Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
5.Price’stwolawsandthe[technologicalrevolution’:thecaseofunbalancedgrowth
ratiointheconventionalsectorisconstant.However,neitherthesavingsratio
northegrowthratesoftotaloutputanditscomponentsneedbeconstant.Letn
withsubscript1bethenumberofworkersengagedinproducingcapitalgoods
forthequalityenhancingsector.Theassumptionthatthecapital-to-outputratiois
constantimpliesthat,asintheprevioussection,theproductivityoftheseworkers
isproportionaltotheaggregateleveloftechnologyT.Hencethegrowthrateof
capitalemployedinthequalityenhancingsectoris
M'=α+n
1
Thegrowthrateofthelabourinputinthequalityenhancingsectoris
R'=n
2
(16)
Price’stwoempiricallawsare
(i)
thatn
1andn
2havebothbeensignificantlygreaterthann,and
(ii)
thattheyhavebeenapproximatelyconstant.
Givenn
1andn
2,wecannowobtaintheinnovationratefrom(2)and(13).
AssumeH(E,T)=EbT1-bandE(M,TV)=Mβ(TV)vwhereVisgivenby(12)and
theelasticitiesβ,b,andνareallconstant.Withthesespecificationsthesystem
determiningαisasfollows:
α'+bα=bE'
E'=βM'+ν(α+V')
V
'
=
λ
λ
−
1
R
'
+
λ
1
n
(18)
(19)
(20)
Thegrowthrateofresearcheffortis,in(18),thepropellingforcethatdetermines
thedynamicsoftheinnovationrate.Thisgrowthrateisinturndeterminedbythe
growthratesofQinputs,themeasureofthelabourinputtakingdueaccountof
thevariationininventiveability,andtheeffectofinnovationonefficiencyinthe
Qsectoritself.
Superimposingthestylizedfacts(16)and(17)onthesystem(18)-(20)yields
thefollowingdifferentialequationforα(t):
(1
−
βνα
−
)
+
1
b
α
'
=
β
n
1
+
[
|
{
|
[
g
λ
1
n
+
(
|
k
1
−
λ
1
N
|
)
n
2
]
}
J
ν
(21)
43
