# Solow–Swan model

From Devec

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

## Contents

## Model assumptions

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

etc.

## Variables in the model

Name | Variable | Unit | Set of possible values | Rival input? | Variable type | Notes |
---|---|---|---|---|---|---|

Output | Y |
Units of GDP (dollar?) | [0, ∞) | – | Endogenous | |

Physical capital (capital stock) | K |
[0, ∞) | Yes | Endogenous | Physical capital includes things like machines, computers, buildings, etc. | |

Labor | L |
[0, ∞) | Yes | Exogenous | ||

Technology (knowledge) | A, T |
No | Exogenous | |||

Consumption | C |
|||||

Investment | I |
|||||

Amount saved | S |
|||||

Growth of X |
||||||

Population growth | (−∞, ∞) | |||||

Depreciation (rate?) | δ, d, D |
Unitless | ||||

Capital per worker | k = K/L |
Endogenous | ||||

Fraction saved | s |
Unitless | [0, 1] | |||

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 | (0, 1) |

## Mathematical formalism

- (sometimes also )

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.

A closed form is possible,[1] but it is possible to play around with the model in non-closed forms to extract useful information.

## Table of comparative statics

## History

## Commentary

## See also

## External links

- Solow–Swan model (Wikipedia)