I should become a psychiatrists and recommend prostitutes to my clients.
Sex therapy's actually a thing. Not very much now in the US (iirc there's like... one or two left in the country at the mo', or something like that), but the concept of introducing sex (of a particular sort, or whatever) into a person's life under controlled(ish) conditions for a person having psych problems related to the subject's been around for a while. Some of it even more reasonable than the old hysteria stuff!
At which point their only goal would be to ramp up the productivity of their population in order to compete overseas. Which begs the question of 'how'.
Whooo, no, no, you've mistaken the primary goal of capitalism and apparently rather incredibly badly. The competition is a side effect, the goal is
profit. Overseas competition only
maybe would be a desired thing in the case of a country wide monopoly, and beyond that specifically targeting areas that are
incapable (for whatever reason) of meaningfully competing is very very much a thing (e.g. US & SA, Europe and much of the world during major colonial times, etc., etc., etc.). What's about as likely to happen as anything is the now-controlled country starts exerting pressure (economic, cultural,
military) on vulnerable areas in order to render competition a non-issue, and then extends their economic control either outright or through proxies. Productivity increases are only one possibility among many, often pretty terrible, ones, and only somewhat likely to be the first (or even seventh or whatev') thing a capitalist attempts.