Assume a steel mill which can sell its steel at a price of36/ton. Its cost function isC(x) = 3x2. Unfortunately, producing one ton of steelxleads to the contamination of two unitsaof water in a nearby river, i.e.x = 2a.

The river is also home to a trout farm. The trout farm can sell its catchFat a pricepFof28/ton and is subject to a cost functionC(F) = F2+ 2aF.

1. a)Please determine the market equilibrium in case the steel mill does not consider its external effect onto the trout farm! Kindly calculate the amount of steel produced x*, the amount of trout farmed F*, and the profit of the steel mill and the trout farm, respectively!
2. b)Assume that the steel mill and the trout farm have merged. Again, please determine the amount of steel produced xnand the amount of trout farmed Fn, and the profit of the new company, respectively!
3. c)Please explain how the result obtained at b) could have been achieved by means of applying the Coase Theorem!
4. d)Could the optimal production also be achieved by means of a Pigouvian tax? If so, please determine the Pigouvian tax!