The '''Averch–Johnson effect''' is the tendency of regulated companies to engage in excessive amounts of capital accumulation in order to expand the volume of their profits. If companies' profits to capital ratio is regulated at a certain percentage then there is a strong incentive for companies to over-invest in order to increase profits overall. This investment goes beyond any optimal efficiency point for capital that the company may have calculated as higher profit is almost always desired over and above efficiency.<ref>{{Cite journal |last1=Averch |first1=Harvey |last2=Johnson |first2=Leland L. |year=1962 |title=Behavior of the Firm Under Regulatory Constraint |journal=American Economic Review |volume=52 |issue=5 |pages=1052–1069 |jstor=1812181 }}</ref>
Excessive capital accumulation under rate-of-return regulation is informally known as '''gold plating'''.<ref name="Gold plating">{{cite news|last1=West|first1=Michael|title='Gold plating' rife, assets in for a hiding|url=http://www.theage.com.au/business/gold-plating-rife-assets-in-for-a-hiding-20130131-2dmjg.html|access-date=6 January 2015|agency=The Age|date=31 January 2013}}</ref>
But the so-called Averch-Johnson effect of overcapitalization does not as a general case involve "gold-plating".<ref> {{Cite journal |last=Johnson |first=L.L. |year=1973 |title=Behavior of the Firm Under Regulatory Constraint: A Reassessment |url=https://www.jstor.org/stable/1817057 |journal=American Economic Review |volume=63|issue=2 |pages=90–97 |jstor=1817057}}</ref>
== Mathematical derivation == Suppose that a regulated firm wishes to maximize its profit:<math display="block">\pi = R(K,L) - wL - rK</math>where <math>R(K,L)</math> is the revenue function, <math>K</math> is the firm's capital stock, <math>L</math> is the firm's labor stock, <math>w</math> is the wage rate, and <math>r</math> is the cost of capital. The firm's profit is constrained such that:<math display="block">\sigma = {R-wL\over{K}}</math>where <math>\sigma</math> is the allowable rate of return. Assume that <math>\sigma > r</math>. We may then form a functional to find the firm's optimal action:<math display="block">J = R(K,L)-wL-rK - \lambda[R(K,L)-wL-\sigma K]</math>where <math>\lambda</math> is the Lagrange multiplier (also known as the shadow price). The derivatives of this functional are:<math display="block">\begin{aligned} {\partial J\over{\partial K}} &= (1-\lambda)R_{K} - r + \lambda \sigma \\ {\partial J\over{\partial L}} &= (1-\lambda)R_{L} - (1-\lambda)w \end{aligned}</math>Taken together, this implies that:<math display="block">R_{K} = {r-\lambda \sigma\over{1-\lambda}}, \quad R_{L} = w</math>The ratio of the marginal product of capital and the marginal product of labor is:<math display="block">{R_{K}\over{R_{L}}} = {r-\alpha\over{w}}, \quad \alpha = {\lambda\over{1-\lambda}}(\sigma - r)</math>Since this new cost of capital is perceived to be less than the market cost of capital, the firm will tend to overinvest in capital.<ref>{{Cite book|url=https://mitpress.mit.edu/books/economics-regulation-and-antitrust-fourth-edition|title=Economics of Regulation and Antitrust|last1=Viscusi|first1=W. Kip|last2=Harrington, Jr.|first2=Joseph E.|last3=Vernon|first3=John M.|publisher=The MIT Press|year=2005|isbn=9780262220750|edition=4th|location=Cambridge, MA|pages=433–436}}</ref>
==See also== *Law and economics *Public utilities commission *Rate-of-return regulation
==References== {{reflist}}
== Further reading ==
* Greer, Monica (2012). ''[https://www.sciencedirect.com/book/9780123851345/electricity-marginal-cost-pricing Electricity Marginal Cost Pricing: Applications in Eliciting Demand Responses]''. Waltham, MA: Butterworth-Heinemann. * Lesser, Jonathan A.; Giacchino, Leonardo R. (2013). ''[https://www.purinc.com/products/fundamentals-of-energy-regulation-2nd-edition Fundamentals of Energy Regulation]'' (2nd ed.). Public Utilities Reports, Inc. * Willis, H. Lee; Philipson, Lorrin (2019). ''[https://www.crcpress.com/Understanding-Electric-Utilities-and-De-Regulation/Willis-Philipson/p/book/9780367392048 Understanding Electric Utilities and De-Regulation]''. Power Engineering. Boca Raton, FL: CRC Press.
==External links==
* [http://regulationbodyofknowledge.org/price-level-regulation/incentive-features-and-other-properties/ Body of Knowledge on Infrastructure Regulation: Incentive Features and Other Properties] * [https://www.e-education.psu.edu/ebf483/node/681 The Averch Johnson Effect]
{{DEFAULTSORT:Averch-Johnson effect}} Category:Economics of regulation Category:Law and economics Category:Mathematical economics Category:Public utilities