Opportunity cost

Reader Xerographica comments about opportunity cost. After a lengthy illustration of opportunity cost — the most valuable thing you have to give up to get something else — he (?) goes on:

We can see that the problem with the current political system is that congress has no idea how much public education I would be willing to forgo for improved medicare. Having attended a public university I certainly value public education but I also valued my grandmother's health. Even though my grandmother and grandfather valued both public goods as well, it's very unlikely that our allocations would be the same.

In the private sector every single consumer is forced to consider the opportunity costs of their spending decisions...and every single donor is forced to consider the opportunity costs of their donations. But in the public sector taxpayers are not forced to consider the opportunity costs of their taxes.

Therefore, we can objectively say that with the current system, the public sector is very inefficient.

To greatly improve the efficiency of the public sector we would simple allow taxpayers to directly allocate their individual taxes among the various government organizations at anytime throughout the year. In other words, donations to government organizations should be 100% tax deductible.

In a few of your blog entries I've noticed that you consider yourself to be pragmatic. That's really interesting because I labeled the above concept "pragmatarianism".

Xero is correct on one point: opportunity cost is central to economics. But after that he goes off the rails.

My original post was about efficiency. His first mistake is to say that "objectively... the public sector is very inefficient." Because there are multiple ways to talk about the efficiency of any system (we might, for example, talk about vehicle miles per gallon, passenger miles per gallon, passenger/vehicle miles per hour, accidents per mile, etc.), even if he's correct, concluding that the public sector is inefficient without qualification ignores all the other measures of efficiency. At best, Xero could have shown that the public sector is less efficient at quantifying opportunity cost.

But Xero actually does not show that the public sector is actually less efficient on this measure. He claims that the government cannot quantify opportunity cost, but of course they can and do quantify them. Congress makes decisions at the margin all the time: they explicitly do reduce this program to increase that program, raise or lower taxes to pay for more or fewer programs. Individual taxpayers can certainly evaluate the opportunity cost of their own taxes, and vote for politicians who will tax at the equilibrium level, where the opportunity cost of one less dollar of private spending equals the actual benefit of one more dollar of taxes. Just because it might be the case that a public body such as Congress does not actually consider the population's view of opportunity cost (because it conforms to the perceptions and preferences of the capitalist ruling class) does not mean it cannot do so.

His preferred method — letting individual taxpayers control the allocation of their own taxes — assumes that the opportunity cost associated with production we typically allocate to the government aggregate additively: the "social" opportunity cost of some public endeavor is the simple sum of all the individual opportunity costs. But anyone who has studied macroeconomics knows that not every variable aggregates additively. For example, the aggregate demand function is not the simple sum of the demand functions for each individual product. The microeconomic demand function for an individual product makes the ceteris paribus assumption that the prices for all other products remains the same. The aggregate demand function obviously cannot include that assumption. Similarly, my individual microeconomic opportunity cost of my taxes for some public good is ceteris paribus, i.e. it assumes that everyone else's behavior remains constant while my own contribution increases or decreases. But however, changes in spending on public goods are not ceteris paribus: if we want to have, for example, more public education, we have more public education for everyone at the same time, and either more taxes or less of something else for everyone.

Opportunity cost, while definitely central to economics, is a particularly bad quantity to use for efficiency. An opportunity cost is necessarily counterfactual: it is the value of what we give up, not what we actually have. Although we can often estimate an opportunity cost, because it is counterfactual, it cannot be measured directly. In the sense that I was using it in the original post, efficiency is a post hoc consideration: it tells you how well your theoretical model works, and you can't create a post hoc consideration on theoretical grounds.

Not only is opportunity cost counterfactual, it's also fundamentally equivocal: the opportunity cost can change based on different ways of setting up the counterfactual. Again, the Prisoner's Dilemma shows this equivocation very simply. If you consider the opportunity cost against the Nash Equilibrium, then the opportunity cost of cooperation is always larger than the opportunity cost of defection, regardless of the other actor's move. On the other hand, the opportunity cost of mutual defection is greater than the opportunity cost of mutual cooperation. Neither construction is "more valid" than the other; it's just the case that the opportunity cost is equivocal in many decisions. Since opportunity costs can be equivocal, any measure of efficiency based on opportunity cost can also be equivocal.

Although opportunity cost is indeed central to economics — everything's a trade-off — precisely because it is central we want to use other, more directly measurable variables to evaluate efficiency. We can measure, for example, value obtained (which might be subjective, but is at least real) and hours worked, to obtain a useful measure of efficiency. These real measures of efficiency can give us a better understanding of our economy than trying to estimate a counterfactual, equivocal quantity.

[Update 10/21/11] There are a lot of other reasons why Xero's idea is really bad, not the least of which is that it turns a (at least nominally) democratic institution into an explicitly plutocratic system. That reason is, however, almost entirely political, and I wanted to make a specifically economic critique of the idea.

I strongly suspect that Xero is not part of the 1%, who would, under his scheme, have near-absolute control over government spending and would use that control for their own benefit, not Xero's (or mine). I'm continually astonished at the propensity of people to come up with schemes to not only justify but also intensify their own slavery.