Production function/Tutorials: Difference between revisions
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===The learning curve=== | ===The learning curve[http://fast.faa.gov/pricing/98-30c18.htm]=== | ||
On a P per cent learning curve, every time the length of the production run is doubled, the unit cost is reduced by a factor p. | On a P per cent learning curve, every time the length of the production run is doubled, the unit cost is reduced by a factor p. | ||
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Revision as of 07:43, 4 September 2008
The learning curve[1]
On a P per cent learning curve, every time the length of the production run is doubled, the unit cost is reduced by a factor p.
(p being the percentage P expressed as a fraction)
The cost, Cn of the nth unit is given by:
- Cn= C1.n-b
where
- b = (-logp)(log2)
The Cobb-Douglas production function
The Cobb-Douglas function has the form:
- Y = A. Lα . Cβ,
where
- Y = output, C = capital input, L = labour input,
- and A, α and β are constants determined by the technology employed.
If α = β = 1, the function represents constant returns to scale,
If α + β < 1, it represents diminishing returns to scale, and,
If α + β > 1, it represents increasing returns to scale.
It can be shown that, in a perfectly competitive economy, α is labour's share of the value of output, and β is capital's share.
Dissenting voices
Supply
Piero Saffra objected on the grounds that, by bidding up the prices of inputs to suppliers of substitutes, the increased output of a product expansion could increase the demand for that product, thus violatimg the necessary condition that demand must be independent of supply [1]. Jacob Viner had justified the long-run diminishing returns thesis by arguing that competitors for the required inputs would bid up their prices [2], but Lionel Robbins argued that Viner's justification was incomplete in cases where the market did not contain other users of an input and raised a number of other more complex objections [3].
Production
References
- ↑ Piero Sraffa: "The Laws of Return Under Competitive Conditions", The Economic Journal December 1926
- ↑ Jacob Viner: "Cost Curves and Supply Curves", in Readings In Price Theory, edited by G. J. Stigler and K. E. Boulding. Irwin, 1952.
- ↑ Lionel Robbins: "Remarks Upon Certain Aspects of The Theory of Costs", Economic Journal March 1934.