Problem
A chemical factory and a mineral water factory operate next to each other by a river. Both products are sold in a perfectly competitive market. Since the chemical factory issues a chemical material into the river, the higher its output is, the more costly it is to produce mineral water. Thus, the profit of the chemical factory is (100 - 2C)*C. and the profit of the mineral water factory is (200 - M -0.8C-)*M where C stands for the output of the chemical factory, and M stands for the output of the mineral water factory.
1. If firms decide independently on their output, how much does the chemical factory produce?
2. How much does the mineral water factory produce?
3. Assume that the chemical factory is obliged to pay the extra cost for the mineral water factory that its own output imposes on the mineral water company. How much does the mineral water company produce now?
4. How much does the chemical factory produce?
5. If the two companies are bought by the same owner who therefore wants to maximize the joint profit of the two companies, how much will the chemical factory produce?
6. How much does the mineral water company produce in this case?