You are in charge of study the tobacco industry and its effects on the society well-being. To tackle that the team of environmental economist (you included, of course) decided to approach this with the theory of externalities (Recall, tobacco is a good that provokes a negative externality in the society) and divide the project in 2 steps:
Step 1.- First step is to find the market equilibrium of the industry so a competitive equilibrium is found using the following functions:
Demand = Marginal Private Benefit (MPB) = 60 - 0.25Q
Supply = Marginal Private Cost = -3 + 0.2Q
Step 2: Trough the team research and literature you have found that the negative externality of smoking to the society accounts for 5% of the total amount (quantity) of cigarettes in the market (Marginal External Cost (MEC) = 0.05Q)
At competitive equilibrium Marginal Private Benefit (MPB) = Marginal Private Cost (MPC) or Supply = Demand
1.- Find the competitive equilibrium Quantity and Price
At efficient equilibrium Marginal Social Benefit (MSB) = Marginal Social Cost (MSC)
2.- Find the efficient equilibrium
Recall (+MPC), we are assuming the Marginal External Benefits are nonexistent ()
3.- Contrast the state of the Industry on both cases. For example Including externalities does the supply increases or decreases? does prices go Up or down? please be specific