Interm Macroecon Theory
Interm Macroecon Theory ECON 100A
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Date Created: 10/05/15
California State University Sacramento ECON 100A 7 Intermediate Macroeconomics Golden Rule in the Solow Model Prof Van Gaasbeck Notes on the Golden Rule capital stock in the Solow Growth Model While a higher capital stock implies higher output this does not mean a higher capital stock is desirable To sustain a high capital stock a lot of output will have to be devoted to investment leaving less available for consumption Golden Rule The capital stock perworker that maximizes consumption perworker In the Solow Growth Model with no population growth and technological progress this occurs where MPK 5 Recall at steady state investment is equal to total depreciation because savings is equal to investment Steady state sfk 1quot Total savings total investment sfk 139quot 3 i ci On the diagram below 0 is the difference between what is produced f k and output used for investment 1quot On the graph the golden rule capital stock is the k that maximizes the distance between the production function and total depreciation Why The difference between the two lines is consumption the golden rule capital stock is the k that maximizes consumption Mathematically this is where the slope of the production function MPK is equal to the slope of the depreciation line 6 y A 9 A country that is saving too much has a steady state capital stock MPK 57 that is above k a country that is saving too little has a steady state capital stock that is below k Notice that only one savings rate 3 f will ensure that the economy achieves the golden rule capital stock at steady state On the graph this savings rate will ensure the y 0 savings function crosses at point A on the graph 9 The golden rule can be interpreted in terms of marginal product of Sf capital and depreciation A oneunit increase in k raises output by MPK this is the added bene t of increasing k It also implies that an extra 5 units of output must be set aside to maintain the capital labor ratio at its new higher level this is the additional cost of 9 V k increasing k The level that maximizes consumption will be where k G the added bene t MPK equals the additional cost 5 If MPK gt 8 then increase in k will increase output by more than the implied increase in depreciation so consumption rises because there is more output leftover for consumption The extra bene t MPK associated with an increase in k outweighs the cost 5 so we should increase k If MPK lt 8 then increase in k will increase output by less than the implied increase in depreciation so consumption falls because there is less output leftover for consumption The extra cost 6 associated with an increase in k outweighs the bene t MPK so we should decrease k In the model with population growth and technological progress the modi ed golden rule is The interpretation in terms of marginal product is somewhat more difficult but the general idea is the same as in the simple model Notice that when there is no population growth n 0 or technological progress g 0 this modi ed golden rule collapses to the simple one at the top of the handout l CHAPTER 4 Money and Inflation 6162008 In this chapter you will learn 39 The classical theory ofin ation 39 effects 39 socialcosts 39 quotClassicalquot assumes prices are exible amp markets clear I Applies to the long run tumour insemination EmNmuA trimmer mummy flation and its trend 19602007 72 malith earlier 12 9 langrlun rend 5 3 la n 1955 lam 1975 WEB 1985 team 1995 mm 2n n5 Kn Murryamilmlulmv trauma inmost manemy m The connection between money and prices I in ation rate the percentage increase in the average level of prices I Price amount ofmoney required to buy a good I Because prices are de ned in terms of money we need to consider the nature o ney the supply of money and how it is controlled NAPYEna Mumeimunm ECUNmuAlmelmadllle mummy slats mm umwmnmunm KaNmA trimmer Mmmnmy llde4 Money Func I medium orexchange we use it to buy stuff I store orvalue transfers purchosino power from the present to the future I unit or account the common unit by which