Macroeconomics+

ECON+321+

Extra+Credit+Quiz+2+

+Given++(a)+y"="Akα"""and""(b)"Δk"="sAkα"–"(n+δ)k"a.  Construct+a+graph+with+k+on+the+xCaxis+and+y,+c,+and+i+on+

the+yCaxis,+show+the+locaGon+of+the+steadyCstate+capitalClabor+raGo,+k,+steadyCstate+investment+i,+steadyCstate+consumpGon+c,+and+steadyCstate+output+y+(all+in+per+capita+terms).++

b.  Show+in+the+same+graph+the+effect+of+a+zombie+apocalypse+that+doesn’t+affect+the+growth+rate+but+decreases+the+populaGon.++Tell+me+what+happens+to+the+growth+rate+in+the+short+and+long+run.+

Extra+Credit+Quiz+2+

+Given++(a)+y"="Akα"""and""(b)"Δk"="sAkα"–"(n+δ)k"c.  In+a+new+graph+(same+one+though)+show+the+effect+of+a+

new+government+policy+that+successfully+induces+a+higher+savings+rate.+

d.  Say+there+is+a+new+super+villain+named+Gru+(Despicable+Me)+who+contaminates+the+worlds+water+supply+with+a+superCferGlity+drug+in+an+aPempt+to+overpopulate+the+earth.++Show+this+effect+in+a+new+graph.+

e.  Find+Kss.+

Neo+Classical+Growth+Model+(one+more+Gme)+

"y"="Akα ""

Δk"="sAkα"–"(n+δ)k""

gy=gA+αgk"

Convergence+y,i,c++

y"="Akα"+

(n+δ)k+

i"="sAkα"+

k+Kss*+kUK+kBrazil+

Different+CharacterisGcs+–+Different+Steady+States+

y,i,c++

y"="A1kα"+(n+δ)k+

i"="sA1kα"+

k+Kss1*+

i"="sA2kα"+

Kss2*+

i1+

y1+

i2+

y2+y"="A2kα"+ The+effect+of+an+

increase+in+the+Technologywith+A2>A1.+

What+is+the+effect+on+the+growth+rate???+

What+is+the+effect+on+consumpGon???+

Historical+Example+:+Post+WWII+y,i,c++

y"="Akα"+

(n+δ)k+

i"="sAkα"+

k+Kss*+

From%1945%to%1965:%gUS++ + +≈+2%+gEU++ + +≈+4+C+5%+

gRussia++ +≈+7+C+8%+

From%1965%to%1991:%gUS++ + +≈+2%+gEU++ + +≈+2%+

gRussia++ +≈+0+–+0.5%+

kEU+kRussia+ kUS+

“We+will+Bury+You.”+

Soviet+Central+Planning+Did+Them+In+

•  Soviet+Central+Economic+Planning+C+Pandora's+Box+

PopulaGon+Growth+Rates+y,i,c++

y"="Akα"+

(n2+δ)k+

i"="sAkα"+

k+Kss2*+

With%n2">"n1,""we+see+in+this+model+increases+in+populaGon+growth+rates+are+bad+for+economic+growth.++But+this+is+not+necessarily+true.+There+is+no+clear+relaGon,+and+there+might+be+effects+going+both+ways.+

+y++++++++++++++++++++++++n+++

Higher+growth+rates+could+lead+to+more+people+with+more+brains+to+innovate,+which+could+increase+growth.+

(n1+δ)k+

Kss1*+

PopulaGon+Growth+Rates:+The+Data+n+

y+

As+Income+rises+people+are+healthier,+we+have+lower+death+rates+and+the+populaGon+growth+rate+is+higher.+

No+clear+relaGonship+exists.+

HarrodCDomar+Model+(In+Fashion+through+1950’s)+

•  Focuses+almost+enGrely+on+physical+capital.+– B=+K/Y+or+Capital+to+Output+RaGo+– Y=(1/B)K+– dY/dt+=+(1/B)+(dK/dt)+– dK/dt+=+ΔK+=+sY+–+δK+– dY/dt+=+(1/B)+(s(1/B)K+–+δK)+– dY/dt+=+[(s/B2)+C+(δ/B)]K+

HarrodCDomar+Model+(In+Fashion+through+1950’s)+

•  dY/dt+=+[(s/B2)+C+(δ/B)]K+•  Sooo…if+you+want+to+increase+growth,+then+raise+the+

savings+rate+(s)+or+raise+capital+(K).+

•  No+Diminishing+Returns.++We+keep+B+Constant,+i.e.+Output+increases+at+a+constant+rate+with+increases+in+K.+

•  Ignored+ProducGvity+Growth+

HarrodCDomar+Model+(In+Fashion+through+1950’s)+

•  Unfortunately+some+like+Brazil+listened+to+this+advice.+•  So+they+built+a+bunch+of+factories+thinking+that+the+more+

physical+capital+the+bePer+for+growth.+

•  Specifically+Brazil+wanted+to+enter+the+auto+industry+•  But+what+abut+car+quality???+

