Cha roduces a oe-chld-law a me, ad herefore he populao growh rae slows dow oce ad for all. Aumg ha Cha was all a a sead sae, use he Solow model o descrbe he mpac of he polc o he capal per worer. I our aswer use wo full labeled graphs: () he law of moo of capal per worer ad () a me pah of capal per worer. sa ' ' Tme 0
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