Harrod–Domar model: Difference between revisions

Latest revision as of 05:02, 16 September 2017

The Harrod–Domar model is a long-run economic growth 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.
Consumption	C
Investment	I
Amount saved	S
Growth of X	$g_{X}={\dot {X}}/X={\frac {\frac {\partial X}{\partial t}}{X}}$	${\text{Time}}^{-1}$
Depreciation (rate?)	δ, d, D	Unitless
Capital per worker	k = K/L			Endogenous
Fraction saved	s	Unitless
Time	t	Time, e.g. years
Production function	F

{\frac {\Delta Y}{Y}}={\frac {c\Delta K}{Y}}={\frac {c(sY-\delta K)}{Y}}=sc-\delta {\frac {K}{Y}}c=sc-\delta

{\dot {Y}}/Y={\dot {K}}/K=(sY-\delta K)/K=sY/K-\delta =sc-\delta

@@ Line 11: / Line 11: @@
 |-
 | 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'' || ||
@@ Line 23: / Line 19: @@
 |-
 | Growth of ''X'' || <math>g_X = \dot{X}/X = \frac{\frac{\partial X}{\partial t}}{X}</math> || <math>\text{Time}^{-1}</math> || ||
-|-
-| Population growth || <math>n = \dot L / L</math> || <math>\text{Time}^{-1}</math> || ||
 |-
 | Depreciation (rate?) || ''&delta;'', ''d'', ''D'' || Unitless ||
@@ Line 31: / Line 25: @@
 |-
 | Fraction saved || ''s'' || Unitless ||
-|-
-| Output per worker || ''y'' = ''Y''/''L'' || || || Endogenous ||
 |-
 | Time || ''t'' || Time, e.g. years ||
 |-
 | Production function || ''F'' || || ||
-|-
-| Elasticity of output with respect to capital || ''&alpha;'' || Unitless ||
 |}
 ==Mathematical formalism==
+===Discrete===
+:<math>\frac{\Delta Y}Y = \frac{c \Delta K}Y = \frac{c (sY - \delta K)} Y = sc - \delta \frac KYc = sc - \delta</math>
+===Continuous===
+:<math>\dot Y / Y = \dot K / K = (sY - \delta K) / K = sY/K - \delta = sc - \delta</math>
 ==History==