Just Deserts Clearly Favors the Minimum Wage Over the Earned Income Tax Credit

In June of last year, Greg Mankiw wrote a widely mocked paper outlining his philosophical perspective on the economy. Mankiw is an economist, not a philosopher, and the result was not pretty. In his paper, he endorsed an approach to economic justice called Just Deserts:

According to this view, people should receive compensation congruent with their contributions. If the economy were described by a classical competitive equilibrium without any externalities or public goods, then every individual would earn the value of his or her own marginal product, and there would be no need for government to alter the resulting income distribution. The role of government arises as the economy departs from this classical benchmark. Pigovian taxes and subsidies are necessary to correct externalities, and progressive income taxes can be justified to finance public goods based on the benefits principle. Transfer payments to the poor have a role as well, because fighting poverty can be viewed as a public good. 
This is a somewhat confusing description of the Just Deserts approach, especially the last sentence. But he captures the general essence of desert theory near the top, which is an economy organized according to the principle that each person get their "marginal product."
One of the odd things about this organizing principle is that it actually tells you way less about what to do with the economy than many of its adherents imagine. It is clear that you are not supposed to deprive someone of their marginal product, but how the government constructs the economic rules themselves help define one's marginal product. For instance, we could ban all schooling in America tomorrow and that would have a pretty serious impact on the future productivity of the country. But would that deprive anyone of their marginal product? No. It would just have the effect of making them less productive. So it appears to be totally consistent with desert theory.
It is with this understanding in mind that I found Mankiw's recent opinion piece in the New York Times so fascinating. In it, he argues that we should increase the Earned Income Tax Credit, not the minimum wage. Why they are put against each other when we can, as Jared Bernstein points out, do both, is mysterious. But his specific argument for why we should increase the EITC instead of the minimum wage is more mysterious still.
First, fairness: If we decide as a nation that we want to augment the income of low-wage workers, it seems only right that we all share that responsibility. [Increasing the EITC] does that. By contrast, [increasing the minimum wage] concentrates the cost of the wage subsidy on a small subset of businesses and their customers. There is no good reason this group has a special obligation to help those in need.
Ask yourself: is this a desert theory argument? The answer is absolutely no. Increasing the minimum wage is clearly a more preferable policy than increasing the EITC under a Just Deserts framework, especially if you believe what Mankiw believes. Why? Because Mankiw's line on the minimum wage is that what happens when you raise the minimum wage is businesses have to lay off workers because they cannot afford to hire workers whose marginal product is below the new minimum wage. But this also means that the workers that remain in these firms are being paid their marginal product. Their incomes are totally consistent with Just Deserts. So when we raise the minimum wage, the extent to which our society is organized along Just Deserts lines remains exactly the same.
On the other hand, increasing the EITC is entirely inconsistent with Just Deserts. Why? Because it deprives upper income people of their marginal product and uses it to increase the incomes of lower income people above their marginal product. Thus when we raise the EITC, our society becomes less consistent with Just Deserts.
So what on earth is Mankiw doing here endorsing a desert-inconsistent EITC increase over a desert-consistent minimum wage increase? They both substantially cut poverty and inequality. So why would someone pick the EITC over the minimum wage if they were a desert theory adherent? Does he actually believe his proclaimed Just Deserts views or is he just an opportunistic conservative who hops between philosophical positions ad-hoc to suit whatever conclusion he wants to argue in favor of?