Where to build markets - only in fertile lands?

[Agent Miles]

Hypothetically, if you have +5 food in 10 provinces from the example:

Make RE (Rice Exchanges) in the top 5 income provinces that have a tax boost from a Metsuke:
(The actual tax rate with Metsuke varies, but I've used 50% with the Metsuke and 25% without to keep the math simple. I also know this to be an attainable rate from experience.)

Each single RE costs 1600 koku
This adds +300 per turn at 50% Metsuke tax rate = 150 per turn
1600/150 per turn = 10.67 or 11 turns
150/turn x 11 turns = 1650
It takes 5 turns to build the RE and an additional 11 turns for a ROI of 50 at one RE.

50 x 5 RE provinces with Metsuke = 250 total ROI after 16 turns.

Unfortunately, for the 16 turns you lose +5 growth for 10 provinces.
5 in ten provinces = 50 per turn lost growth
So after 16 turns, that's 800 total lost growth.
Breaking this down:
400 total lost growth for the 5 Metsuke provinces at a tax rate of 50% = 200 lost income
400 total lost growth for the other 5 provinces at a tax rate of 25% = 100 lost income
So, 300 total lost income after 16 turns.

250 (total ROI) - 300 (total lost income) = -50 net loss after 16 turns.

However, you would continue to make (5 x 150 = 750/turn) total RE income from the 5 provinces with Metsuke.
You would now also get +5 growth from the RE over the Market in each of the 5 Metsuke provinces. The +5 replaces the lost +5 growth.
(-5 x 25% = -1.25 at each 5 remaining provinces) = -6.25 rounded down to 6 continuing lost income

750 (total RE income) - 6 (continuing lost income) = 744 koku/turn added income

Thus, you get (744-50 = 694) koku profit after 17 turns and 744 koku profit every turn thereafter. Further, if you conquered the whole map, you would continue to make a profit.
So, build Rice Exchanges as described.

P.S. Here's the argument presented in the extreme cases.

A. 10 provinces with a Stronghold, Land Consolidation, and a Market
or
B. 10 provinces with a Stronghold, Land Consolidation, and a Merchant Guild

With A, you get +20 Food and each province gets +5 growth from the Market for +25 overall growth.

With B, you get zero Food and each province gets +20 growth from the Merchant Guild for +20 growth overall. However, you also get an extra +800 commerce.

At a delta of +5 growth, the total wealth in A would catch up to B after (800/5 = 160 turns). Of course, the wealth in B would have been generating much more in taxes from the additional commerce for those turns. Let's start at A and spend 5,000 koku and 11 turns for the Rice Exchange and Merchant Guild to build up each province to B. Even at 10% tax, that would then get us 80 x 149 remaining turns = 11,920 koku per province. So 11920-5000 for the build up still gives 6920 profit. At the same tax rate, A would need over a hundred turns to earn this sum through the continued difference in growth and would thus seldom ever catch up before the end of the game.