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The Basic Solow Model Notes

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This is an extract of our The Basic Solow Model document, which we sell as part of our Macroeconomic Principles Notes collection written by the top tier of LSE students.

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The Basic Solow Model 20 October 2010

Topics

* The basic Solow model:

* The Solow model with technological progress:

Reading

* Williamson (Chapter 6, p207-224)

* Weil (Appendix of Chapter 8)

Key Points

* Basic Solow model

* Cobb-Douglas production function

* Competitive equilibrium in the Solow model

The Basic Solow Model

* The Solow model is the basis for the modern theory of economic growth

* It is based around capital accumulation

* A key prediction is that technological advancement is necessary for sustained increases in living standards

* Population is assumed to grow at a constant rate :
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* Consumers are assumed to save a constant fraction of their income, consuming the rest:
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* Representative firm's production function is neoclassical:
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* We drop land from the model, so that output depends on capital and labour

* Capital accumulation equation:
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* Key assumption in the Solow model

* Investment becomes future capital which becomes future investment etc.

* The constant-returns-to-scale (CRS) property allows us to focus on output per worker and capital per worker:

* Plotting the steady state

* Summary of steady state

* Multiple steady states

* Stability of steady state

* Comparing countries

* Conditional convergence and absolute convergence

* The golden rule

* Effects of changes in savings rate g

* Effects of changes in population growth rate

* Effects of technological progress

* Solow model with technological progress

* Labour augmenting technological progress

* Dynamics of capital per effective worker

* Steady state with technological progress

* Summary of Solow model with technological progress

* Kaldor stylized facts

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? Where
* This then produces a 2-dimensional graph rather than a 3-dimensional The Cobb-Douglas Production Function
* The Cobb-Douglas production function is the most widely used production function i.e. f in the Solow model
* It has constant returns to scale:

* We assume that firms are competitive
* The coefficient is the capital share (the share of income that capital receives)
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Formulae

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* Using the Cobb-Douglas production function:
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Competitive Equilibrium
* The income-expenditure identity holds as an equilibrium condition:? We've simplified by saying there is no G or NX
* Consumer's budget constraint:* Because of this, in equilibrium:* The capital accumulation equation becomes:? Which is the key of the Solow model
* We then transform the capital accumulation equation into per-worker form by putting in the production function:* This is a dynamic equation showing that future capital per worker is related to current future capital per worker and saving Plotting the Steady State for Capital Per Worker
* We plot current capital per worker against future capital per worker
* Graph showing steady state for capital per worker
* The blue line tells us how k' depends on k
* Again the steady state is when the graph meets the 45 degree line
* We can then solve for k* because of the facts of steady state:? -
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* Graph demonstrating solving for steady state as the intersection of the 'savings curve' and the 'effective depreciation curve' Summary of Steady State Growth rates are as follows:

Course Notes Page 11

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