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Efficiency, Optimality and Values

For the record, I see this post as a continuation and (yet another) response to the Sargent-Smith/KrugmanHouse debate over Sargent’s equity-efficiency assertion which I’ve commented on before.   The latest round of posts related to the topic have this debate trending in what I think is an odd direction putting me in the awkward position of defending a concept, Pareto efficiency, which I’d be more comfortable criticizing.

My proximate purpose  is to respond to Simon Wren-Lewis’s new post which I think illustrates the problem–this is, I think, one of the biggest confusions among economists about our own subject (not that Wren-Lewis is necessarily confused here, but he’s at least bringing up the problem).   The key graf:

Why is there this emphasis on only looking at Pareto improvements? I think you would have to work quite hard to argue that it was intrinsic to economic theory – it would be, and is, quite possible to do economics without it. (Many economists use social welfare functions.) But one thing that is intrinsic to economic theory is the diminishing marginal utility of consumption. Couple that with the idea of representative agents that macro uses all the time (who share the same preferences), and you have a natural bias towards equality. Focusing just on Pareto improvements neutralises that possibility. Now I mention this not to imply that the emphasis put on Pareto improvements in textbooks and elsewhere is a right wing plot – I do not know enough to argue that. But it should make those (mainstream or heterodox) who believe that economics is inherently conservative pause for thought.    

The problem is that Pareto efficiency and optimality are not the same things, cannot (or should not) be used interchangably.  In fairness, when I’m being a sloppy, I do the same thing; but it’s important to remind ourselves why this is a mistake.

So to remind ourselves, what is optimality and what is efficiency?

Optimality is the solution to a kind of thought experiment; the answer to the question of what would a benevolent, god-like social planner do if it had complete control of the economy (or “constrained optimal” if the social planner must work under constraints).   The advantage of the approach is that it produces unambiguous outcomes (often a single point in allocation-space).   The disadvantage is that  the planner’s problem is by definition not values-neutral.   Why do I say it’s not value’s neutral?  Because you need to define the planner’s objective function (i.e. the social welfare function) and the social welfare function defines the trade-offs the social planner is willing to make, for example, when balancing equity/efficiency.   “All I care about is Bill Gates’ wealth” is an acceptable, if odd, social welfare function, as is “complete equity at all costs”.   The general case is somewhere in between these two.

Efficiency means that there are no unexploited gains (no one can be made better off except at the cost of making another worse off):  contra Wren-Lewis, I want to argue that this is very much a values-neutral idea.   To see why consider this little factoid: regardless of the social welfare function you choose, the solution to every planner’s problem is Pareto efficient.  The converse is not necessarily true (Pareto efficiency is a necessary, not sufficient condition of optimality… as an aside this is where the confusion–I think–comes from, since economists often refer to the planner’s solution as “efficient”).   So here’s the thing, for every point in the Pareto set there is a social planner who would choose that point as the optimum (or you might say there’s a set of values which corresponds to each point in the Pareto set).   That’s the sense in which Pareto efficiency is values-neutral.

What Wren-Lewis is arguing about is slightly different issue.   Is the search for Pareto improvements also values neutral?  I think most economists would say ‘yes’.   After all, no social planner would be any worse than indifferent to a Pareto improvement (a valid social welfare function is weakly increasing in the well-being of every individual agent in the economy).

Does that actually make a Pareto improvement values neutral, however?   No, of course not (this is what I think Wren-Lewis has in mind, but I’m only guessing).   A Pareto-improvement shifts the outcome in allocation-space, but as a general matter a Pareto improvement “picks a direction”–different social planners will disagree that it is the correct direction to take.   Some social planner’s would even prefer to take away from some agents to give to others.   To put it more simply, if you keep exploiting Pareto inefficiencies randomly until you reach an efficient outcome, is the result optimal?   The answer is that with probability one, it will not be.

I’m not sure if I have any other comments to make… just a reminder to myself and others to be careful regarding efficiency and optimality.   I do suspect that the “confusion” here reflects a preference among some economists for the “core” solution concept of cooperative games… but I need to think about that a bit before I make that argument.  So I’ll leave this post here for now.

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  1. May 14, 2014 at 1:33 pm
  2. May 30, 2014 at 5:23 pm

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