As for the price, the official numbers are $67m for a new F9 and $97m for a reusable FH (from their respective Wikipedia pages).
Additionally, my reasoning is (as you mention) related to cadence. FH flies very infrequently and requires more ground expenses to prepare, recover and then refurbish 3 boosters. Additionally there's the opportunity cost of keeping a center core on standby (as it's purpose built for FH [1]) and the opportunity cost of keeping the side boosters either on standby or converting them to F9s.
Elon has previously mentioned that with Falcon rockets the main costs per flight are the second stage (~$10m, expended), fairings (~$3-4m, reusable), refurbishment (~$1m) and fixed ground costs, which can be reduced by increasing cadence [2]. In the case of FH the second stage and fairing costs are the same, the refurb costs are tripled and due to much lower cadence the ground costs are higher. Meanwhile, F9 flies frequently, so it has lower ground costs per launch and the booster's cost can be more easily amortized via several flights before the expendable launch.
Additionally, [2] mentions that the marginal cost of building an F9 booster is ~$15m, so all the extra costs of FH only need to be greater than $15m to make it worth just using an expendable F9.
Hmm yeah, digging around it seems that Wikipedia is probably incorrect with the expendable pricing. Seems like there aren't really any recent numbers available for expendable F9s as the last intentionally expended F9 was 3 years ago.
As for the price, the official numbers are $67m for a new F9 and $97m for a reusable FH (from their respective Wikipedia pages).
Additionally, my reasoning is (as you mention) related to cadence. FH flies very infrequently and requires more ground expenses to prepare, recover and then refurbish 3 boosters. Additionally there's the opportunity cost of keeping a center core on standby (as it's purpose built for FH [1]) and the opportunity cost of keeping the side boosters either on standby or converting them to F9s.
Elon has previously mentioned that with Falcon rockets the main costs per flight are the second stage (~$10m, expended), fairings (~$3-4m, reusable), refurbishment (~$1m) and fixed ground costs, which can be reduced by increasing cadence [2]. In the case of FH the second stage and fairing costs are the same, the refurb costs are tripled and due to much lower cadence the ground costs are higher. Meanwhile, F9 flies frequently, so it has lower ground costs per launch and the booster's cost can be more easily amortized via several flights before the expendable launch.
Additionally, [2] mentions that the marginal cost of building an F9 booster is ~$15m, so all the extra costs of FH only need to be greater than $15m to make it worth just using an expendable F9.
[1] https://spaceflightnow.com/2022/01/27/spacex-gives-converted...
[2] https://www.inverse.com/innovation/spacex-elon-musk-falcon-9...