No, the costs of the expansion are independent from which resource you use. So the first expansion can be bought with either 2 Axes, 2 Mead, 2 Horns, or 2 Wool. The second one can be bought with either 7 Axes, 2 Mead, 2 Horns, or 2 Wool. Third one can be bought with 15 Axes, 2 Mead, 2 Horns, or 2 Wool. Fourth one can be bought with either 27 Axes, 7 Mead, 2 Horns, or 2 Wool. Etc.
So the costs are predefined, and while you can choose which goods type you use to buy the expansion, that doesn't influence how the cost increases (always using 'Mead' doesn't mean the Mead cost will keep increasing and the rest stay the same).