Chapter 38: The Theory of Second Best and Third Best
Wai Chiu Woo The generalized theory of second best developed by Lipsey and Lancaster (1956) not only creates a devastating effect on welfare economics but also a challenge on how to draw a simple diagram to express the theory. The central message of the theory is simple: Pareto optimality in the first-best situation (absence of constraints additional to those of limited resources and given technology) requires the equality of marginal rate of substitution (MRS) for consumers and marginal rate of transformation (MRT) for any pair of commodities. Suppose in one (or some) sector(s) there is some irremovable distortion (due to, say, an unbreakable monopolist, tariff or other reasons) so that a (some) first-best optimality condition(s) cannot be fulfilled. Subject to this extra constraint, to attain the (second-best) welfare optimum, should we fulfil as many remaining first-best conditions as possible? The answer from the second-best theory is ‘no’. The challenge to graphical economists is that the problem involves at least three sectors. Optimum condition is not fulfilled in one sector. We would like to see if attaining one or more equality conditions in the remaining sectors is welfare-improving. However, a diagram simultaneously portraying three sectors is normally three-dimensional and difficult to read and draw. McManus (1959) pioneered a two-dimensional diagram, using a right triangle, to illustrate the problem. Winch (1971) modified it to a normal triangle (although looks like an equilateral) and Ng (1979 and also 2004) explicitly used an equilateral triangle, taking advantage of the property that, at...
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