Hey, I've been partially doing this for me, however I didn't write all the prices down while upgrading my mine. We could collect the upgrade costs here from people with mines at different stages. When there's a comprehensive list I will be happy to make the calculations and post them here.  .

Btw, if you want to optimize upgrading your mine, consider the following examples:

What I did was that I calculated which upgrade would give me the most additional gold for the lowest price.

If you e.g. add a worker it is generally more expensive than a pickaxe but a pickaxe will give you only 0.02  gold per worker and  gold ore.

So for every pickaxe you buy you get "number of workers x number of gold ores x 0.02" more gold. For every worker you add you get "1 x number of gold ores x (1+ number of pickaxes x 0.02)" more gold.

Divide the cost for the upgrade by the additional gold it will give you and you can easily decide which delta gold is the cheapest and thus fastest upgrade.

I hope this can help you in the meantime.