What would a leveled-up City cost?
We can get a fairly good indication using multiple non-linear regression.
This technique looks at the attributes and costs of other Dominion cards and develops a formula for their worth.
I won't go into a lot of detail on the technique since it's rather involved and you can read about it online.
Let cards = extra cards drawn by playing a card.
Let actions = actions gained by playing a card.
Let buys = plus buys gained by playing a card.
Let coins = treasure gained by playing a card.
The formula I modeled is cost = a * cards + b * actions + c * coins + d * buys + e * cards^2 + f * actions^2 + g * coins^2 +
h * buys^2 + i, where the coefficients a, b, c, d, e, f, h, and i are determined by least-squared error fit of the input data
against known card costs.
The difficult part is determining the base set of cards to generate the model.
We can only use "plain vanilla" cards that only grant +cards, +actions, +buys, or +coins and do not have any other side
effects that would skew the cost.
I used Smithy, Festival, Worker's Village, Bazaar, Village, Laboratory, Market, and Woodcutter.
I also included Grand Market, ignoring the cost restriction against copper.
And to better guage the worth of +coins, I added the treasure cards Copper, Silver, Gold, and Platinum.
To put these cards on an equal footing with the action cards, I had to indicate that they gave plus one action.
That seemed reasonable since they do not use up an action to play them.
Crunching the numbers then yielded the above formula:
cost = 3.69 * cards + 0.88 * actions + 2.04 * coins + 0 * buys - 0.52 * cards^2 + 0.076 * actions^2 + 0.0074 * coins^2 + 0.7
* buys^2 -2.08
Here's the kingdom cards with their actual costs and modeled costs.
Copper 0 0.92
Silver 3 2.98
Gold 6 5.06
Platinum 9 9.25
Smithy 4 4.28
Festival 5 4.79
Worker's Village 4 3.85
Bazaar 5 5.20
Village 3 3.15
Laboratory 5 4.16
Market 5 4.79
Woodcutter 3 2.72
Grand Market 6 6.85
As you can see, the predicated worth is close to the actual costs.
Using the formula on the three levels of the City card yield:
City 1 5 3.37
City 2 ? 7.06
City 3 ? 9.09
So the analysis would suggest that prices of 7 coins and 9 coins are appropriate.