Solow–Swan model

The Solow–Swan model is a long-run economic growth model.

Model assumptions

• single-sector economy
• closed economy (no trade)
• no taxation

etc.

Variables in the model

Name	Variable	Unit	Rival input?	Variable type	Notes
Output	Y	Units of GDP (dollar?)	–	Endogenous
Physical capital (capital stock)	K		Yes	Endogenous	Physical capital includes things like machines, computers, buildings, etc.
Labor	L		Yes	Exogenous
Technology (knowledge)	A, T		No	Exogenous
Consumption	C
Investment	I
Amount saved	S
Growth of X	$g_{X}={\dot {X}}/X={\frac {\frac {\partial X}{\partial t}}{X}}$
Population growth	$n={\dot {L}}/L$
Depreciation (rate?)	δ, d, D
Capital per worker	k = K/L			Endogenous
Fraction saved	s
Output per worker	y = Y/L			Endogenous
Time	t	Time, e.g. years
Production function	F
Elasticity of output with respect to capital	α	Unitless

Mathematical formalism

$Y=K^{\alpha }(AL)^{1-\alpha }$ (sometimes also $Y=AK^{\alpha }L^{1-\alpha }$)

${\dot {K}}=sY-\delta K$

TODO show that the model satisfies (1) constant returns to scale; (2) diminishing returns to capital; (3) diminishing returns to labor; (4) the Inada conditions.

External links

• Solow–Swan model (Wikipedia)