everyone rneosures prices ono volues martu Mammuimunm EmNmuA nnmmmnm Mmunmy sluts 6162008 Money Types 1 at money nas no intrinsic vaiu examoie tne paper currency we use 2 commodity money nas intrinsicvaiue exampies oio coins cigarettes in POW camps in MomVir imiilion nonhuman immune Mammy siid Dlscussion Question wnicn ottnese are money 3 Currency h Checks Deposits in checking accounts illoemano oeoos39ts39i a Credit cards Certi cates of deposit l ti39me oeoosits39i cmwin Meevamrenen 5mm immune Matmrreerv siivev The money supply and monetary policy de nitions ine monevsupplvi39s tne ouantity otmoney avaiiaoie in tne economy Monetary policy is tne controi over tne money suooiy cram Meevamimanen acouxmn immediate MiszneDN The central bank Monetary ooiicy is conducted by a country39s central bank 39 e r tne centrai bank is caiieo the Federal Reserve quottne Fedquot h 7712 Fedzml Reserve Building Wilshmgtzm DC MS cmwzm Mama new Emuimn inemaiae MmrrecW mg l The Quantity Theory of Money Velocity basic concept tne rate atwnicn money circuiates A simoie tneory ii39nki39ng tne intiation rate to growth rate of the money M iv oetinition tne numoer ot times the average ooiiar bi39H cnanges nands in a given time peri39 Beginswitn tne concept of velocity aampie in 2007 39 500 biiiion in transactions money suppiy 100 biiiion ine average ooiiar is used in rive transactions in 2007 So veiocity 5 cram Mmyaainiaciea mailman immune Manama W m cmwzm Mmyamineciea Emuimn inemaiae MmrrecW W H I Velocity mm This suggeststhe following definition 6162008 V L M where V velocity T value of all transactions Velocity mm Use nominal GDP as a proxyfortotal transactions Then PgtltY Where P pnce ofoutput GDP delator Y quantity ofoutput real GDP M m quoteY suPP39Y va value of output nominai GDP mom Momentum Kailth Marmot Mummy W 1 mnm Mam mammal mum m Womenquot Mammy 5W 3 Mone demand and the uanti The quantity equation 4 q w equatlo I The quantity equation xVPxY follows from the preceding definition ofyelocity 39 Itis anl39 dentin it holds by definition ofthe variables mum Mohair Minion myth intWat Mummy side or WW I MP real money balances the purchasing power ofthe money su I A simple money demand function MP kv where w much money people wish to hold for each dollar of incom k is exogenous more MmmMin htiun EmNmuA thermalquot MIAwYVemV silde t5 Money demand and the quantity equation I money demand MP kv I quantity equation M xv my I The connection between them k IN I when people hold lots ofmoney relative totheir incomes k is ig mone y changes hands infrequently v is low new Murryamiiminimv noun maimed mommy slat 16 Back to the quantity theory of money I starts with quantity equation I assumes v is constant lat exogenous i 7 I with this assum tion the uantit equation can be written MWny weir MumMimhlion EmNmuA memeneuwawny shde o 6162008 I The quantity theory of money unit I The quantity theory of money mnt Mx V Px Y Remfrom Chapterz Howthe price level is determined quot 9 WM 3 0 a PM M39s the sum olthegrowth rates with v constant the money supply determines nominal GDP p X The quantity equation in growth rates Real GDP is determined bythe economy39s supplies and the production lunction iChap 3 M F 39 quot 9 P i 399quot939 is The quantity theory of money assumes P inomrnal GDPireal GDP AI l is constant so l we Mmym mumquot m mu new mommy W 5 mm Mmym morequot than mu immerse mommy W 9 I The quantity theory of money unit I The quantity theory of money mnt iereek letterquotpiquot Ap denotesthe in ation rate To The muquot quotom me AM AP Ay Normal economicgrowth reduiresa certain preceding slide was 7 T amount olmoney supplygrowth to lacilitatethe growth in transactions Solve this result Money growth in excess olthis amount leads to Torn to gel inflation 0 me newquot mom mm mm newer mommy W m 0 me newquot him mm mm newer Mummy We 2 Confrontin the uantit theo with I The quantlty theory of money unit I a E q y w The quantity theory ofmoney implies 1 countries with higher money growth rates AVV depends on growth in thelactors or should have higher inflation rates Pmdmmquot and 0quot Chmk gica39 my 2 the longrrun trend behavior