1. I the United States, t apita sare of DP is abt 5%, te averagegrow intotal otput is % pe ear， te dpreiaterate 5per yar, he capitoutpu rio is 4.uose thtth pructin functonisCobb-Dulas, o tat the cptalshare of otputis onstant, and thUnied tes a ben in stady ste. (10pints)a) What must te savinrab in thenii steady sate?Y/Y 003= n = sf(k)= （n +）ks= (）/()= (0.0 0.0) 4 = 32b) Wht is the marinal prodct ofcatalin he iita stayate?M* K/Y = 0.5=MK ./(K/Y) = 0.5/4= 025c) Wat will the apial-otpt rato be t th Golden Rul teaytate?PK = (n+) = 0.3 0.050.8MPK *K/Y = 5 K/Y =.5/0.8 .25d) Wh mst the sngrat b t reatheGode atetedy stae?sf（k） = （ ) s = (n +)k() 08 *6. = .2. Preah of he folowigstaeents otthe stedy stat of the Solow moe i population grth and tecnlogalprogress. (10 points)a) Te pital-outputrat i constant the stay stte, e know ha sy = （+ n + g). This impes hy = s( + n+ ).Snc s, , n, d gre contnt, thsmen tt the raio k/y is l constan. Since k/y= K/(L* E）Y/（L* ) KY,we can nclude that n thestedystae,t capt-output rato isconstanb) apilandlboreach earnonst shr oa es income.e knowtha capt sareof ncm =PK (K/Y).In the tedy state， we knw fpa(a) tht th cpital-outut atio KY s costat. W lso ow that he MKis a functin of , which is constat n testeay sae； thrfo the MK itlf mus e costan. hs， capitalsshare f iome is constant. Labors sare one is 1 - cptals hr. Hnce, if capitalshae s cotant, we see tht laborsareofincome is locnstantc) Total cptal icoe n olaborinoeboth grow at te rate of populatin gowthplusthe rte o technoloical progres， .We know tht i th sady se，total icoe growsat n+ g-hrate of ulatio growt lus teat otechnologcal hang. pt （b） we sowed ha labos and aias sare of icomeis contant.If th ares re constant, antl imeros at t rateng， tn laorinoe and capitalinom mu alsgrow t he ate n d) he rel tal rice cital is constt, ndereal waggrs thereof tenologal progress g.efin the re rna rice ofcapialR as:R =Totl apital Inme/Capitl Stok= （MP *）/= K.We knw thtint teadystate, the MPK nstant because cial prefeti worke is onstt. Tefore, we ca concludeha thereal rentalpric of ctal is constnt in th steystate.Otu isdivdd btweencpitalincom and ince Theefore， he wag prffiienc it of lao cn e presseds:w = f(k) MPK k.In the stea tt，f（k), K k are all constantnumers beaus capitalper fectv wrkerk is constn.Threfore,the wag e efficieny unit of lbr s costant. Te wae per unit o labr is related tothe we pr effciey ni of labor by he equatoae pUt L = wThus,the growh rate of rea wage equals the growth ate o E,g3. The ouy of Lerett is a small open ecnomyuddenly, hangn wld shiones he expots f Leverett unpouar. (10 onts)a) What hpps nLverett tosvi,ivstmen，n expot,the interestte,ad te exhange ate?Weevetexport becm lssopular， it ome aving YC dos notchange.Thisbecuseweasume thaY is deteri b th amouno atal and laor, cosumpiondepeds l ondissble ncome,n goernment pegis fixed exogn varable.Investmn alsooes no change, since nvestmen depens othe ierestrate, an Leverett is all openeconmy hat taksthe word ierest ra a ive. Becaseneihrsavinnor nvent chnges,netexports, which equal S , do t hang ither This i shon te Fiure aste umoving S Iure he decresed poplarityof Leverets exprt leadso a sit inwar ofhe nexpot cuve, as hown n the Fgre. Athe nw equiliru， net eor are unchanged bu the crreny has dpeciatEven tou Lerettsexports areless uar， its deale has emaine he same.The rson r ti s tht te erciated urrenc prids tiulusto ne expors, hichovec theunpopulary of i eports b makig hem cha.b) Thectzensof Lveret le to traelaroa. How wil is hanginthe excha reaftthem?everetts currencynow usess freign ceny, otravlinabrodis ore xpensive.Thisisn exle of te f tht imort (inluingforeign trave） have become moe xpensivearequire t