Macroeconomics+Two+Endogenous+Growth+Models+

ECON+321+

Prac=ce+Problems+1.  Neoclassical+growth+model+(Solow)+

+How+do+increases+in+the+savings+rate,+the+popula=on+growth+rate+and+technology+affect+growth+rates+in+the+short+and+long+run?+

2.  HarrodJDomar+Model++How+does+growth+mainly+occur+in+this+model,+and+what+is+the+major+drawback+compared+to+the+Solow+model?+

3.  Malthusian+Model+! !What+does+this+model+focus+on+as+the+main+factor+for+growth?++ +Fill+this+in:+______++Food++_______++Babies++a+decrease+in+consump=on+per+person++subsistence+trap.+

! !What+does+this+model+ignore?+

AK+Model+

•  Breaks+diminishing+returns.+Y=AK +(L+leW+out+for+simplicity)+

y=Ak'

Δk'='y)'(n+δ)k'='sAk'–'(n+δ)k''

AK+Model+y,i,c++

(n+δ)k+

i'='sAk'+

k+

AK+Model+

•  y'='Ak''where+k=K/L'is+the+capital'to'labor'ra+o.''ln(y)'='ln(A)'+'ln(k)'dln(y)/dt'='dln(A)/dt'+'dln(k)/dt'gy=gA+gk'

•  Net+Investment+Δk'='sAk'–'(n+δ)k''Δk/k'='gk''='sA–'(n+δ)'''Where+we+now+have+constant+returns+to+k.'

AK+Model+

•  We+see+here+there+are+constant+returns+to+capital.+But+Is+this+reasonable???+++–  +No+not+really,+but+there+are+arguments+for+constant+returns+to+k. ''•  Missing+human+capital?+With+an+increase+in+K,+people+will+learn+how+to+use+the+capital+more+efficiently…Learning'by'Doing.+•  Missing+Public+Infrastructure.+

–  +The+real+problem+though+is+that+we+never+see+any+convergence.'In+fact+we+see+divergence.'

Human+Capital+

•  Y'='AKαHβL1)α)β'–  where+H+is+human+capital+and+0<β<0'

•  y=c+sy+uy'–  where+u+is+the+frac=on+of+income+spent+on+acquiring+human+capital.+

•  Y/L'='(AKα''HβL1)α)β)/L'•  y'='Akαhβ''where+h=H/L'is+the+capital'to'labor'ra+o.''•  Δh'='uAkαhβ'–'(n+δh)h''–  where+δh+is+the+deprecia=on+of+human+capital.++Some+things+you+learn+become+obsolete,+or+some+skills+are+forgo\en,+ect.+

Human+Capital+y+

y'='Akαhβ'+

(n+δh)h'+

uAkαhβ'+

h+hss*+

So…the+model+is+more+empirically+valid,+but+we+are+s=ll+trapped+with+diminishing+returns.+

Romer+Model+(Two+Sector+Model)+•  Y'='AKαLy1)α'

•  Ly"="Labor+used+in+the+produc=on+of+final+goods.+•  ΔA+=+dA/dt+=+σALA+

»  LA++=+Labor+used+in+R&D.+»  σ+++=+efficiency+of+the+R&D+sector.+

•  L'='Ly"+"LA+•  λy++++=++Ly""/'L'='frac=on+of+labor+producing+final+goods.'

•  Per+capita:+•  Y/L+=+[AKαLy1)α]/[L]'='[AKαLy1)α]/[LαL1)α]'

» where'L'='LαL1)α' 'Do+the+math.+

•  Y/L+=+y+='Akαλy1)α'

Romer+Model+(Two+Sector+Model)+•  y+='Akαλy1)α'

•  ln(y)+='ln(A)'+'αln(k)'+'(1)α)ln(λy)'

•  gy='gA'+'αgk'+'(1)α)gλy'

•  ΔA+=+dA/dt+=+σALA+»  ΔA/A+=+[dA/dt]/A+=+(σALA)/A+»  gA''''''''''=''σLA+

•  where+σLA+is+the+number+of+workers+in+R&D+=mes+efficiency.+

•  gy='σLA'+'αgk'+'(1)α)gλy'

Romer+Model+(Two+Sector+Model)+

•  Sources+of+Growth+1.  σ++: +produc=vity+of+the+R&D+sector.+

2.  LA+: +number+of+R&D+workers.+3.  gk''': +growth+rate+of+the+capital+labor+ra=o.+4.  gλy': +growth+rate+of+the+frac=on+of+workers+in++

+ +produc=on.+  where+λy'''is+empirically+stable,'so'gλy'='0….'

  gy='σLA'+'αgk'

Romer+Model+

•  Scale+effect+

•  LA++is+a+li\le+problema=c+when+it+comes+to+empirical+evidence+because+it+introduces+a+scale+effect.+LA+is+the+number+of+workers+in+R&D,+so+the+larger+the+workforce,+the+fast+the+growth+:++gy='σLA'+'αgk'+'(1)α)gλy'

Scale+Effects+We+do+see+a+coinciding+of+popula=on+growth+rates+and+GDP+growth+rates.+

0 091400

Figure 3: Total FTE R&D Personnel and Productivity Growth

0.06

0.09

1200

1400

ands

)

0.03

800

1000

wth

Rat

e

nel (

Thou

sa

-0.03

0

600

PB

P G

row

&D

Per

sonn

-0.06200

400

FTE

R&

-0.0901960 1965 1970 1975 1980 1985 1990 1995 2000

FTE R&D Workers PBP Growth Rate

However+

Ideas+as+a+Good+

•  Between+Solow+and+Romer+we+start+to+recognize+how+cri=cally+important+is+the+element+of+knowledge+as+an+economic+good.+

•  Idea+are+a+Kind+of+Good:+•  Rival'Good':+is+used+by+one+person+it+can’t+be+used+by+another+simultaneously.+

•  Non8Rival'Good':+When+used+by+one+person+there+is+no+reduc=on+of+the+quan=ty+available+for+others+to+use.+

Ideas:+Another+Important+Dimension+

•  Appropriability+•  Excludable+(i.e.+patented+inven=ons)+vs+Non8Excludable'(i.e.+Na=onal+Defense)+

Policy+Ques=on+

•  Are+patents+good+or+bad?+

–  ++They+give+companies+monopolis=c+power…but+if+there+are+no+patents+then+there+is+no+incen=ve+for+companies+to+conduct+research+and+development.+

Monopolist++

Policies+to+Promote+R&D+

1.  Patents:+gives+firms+a+limited+=me+for+exclusive+rights.+ ++1.  But+some+firms+don’t+like+patents+because+you+have+to+

reveal+your+exact+specifica=ons…like+Coke.+

2.  More+complicated+products+are+oWen+not+patented+because+they+are+hard+to+copy.++This+is+as+opposed+to+drugs,+which+are+easy+to+reverse+engineer.+

Policies+to+Promote+R&D+

2. +Subsidies+for+R&D.+++1.  Private+rate+for+firm+R&D+is+about+20%.+

2.  Social+Rate+of+return+is+about+60%+to+80%.+

3.  But+to+which+firms+do+we+give+the+subsidy?++Which+firms+do+we+pick+as+winners?+

3. +Tax+Breaks+for+R&D.+ ++1.  We+don’t+have+to+pick+winners+here.+

2.  But+how+much+R&D+is+going+on+and+how+much+cost+shiWing?+