or a country39s inllation 3 W we take as WM 039 quotWi should he similarto the longrrun trend in the rice 39t g ghantl39tyThearlqpreafctg COUMI Y39S money Emwth rate 0 Are the data consistent with these implications churle mom wow mm mm new mommy We 2 churle Mmmu mm mm mm new Mummy W I 6162008 I international data on in ation and money growth Us inflation and money growth 19602007 15W Overlhe 7 Y ong run the in ation and one growth rates move together as the quanllly theory predlcls 12 l 4 E m leWllllal 9 5 3 n 1955 lam 1975 WEB 1985 WEB 1995 mm 2n us ll Mull ylmlmlatlun mlmnA Women Mammary Md I Seigniorage I To spend more without raisingtaxes or selling bonds the govt can print mone I The revenue raised from printing money is called seignio age pronoun ed SEENryourridge I Theinflationtax Printing m o raise revenue causes in ation in ation is like a tax on people who hold money MerKA anryumllmlulun rmmma Women warhead Inflation and interest rates I Nominal interest rate i not adjusted for in ation I Real interest rate r adjusted for in ation ri77r mm mama Mmmmanan rrammainermelurenmmew my Inflation and nominal interest rates in the The Fisher effect I 19551007 percent I The Fisher eduation r Hr Pg39lfg39 nominal I Chap 3 s 1 determines r 12 interest rate I Henceaninc e seirur 9 causes an equal increase in i 5 39 This onerforrone relationship is called the Fisher effect 3 Wu ln all n rate 1955 men 1955 mm 975 man 1985 WEB 1995 mun zuua rwrrra Murryamilmlatlun rrauimaimnmaaimnmsmw was warm memunan Emumunlnralmu llemumeuly mp 6162008 Inflation and nominal interest rates across Exercise countries Suppose v is constant M is growing 5 peryear v isgrowing 2 peryear and 4 a Solve for i b the Fed increases the money growth rate by 2 percentage points per year lind Ai Supposethe growth rate ol v lallsto 1 peryear what will happento xv whatmustthe Fed do if it wishes to keep xconstantV r a s JvIrgenljo namesaia mm mama Mmmamunan cIllmAlmelmu lszzcheuly 5M I Answers Two real interest rates V is constanlM grows 5 peryear V g 4 I rows 2 peryear r 7 actual in ation rate not known until after it has occurred a I f expected inflation rate I e Ar 2 same as the increase in the money growth E 3quot quotquot L m39 were me mm the real interest rate people expect at the time they buy a bond ortake out a loan c IHhe Fed does nothingAs 1 To prevent in ation from rising 39 if PD rea39 were 393 Fe must re use the money growth rate by the real interest rate actually realized 1 percentage point peryear mm Mmmnmman KaNmA Women Warmly My Nevin ummmanan mum maimed Mnmmeulv my Mone demand and y The money demand function the nominal Interest rate d MP lI Y I in the duantitytheory of money d for real money balances lMP real money demand depends depends only on real income v negatively on I Another determinant ofmoney demand I39is the 099 cost of holding money the nominal interest rate i positively on v I the opportunity cost of holding money linstead of higher v more spending bonds or other interestrearning assets so need more money I Hence Ti l in money demand lquotlquot is used lorthe money demand lunction because money is the most liquid asset mmm Mammalian KaNlmA Warmer mammary my warm umwmunan Column moment Warmly We The money demand function MF d 101 Lr7re Y When people are deciding whether to hold money or bonds they don39t know wnat inrlation will turn out to be Hence the nominal interest rate relevant for money demand is r 119 CHAPTER 4 Money and Inflation ECDN 100A Intermediate Macro Theory slide 36 6162008 Equilibrium Lr7re Y p The supply of real money balances Real money demand CHAPTER4 Money and In ation ECDN 100A Intermediate Macro Theory slide 37 variable M CHAPTER 4 Money and Inflation ECUN 100A Intermediate Macro Theory Lr7re Y p how determined in the lonq run exogenous the Fed adjusts to make 5 I 7 HP 2 M adjusts to make F LI Y slide 38 I HowP responds toAM Lr7re Y p 39 For given values of r Y and are a change in M causes P to change by the same percentage just like in the quantity theory of money LHAPTER4 Money and In ation ECDN 100A Intermediate Macro Theory Slide 39 I What about expected inflation 39 