Auto-translated
to Eraser and Kor
Yeah... it's an important question. If you calculate it, building a Prefecture costs money that pays for itself in 5 days.
(Investment - 2500. Each day, starting from the second, brings in an extra 500 gold. In total, 6*500=3000)
But it's also important that, starting from the second week, you'll receive 500 gold more each day, i.e., you'll be able to buy twice as much army as without the Prefecture.