I don't think Mounjaro will be particularly cheap even if prescribed in Japan

‌Even if a Korean person visits Japan for tourism,
they won't be eligible for Japanese health insurance.
In that case, when prescribing to Korean travelers,
Japanese clinics or hospitals will likely set high consultation fees or prescription prices.

Based on a 4-pen standard, it is around 300,000 KRW in Korea,
but they say it is around 100,000 KRW in Japan (under insurance coverage).
Since it is non-reimbursable, there is no reason for this price to be fixed,
and if Japanese medical fees are not covered by health insurance,
the initial consultation fee is roughly around 30,000 KRW.
Even if they set the prescription price at around 50,000–60,000 KRW, there won't be much resistance,
and they will definitely charge more for the medication itself. If you combine them, a one-month supply of 4 pens might be settled at around the 200,000 KRW level for the low dose.
Still, it would be good if it's cheaper than in Korea.
However, as more people flock there, clinics will likely keep raising prices. Pharmacies will too.
Because that's all margin,
and as long as they keep it cheaper than Korea, there will be demand.