Solow growth model - physical capital
Please write a 500 word essay explaining the major contribution(s) of the Solow model and how to use the concepts to help explain cross-country differences in the level of output per worker and the growth rates of output per worker. Please refrain from using "technical model jargon". Write the essay as though you were explaining the ideas to a person who is not familiar with the equations and graph associated with the Solow model. That is, explain the ideas without referring to the equations or graph.
Solow growth model
The Solow growth model contains two key equations:
1. The production function - describes how the capital and labor inputs are transformed into output.
2. The capital evolution equation - shows that net additions to K arise when investment (which equals saving in a closed economy) exceed capital depreciation.
We began by writing down the two equations in their aggregate form. Since we really want to focus on output per capita or output per worker, we will transform the two equations to per worker form.
The model focuses on the role of capital and capital accumulation for explaining cross-country differences in income levels and growth rates. The level of productivity is taken to be exogenous as is the savings rate and the population growth rate.
To analyze the model we graphed both terms (on the right hand side) of the capital evolution equation. In this setting, we showed that the equilibrium is the steady-state of the model - where the flows into capital per worker (investment per worker) are just equal to the depletion of capital due to depreciation and labor force growth.
Things you should be able to do with this graph:
• Explain why each line is shaped as it is.
• Explain why the steady-state is an equilibrium (i.e. if the economy begins at some point other than the steady-state, economic forces will push the economy toward the steady state.) To do this you show that if you begin a level of capital per worker that is less than the steady-state level, then additions to capital per worker will exceed depletions and the capital stock will grow toward the steady-state level. A similar dynamic works when we begin at a level of capital per worker that exceeds the steady-state level.
• Understand the role of diminishing marginal product of capital in generating a steady state.
o Without productivity changes, each additional unit of capital adds less to output than the previous unit (diminishing marginal returns to capital). Eventually the benefit of adding more capital (more output) will peter out (while the depreciation rate continues at a linear rate) and capital accumulation will come to a steady-state
• Show what happens to the growth rate and the level of capital per worker and output per worker when
o the saving rate changes
o the population growth rate changes
o when the level of productivity changes
The Solow model is our framework for explaining why the level and growth rate of capital per worker may differ across countries and how the differences in capital per worker affect differences in output per worker. In the basic Solow model, we have not included a role for human capital or productivity. When these extensions are added onto the basic Solow model, we have a more general model we call the neo-classical growth model.