Ross Douthat provides an array of explanations for the curious absence of socially conservative economics.  His top stories:

1. There’s more socially conservative economics than meets the eye.

The first is that social conservatives actually do make such
arguments, even if the phrase “negative externalities” isn’t deployed
with quite the frequency Caplan would like… Indeed, the entire corpus of
socially-conservative intellectual efforts, from 1970s-era
neoconservatives like Richard John Neuhaus and James Q. Wilson down to
the present era, is shot through with arguments that are, if not purely
economic, at least heavily informed by economic questions.

2. Belief in homo economicus conflicts with religious conviction.

But note that very few of the writers and intellectuals I’ve just
mentioned are practicing economists: They’re political scientists,
sociologists, journalists, and so forth… So maybe the question is, why don’t social
conservatives become economists? Probably it has something to
do with their frequent religio-philosophical commitments: Social
conservatives are not uniformly religious, but they tend to be
religion-friendly in ways that make an uneasy fit with the homo economicus assumptions that undergird so much of the work of the economics profession, left and right.

3. Academic stigma.

The simplest explanation for “the curious absence of socially
conservative economics” the same reason that there aren’t many social
conservatives in any academic field: Because social conservatism is
considered uniquely socially disreputable in elite culture, in
ways that libertarianism and economic conservatism are not. (A thousand
conversations: “Are you a Republican?” “Yes, but socially liberal,
fiscally conservative, don’t worry!”)

All good points, but Ross’ response makes me realize that I should have given the original puzzle more context.  The absence of socially conservative economics is odd because – unlike all the other disciplines Ross names – economics has intellectual rules that weigh heavily in social conservatives’ favor – especially textbook analysis of economic efficiency.

Efficiency analysis rejects the view that policy decisions are merely a matter of distribution – of who gets their way and who doesn’t.  Instead, efficiency analysis insists that – distribution aside – some outcomes are more efficient than others.  How do economists measure efficiency?  Simple: They count anything that anyone is willing to pay for. 

Take illegal drugs.  Efficiency analysis tells us to estimate the willingness to pay of everyone who gives a damn one way or the other.  So in addition to the preferences of potential users, we must – at minimum – count the preferences of potential users’ parents.  If your parents’ willingness to pay to stop you from using drugs exceeds your willingness to pay to use drugs, it is inefficient for you to get your way.

Non-economists could of course simply reject efficiency as the supreme normative standard.  That’s what I do.  But most economists are very reluctant to explicitly adopt any other normative standard.  This in gives social conservatives a great intellectual opportunity: Economics is a high-status academic game with established rules that genuinely allow social conservatives to win.  Hence my puzzlement for the absence of socially conservative economics.