# Intermediate Macroeconomics

## 6. Growth Models

Here we present two models to explain long-run trends in economic growth. The first model is the Malthusian growth model, which is based on Thomas Malthus's 1798 book, An Essay on the Principle of Population, which advances a theory that population growth depends positively on economic well-being. In these Pencasts, we present a formalization of the theory in which production depends positively on land availability and population (labor). The theory suggests that improvements in technology lead only to temporary improvements in economic well-being and permanent increases in population size. The second model is the Solow growth model, a theory advanced in the 1950s by Robert Solow, and which won him the Nobel Prize in economics in 1987. In this theory, production depends positively on labor and capital. This theory suggests that improvements in technology lead to permanent improvements in economic well being, with increases in capital stock per person and output per person.

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## Malthusian Growth Model FrameworkHere we introduce the Malthusian growth model framework. We describe a theory for production where output is built with labor and land. Population growth depends positively on nutrition and so positively depends on consumption per capita. We write down some functional relationships for these relationships that we use in the Pencasts that follow. |

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## Malthusian Growth Model OutcomesWe build off the Malthusian model foundations developed in the previous Pencast to describe long-run outcomes for population and consumption per capita, which is our broad measure of economic well-being / standard of living. We show how population grows until it reaches a long-run equilibrium, and we show the corresponding long-run outcome for consumption per person. |

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## Technology Improvement in the Malthusian ModelHere we use the Malthusian growth model to describe and illustrate the long-run affects of an improvement in technology. We find that improvements in technology lead to increases in population level, but perhaps counter-intuitively, there is no long-run change in standard of living. |

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## Solow Growth Model FrameworkHere we describe the framework for the Solow growth model. In this model, output is produced with capital and labor. We describe some assumptions for the production function and derive an expression for output per person. |

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## Capital Evolution in Solow Growth ModelHere we derive an expression for how capital per person evolves, based on how quickly capital depreciates and how much businesses invest in new capital goods. |

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## Solving the Solow Growth ModelHere we solve the Solow growth model to derive an expression for capital growth that depends only on the exogenous parameters of the model: the savings rate, the population growth rate, the depreciation rate, and the state of technology. In the Pencasts that follow, we graph this equation and use it to discover how economies grow and find out the consequences to long-run economic outcomes when the exogenous parameters change. |

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## Growth in the Solow ModelWe graph the expression for capital growth that was derived in the previous Pencasts and use it to show how an economy grows, and what the long-run outcome is for capital accumulation and output per person. |

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## Steady State in the Solow ModelWe derive an expression for the long-run, steady state level of capital stock per person, and use a graph to illustrate the solution. We will use this graph in Pencasts that follow to describe and illustrate the long-run consequences to changes in exogenous parameters in the model, including the savings rate, the population growth rate, the depreciation rate, and the state of technology. |

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## Saving in the Solow ModelHere we find the consequences to long-run capital per worker and output per worker when consumers increase the fraction of income that they save. We find that steady state capital per worker and output per worker both increase. |

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## Technology in the Solow ModelHere we find the consequences to long-run capital per worker and output per worker when there is an improvement in technology. We find that steady state capital per worker and output per worker both increase. |

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## Capital depreciation in the Solow ModelHere we find the consequences to long-run capital per worker and output per worker when there is an increase in the depreciation rate of capital, perhaps due to poor maintence of the capital stock. We find that steady state capital per worker and output per worker both decrease. |

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## Population Growth in the Solow ModelHere we find the consequences to long-run capital per worker and output per worker when there is an increase in the population growth rate. We find that steady state capital per worker and output per worker both decrease. |