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Notes
- 1.
In fact, though the fundamentals of General Equilibrium Welfare Theory are taught as bedrock economic principles in introductory and intermediate economics, public policy, law, political science, and other mainstream social science textbooks; most current theoretical NC microeconomists ignore General Equilibrium Welfare Theory, focusing instead on game theory applications that eschew any concern for “general welfare”—see footnote 6 in chapter 9.
- 2.
Consider for example Krugman’s discussion of a carbon tax that, without a second thought, characterizes other noncarbon measures to address global warming as “second best” solutions (Krugman 2014).
- 3.
See also any standard introductory microeconomic text, for example Mankiw (2008), for further explanation.
- 4.
This is necessary so that the assumption of diminishing returns or increasing marginal costs will generate an upward sloping supply curve. If, as the DCM shows, the supply curve does not exist, neither will the definitive market equilibrium point.
- 5.
Needless to say, this arbitrary weighting of CS and PS does not address issues of either dynamic efficiency over time, as opposed to purely static efficiency at one point in time, or the question of how and who should determine the proper level of investment and benefit from it, see later discussion.
- 6.
These include the assumptions of a PCFM composed of price taking firms that price at marginal cost along a rising, and above average-cost, marginal-cost curve.
- 7.
Another, closely related sales tax version of the Ramsey pricing inverse-elasticity rule stipulates that consumer welfare is maximized when sales taxes on different goods obey the inverse-elasticity rule so that, for every good, when cross-tax effects are negligible t i p i = k/E i , where t i is the sales tax on good i, p i is the price of good i, k is a constant, and E i is the own-price elasticity of demand of good; (Varian 1992, p. 412). Also, the simple own-price Ramsey pricing rule of (10.2) is strictly applicable only when “cross-price” effects are small or compensating. Baiman (2001) Appendix B derives a generalized “Progressive Ramsey pricing rule” for cases when cross-price effects are non-neglible or compensating that is analogous to the own-price progressive Ramsey Pricing Rule (10.6) discussed in this chapter.
- 8.
Strictly speaking Ramsey pricing will be regressive and social pricing progressive only if own-price elasticities of demand are inversely correlated with income-wealth. As is explained in the text, this will often (but not always) be the case. However, the central point of this chapter, that equity must be explicitly taken into consideration in welfare evaluation and pricing, will be unaffected by the progressive or regressive net result of its incorporation.
- 9.
Figures 10.2 and 10.3 below, are for illustrative purposes only, as they refer to Demand Curves (DCs) for two products at similar prices and quantities demanded. Elasticities for DCs at different quantities and prices will not generally relate to each other in this way. However, since targeting lower-elasticity markets for higher relative price increases will lead to more (absolute) dollar valued CS loss than progressive or flat pricing, Ramsey pricing will generally result in aggregate CS, or welfare, loss, regardless of the slopes of the DCs in the region of the price increases.
- 10.
The following discussion follows a more comprehensive presentation in Baiman (2001) p. 210–212.
- 11.
If the Ramsey effect, which increases CS for a fixed level of profit by reallocating it to high-elasticity segments, more than offsets the price discrimination effect which increases profits by reducing CS, aggregate unweighted CS might increase. In practice however, percentage profit increases from deregulation are generally large and will, therefore, most likely swamp Ramsey effects. Moreover, when CS is weighted before aggregation, the net progressive social pricing rule will generally work in a progressive direction eliminating this offset possibility, see text below and Baiman (2001).
- 12.
Formulas (12–14, 372), (12:38; 378), (12–58, 388) and (15–25; 470) in Atkinson and Stiglitz (1980), and equation (6a) Feldstein (1972; 33), are equivalent or generalizations of (10.6) above. However, as is noted in the text below, these derivations are incomplete as, even though the consumer welfare maximand is clearly convex in price they do not include a demonstration that second order conditions necessary to maximize the Lagrangian are satisfied.
- 13.
See discussion in summary section of this chapter.
- 14.
And similar, in terms of legitimating impact but more complex in the details “triumphs” of NC free market ideologically driven “efficient market theory” led to the even more catastrophic financial collapse of 2007 (Crotty 2011).
- 15.
Neither Feldstein, nor Atkinson and Stiglitz, provided a complete proof of the progressive Ramsey pricing formula as they did not demonstrate that all of the necessary inequalities hold or prove that second order conditions are satisfied—a gap that turns out to be nontrivial as the progressive welfare maximand on its own (without the constraint) in this case is convex rather than concave (Baiman 2000).
- 16.
Baiman (2000) proves that the concavity of the (PS) constraint outweighs the convexity of the welfare term so that the overall Lagranian maximand is concave—see previous footnote.
- 17.
In this more general application, cross-price effects, for the most part ignored in standard flat or progressive Ramsey pricing and for that matter in standard marginal cost theory as well, are likely to be more important. But though the formulas are more complex, Baiman (2001, Appendix B) shows that similar progressive pricing results hold with cross-price effects (with or without Slutsky symmetry).
- 18.
As the subject matter of these papers directly addressed prior published papers by prominent mainstream economists and included the kind technical content highly encouraged in mainstream economics journals, with the intention of reaching broader exposure, I initially submitted them to a number of mainstream economics journals. However, after repeated cursory rejections that showed no evidence that any serious review had actually been conducted, even after appeals to the Editors challenging the specious arguments, when any were given at all, for rejection, as I was running out of time on a tenure decision (a common problem for younger and often more productive academics), I abandoned this futile effort to bore from within. This exercise was not entirely futile however as James Mirrlees, a “Nobel” prize winning Cambridge University microeconomist to whom I sent an early draft of the manuscript before submitting it for publication, did send me a thoughtful note advising me that with the constraint, the Lagrangian might be concave, which turned out to be the case. Joe Stiglitz, subsequently a “Nobel” prize winner, also sent me an encouraging note, and for the record, William Baumol also responded kindly to my inquiries on an earlier draft that did not include references to the Edison Institute paper that I had not yet discovered. I was grateful to be able to eventually publish these papers in the Review of Radical Political Economics (RRPE), and I think this example shows the importance of maintaining even just a small number of “heterodox” journals in economics like the RRPE though those of us who have served on the Editorial Boards of these renegade journals may sometimes wonder if our efforts to preserve this marginalized and ignored intellectual production served any useful purpose. I am also indebted to Vince Snowberger of the Colorado Public Utilities Commission, a fellow radical economist (and MIT alumnus, formerly at the University of Colorado at Boulder) who discovered an error in Equation 2.15 Baiman (2001, p. 208). This led to the corrected derivation of Equation (A7) Appendix A and Baiman (2002, Equation 5, p. 315).
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Baiman, R.P. (2016). From Amoral High Theory to Immoral Applied Theory. In: The Morality of Radical Economics. Palgrave Macmillan, New York. https://doi.org/10.1057/978-1-137-45559-8_10
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