A cement factory and a hotel are situated next to each another. The cement factory’s demand is described by the inverse demand function: PCement = 200 – C. The factory’s cost function is CCement =...

A cement factory and a hotel are situated next to each another. The cement factory’s demand is described by the inverse demand function: PCement = 200 – C. The factory’s cost function is CCement = 2C2. The inverse demand function for the hotel is given by: PHotel = 100 – H – 2C (in essence, as the factory produces more cement C, the hotel’s demand goes down because of the pollution the factory generates). The hotel’s cost function is: CHotel = ½ H2.

Suppose a good-natured “social planner” wants to impose a Pigouvian tax on the cement factory. Find the equilibrium tax rate T* that would allow achieving the socially optimal outcome