–  Faced+sGff+compeGGon+from+U.S.+–+real+compeGGve+disadvantage.+

–  So+Brazil+slaps+huge+tariffs+on+imported+cars.+

–  Auto+factory+makes+huge+profits+with+no+compeGGon,+but+they+don’t+care+about+producGvity+improvements.+

–  Junk+products+–+if+you+remove+tariff,+the+auto+factory+will+loose+profits+–+this+leads+to+rampant+corrupGon.++It+all+fell+apart.+

Malthusian+Model+(1798)+

•  Y+=+F(L,R)+– Where+R+=+natural+resource+(Arable+land)+

•  Y+=+RαL1Cα+

•  Lt+1/Lt+++=++1+(Birth+Rate+–+Death+Rate)+– Lt+1/Lt++=+g(Ct/Lt)+++– Where+Ct++is+consumpGon+and+Lt+++=+Labor+Force+=+PopulaGon+

Malthusian+Model++Lt+1/Lt+++=+(Ct/Lt)γ++where+0+<+γ+<+1+

C/L+

Lt+1/Lt++

Malthusian+Model+

•  C+=+Y+=+F(L,R)+=+RαL1Cα+– Assume+whatever+income+comes+in+is+consumed.+

– Lt+1/Lt++=+g(C/L)+=+(C/L)γ+=+(RαL1Cα/L)γ++++–  +(C/L)γ+=+(RαL1Cα/L)γ+=+(Rα/Lα)γ+

– Lt+1+=+(R/L)αγ+Lt+

Malthusian+Model++Lt+1+++=+(R/L)αγ+Lt++

Lt+1+

Lt+

45o+

Lt+1+=+Lt++

Lss+

With+a+low+level+of+populaGon,+there+is+a+lot+of+land+per+person+and+we+can+grow+a+lot+of+food+per+person.++This+leads+to+more+and+more+babies.++Then+we+start+to+exhaust+recourses,+so+eventually+everyone+is+back+to+subsistence+level.+

C=+RαL1Cα++C/L+=+c+=+(R/L)α+

Dc/dL+=+CαRαLCαC1++<+0++

Enough food on this side Not Enough food on this side

Food,+PopulaGon+and+Time+

OverpopulaGon+Video+

•  OverpopulaGon:+The+More+the+Merrier?+•  OverpopulaGon+video+•  OverpopulaGon+is+a+Myth+

Three+Models+of+Exogenous+Growth+Recap+

1.  Neoclassical+growth+model+(Solow)+1.  Savings+rate:+Increases+in+the+savings+rate+increase+the+

growth+rate+unGl+a+new+steady+state+is+achieved.++ConsumpGon+will+iniGally+go+up,+but+if+the+savings+rate+is+too+high,+consumpGon+will+decrease.+

2.  PopulaGon+Growth+Rate:+Increases+in+the+populaGon+growth+rate+decrease+the+growth+rate+and+lower+standards+of+living,+but+eventually+the+growth+rate+will+return+to+a+new+steady+state.+

3.  Technology***:+Technology+is+key+and+increases+will+increase+the+growth+rate+unGl+a+new+steady+state+is+reached.++Perpetual+growth+in+technology+will+result+in+permanent+growth.+

Three+Models+of+Exogenous+Growth+Recap+

2.  HarrodCDomar+Model+ +Growth+occurs+through+accumulaGng+physical+

capital,+neglecGng+diminishing+returns.+ +Historically+has+led+to+countries+imposing+import+

tariffs+to+protect+against+compeGGve+disadvantage.++This+leads+to+monopolies+and+inefficiencies+and+o|en+corrupGon.+

Three+Models+of+Exogenous+Growth+Recap+

3.  Malthusian+Model+" +Focus+on+Land+as+the+main+factor+for+growth.+

+ +Land++Food++ConsumpGon++Babies++a+decrease+in+consumpGon+per+person++subsistence+trap.+

" +Ignores+Total+Factor+ProducGvity+(A).++The+debate+comes+down+to+whether+A+will+conGnue+to+grow.+

Last+Gasp+of+Solow+for+this+Class+

•  2+Main+Lessons+1.  Sustained+longCrun+per+capita+GDP+growth+must+

come+from+ProducGvity+improvements+(A),+parGcularly+for+industrialized+economies.+

2.  The+model+and+evidence+support+condiGonal+convergence,+which+means+that+developing+economies+should+seek+policies+to+model+the+economic+characterisGcs+of+industrialized+countries.+

Last+Gasp+of+Solow+for+this+Class+

•  Main+Flaw+–  (A)+is+exogenous,+so+this+isn’t+really+a+growth+model.++(A)+is+the+“black+box.”+