Over the long run people don39t consistently over or underforecast inflation so ire iron average 39 In the short run are may change when people get new information 39 EX Fed announces it will increase M next year People will expect next year39s P to be higher so ire rises 39 This affects P now even though M hasn t changed yet CHAPTER 4 Money and Inflation EDDN 100A Intermediate Macro Theory slide 40 I How P responds to A 39e Lr7rquot39Y P 39 For given values of r Y and M T are 3 T i LIIC Fisher effect 3 i MPd 2 TP to make MP fall to reestablish eq39m CHAPTER 4 Money and In ation ECDN 100A Intermediate Macro Theory slide 41 6162008 I Discussion question A common misperception WhyisinIutiun bud 39 Common misperception l nfatl on reduces real wages what costs does inllation impose on society List all the ones you can think or This is true only in the short run when nominal wages aretixed by contracts Focus on the long run I Think like an economist I Chap39 3 Mhe39ongmn 39 the real wage is determined by labor supply and the marginal product otlabor not the price level or inflation rate Considerthe data manna Momyamilmlulml KaNmA Woman mommy We mama Mamamanan Kahunaimlmelaananan ly WM l Average hourly earnings and the CPI 19541007 The classical View of Inflation 18 I Tnecasslcavl ew 339 m A A ange in the price level is merely a change in the a W E units of measurement E M lSEI i w a1 E 58 mm g 80 why tnen ls Inflation a 52E CPl llghi scale 5 social problem 54 wage in ounent dullals 5n 239 Wag2 ln 2mm dollars lees lam lws lean lads teen was man 2on5 mam maymnmmal aoaiaaalmnmelmmamly WM mama Mmm MWWEquot zmmmalmavmutlmMumew mug I The social costs of in ation The mm M p238 quotmam 1 Shoeleather co quotfaquot mm two categories del the costs and inconveniences oi reducing money halancesto avoid the in ationtax 1 costs when inflation is expected is Ti 2 costs when inflation is dillerent than people d expected m lrealm n balances Remember In long run inllation does not arlect real income or real spending 5o same monthly spending but lower ayera money holdings means morelreduent tripsto the bank to withdraw smaller amounts oi cash llama Murryamilmlnlmv KaNmuA maimed Mammary 3mm mama anumuian mama intermenawoawny m4 6162008 39de cwrrxu Mam wininun The costs of expected inflation 2 Menu CDStS Examples cost of priming amp mailing new catalogs The higher is inflation the more frequently firms must change their prices and incurthese costs f The costs of changing prices cost of printing new menus KEN um Werner We Timmy The costs of expected inflation 3 Relative price distortions Firms facing menu costs change prices infrequently Examp e A firm issues new catalog eachJanuary Asthe general price level risesthroughout theyear the firm39s relative price will fall Different firms changetheirprices at different times leading to relative price distortions causing microeconomic inefficiencies inthe allocation of resources WE Mmmwuusquot Womeuavmmu 5 l The costs of expected inflation The costs of expected inflation fairtax treatment quot 5 General inconvenience Someiaxes are not adiustedto account for inflation inflation makes it harderto compare nommal such as the capital gains tax values from drfferenttrme perl Example Th39s com l39cateslon rran efnanc39al lann39n Janl you buy 10000 worth of IBM stock 39 p39 g g 39 39 p 39 g Dec 31 you sell the stockfor 511000 so your nominal capitalgain is 5100011004 Suppose a 10 during the year your real capital gain is so Butthe govt requires you to pay taxes on your 1000 nominal gainll vmmwum eovmamwdimveumy mm vwmwausn nemdivevuwm W54 but based Example new Martyn Additional cost of unexpected inllatio Arbitrary redistribution ofpurchasing Many long if liurns out differentfrom r then some gain at others39 expense hen li x lt ii and purchasing power istra D bler ers if nlt r then purchasing power is transferred from borrowersto lenders n power rierm contracts not indexed on r borrowers amp lenders lfn r t r nsferred from lenders w M milmun eon um new We new m 52 Additional cost of high inflation I when inflation is high it s more variable and unpredictable turns out different from