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Hotelling (1929) - Stability In Competition (view source)
Revision as of 19:14, 29 September 2020
, 19:14, 29 September 2020no edit summary
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|Has article title=Stability In Competition
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|Has year=1929
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*This page is referenced in [[BPP Field Exam Papers]]
*Hotelling, H. (1929), "Stability in competition", Economic Journal 39, 41-57. [http://www.edegan.com/pdfs/Hotelling%20(1929)%20-%20Stability%20in%20competition.pdf pdf]
@article{hotelling1929stability,
title={Stability in competition},
author={Hotelling, H.},
journal={The economic journal},
volume={39},
number={153},
pages={41--57},
year={1929},
publisher={JSTOR}
}
==Abstract==
==Ernesto Dal Bo's The Hotelling ModelWith Prices==
As per Hotelling, there is a two stage game:
*<math>mc=0\,</math>
*unit demands
*consumers are homogeneous with valuation <math>v \,</math> (assumed large enough to cover the market)
*there are transportation costs
:<math>p_1 + t(x-a)^2 = p_2 +t(1-b-x)^2 \,</math>
Rearranging for <math>x \,</math> gives us the demand function for <math>q_1\,</math>, and likewise <math>1-x = q_2\,</math>.
Doing comparative statics on the demand we find:
*Demand is less sensitive to the price differential as <math>t \,</math> (transport cost) increases
*Equal prices gives the firm captive demand plus half of intermediate segment <math>\frac{(1-b-a)}{2}\,</math>
*Taking <math>\frac{dq_1}{da}\,</math> shows that (for equal prices) getting closer steals demand: the '''demand effect'''
This gives us a theory of product differentiation - firms differentiate to create monopoly and soften price competition. However, this is inefficient from a social welfare standpoint. The prices are transfers, but the transportation costs are lost. The welfare maximizing location would be <math>\left (\frac{1}{4}, \frac{3}{4} \right) \ne (0,1).\,</math>
If prices are fixed, because of regulation, or as in politics, the competition effect is gone and only the demand effect remains. This leads firms to locate in the center, which is also inefficient (as in Downsian competition for political parties). The `Political ' Hotelling Model is the same as choosing firm location without prices.
