Editing Endogenous growth theory (section)

== Models ==

In the mid-1980s, a group of growth theorists became increasingly dissatisfied with common accounts of [[exogenous]] factors determining long-run growth, such as the [[Solow–Swan model]]. They favored a model that replaced the exogenous growth variable (unexplained technical progress) with a model in which the key determinants of growth were explicit in the model. The work of [[Kenneth Arrow]] (1962), {{harvs|txt|first=Hirofumi|last=Uzawa|year=1965|author-link=Hirofumi Uzawa}}, and [[Miguel Sidrauski]] (1967) formed the basis for this research.<ref>{{cite web |url=http://www.newschool.edu/nssr/het/essays/growth/moneygrowth.htm |title=Monetary Growth Theory |work=newschool.edu |year=2011 |access-date=11 October 2011 |url-status=dead |archive-url=https://web.archive.org/web/20151021205217/http://www.newschool.edu/nssr/het/essays/growth/moneygrowth.htm |archive-date=21 October 2015 }}</ref> [[Paul Romer]] (1986), {{harvs|txt|first=Robert|last= Lucas|year=1988|author-link=Robert Lucas Jr.}}, {{harvs|txt|first=Sergio|last=Rebelo|year=1991|author-link=Sergio Rebelo}}<ref>{{cite web |url= http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/Growth/RebeloAK.pdf |title= The Rebelo AK Growth Model |first= C.|last= Carroll |work=econ2.jhu.edu |year=2011 |access-date=11 October 2011 |quote= the steady-state growth rate in a Rebelo economy is directly proportional to the saving rate.}}</ref> and {{harvs|txt|last= Ortigueira|last2= Santos|year=1997}} omitted technological change; instead, growth in these models is due to indefinite investment in [[human capital]] which had a [[spillover effect]] on the economy and reduces the diminishing return to [[capital accumulation]].<ref name= "BX">{{cite book |first1= R. J. |last1= Barro |first2= Xavier |author-link2= Xavier Sala-i-Martin |last2= Sala-i-Martin |title=Economic Growth |location=New York |publisher=McGraw-Hill |year=2004 |edition=2nd |isbn=978-0-262-02553-9 }}</ref>

The [[AK model]], which is the simplest endogenous model, gives a constant-savings rate of endogenous growth and assumes a constant, exogenous, saving rate. It models technological progress with a single parameter (usually A). The model is based on the assumption that the production function does not exhibit diminishing returns to scale. Various rationales for this assumption have been given, such as positive spillovers from capital investment to the economy as a whole or improvements in technology leading to further improvements. However, the endogenous growth theory is further supported with models in which agents optimally determined the consumption and saving, optimizing the resources allocation to research and development leading to technological progress. Romer (1986, 1990) and significant contributions by Aghion and Howitt (1992) and Grossman and Helpman (1991), incorporated [[imperfect market]]s and R&D to the growth model.<ref name= "BX"/>

=== AK model ===
{{main|AK model}}

The AK model production function is a special case of a [[Cobb–Douglas production function]]:
: <math>Y=AK^aL^{1-a}\,</math>

This equation shows a Cobb–Douglas function where ''Y'' represents the total production in an economy. ''A'' represents [[total factor productivity]], ''K'' is capital, ''L'' is labor, and the parameter <math>a</math> measures the [[output elasticity]] of capital. For the special case in which <math>a = 1</math>, the production function becomes linear in capital thereby giving [[constant returns to scale]]:<ref name= "BX"/>

: <math>Y=AK.</math>