t more often and the differences tend to be lar er though nosystemallm yposmve or negative Arbitrary redistributions of wealth be ome more likely This creates higher uncertain y making risk averse people worse off mam memuuan Emulmn memenevwewnv siaeea I Dne benefit of inflation 6162008 Nominal wages re rarely reduced even when the equilibrium real wage This hinders labor market clearing in ation allows the real wages to reach equilibrium levels without nominal wage cuts Therefore moderate in ation improves the functioning of labor mar manna Merlylrdlmllrlmi KaNmuA maimed Mumrhamy ll1e54 Hyperin ation def are 50 per month All the costs of moderate in ation described above become huge under hyperin ation Money ceasesto function as a store ofvalue and may not serve its other functions lunit of account medium of exchange I People may conducttransactions with barter or a stable foreign curren mama Mam email Katrina internadir mammary sllrln 55 I What causes hyperin ation Hyperin ation is caused by excessive money supply growth when the central bank prints money the price level rises it it prints money rapidly enough the result is hyperin ation mama Mvallmlulell Kaumna momma Menarreau siiaesa Afew examples of hyperinflation manea Maneynuinanan ElemA llrtelmedlure Mmarreaiv slide57 I Why governments create hyperinflation when a government cannot raise taxes or sell bonds it must nance spending increases by printing money in theory the solution to hyperin ation is simple stop printing m in the real world this requires drasticand painful scal restraint lmvrz a Murrymilmlnlmv KaNlmA maimed Mulcrtmry I The Classical Dichotomy Real valiables Measured in and relative prices fur x mumf physical units quantities ple N Way tm edy dd in moneyunits e g hwima agvspemeepmm PM I39niil 39 Pb t il f Fral lpBW ed m lH llllil re layimam ans mar Maw today I the price level The amount oldollars needed to uy a representative basket olgood siiaeaa prawn anumanan EmNmnA interminauwamaiv slide g 6162008 I The Classical Dichotomy Note Realvariables were explained in Chapa nominal ones in Chapterzl Classiml dichotomy the theoretical separation of real and nominal variables in the classical model which implies nominal variables do not affect real variables Neutralitynfmnney Changes in the money supply do not affect real variables ln the real world money is approximately neutral in the long run lmvrina Momma lmlulun Chapter Summary the stock of assets used fortransactions servesas ofaccount Lommo lty money has lHUlHSlC value hat money does not Central bank controls the money supply conclude Quantitytl39leofy ofmoney assumesvelomy is stable s that the money growth rate determinesthe rate inflation a medium ofexcl lange store ofvalue and Lmlt Karimmemedlaauwartemy 5mm charm Mamuihunan mummommieuwarteny New Chapter Summary Chapter Summary Nominal interest rate Cm of in ation edu real interest rate inflation rate Expectedln atlon 39 quot 9 0W 5 0 D39d39ngm mey shoeleather costs menu costs Fisher effect Nominal interest rate moves am relative p be din n onequotDr39unew Weed quot quotB i m inconvenience of correctingfigures for in ation Mun demand Unexpected l39nflatl39on devends unlv an income in the Quantity Theory all of the above plus arbitrary redistributions of wealth also depends on the nominal interest rate between debtors and creditors ifso then changes in expected inflation affectthe current price level warm nonhuman commamelamineuwarteaiy mm Mvrzhn Mawmnunan staminamamauueuwarteaiv 3mm Chapter Summary Hyperinflation caused by rapid money supply growth when money printed to finance govt budget deficits stoppingit requiresfiscal reformsto eliminate guvt s needforprinting money mum Moneymmlmah KaNImA maimed Mummle may Chapter Summary classical dichotomy In classicaltheory money is neutralwdues not affect real variables we can study how real variables are determined wo renCe D nominal Ones Then money market eq rrl determines price level and all nominalvariables Most economists believe the economy works this way in the longrun Wm WM myahnl l mm imam lm Mme new slaeos
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