Do you think child support reduce rich men’s fertility or just out of wedlock rich men’s fertility?

3 economists say it reduces out of wedlock fertility among rich men.

Economic research—specifically from Daniel I. Tannenbaum (2020) and Anna Aizer & Sara McLanahan (2006)—concludes that strict child support enforcement reduces out-of-wedlock births, particularly among high-income men. They argue this is a "commitment mechanism" that increases "maternal quality" (men become hyper-selective about who they have children with).

Basically, rich guys, athletes, or celebs that date and fuck many women wouldn't use condom if, worse come to worse, child support is "trivial" compared to their income. If government child support demand is $500 a month (median child support) or something can be negotiated before conception then someone making $1 million per year wouldn't bother wearing condom.

And 3 economists agree. The reasoning is exactly as I said. Child support laws are effectively price floor for getting knocked up by the like of NBA stars. If the price floor is higher than normal market price then the deals are off. We got deadweight loss and kids with rich father is simply under produced.

But all 3 say it's for outside wedlock birth rate.

They don't say anything about rich men's fertility total. It is possible that

1. Rich men simply get married and hence total fertility doesn't drop.

2. It is also possible that rich men fertility simply drop. Marriage, after all doesn't remove child support, but simply add alimony on top of it.

Which one do you think is true?

I think marriage is so shitty for rich men that out of wedlock lower fertility is all that matters. But I think it lowers total fertility too. I am just curious.