The production of batteries for eBikes is polluting and causes a negative externality

whose marginal costs are estimated at 2q. The inverse demand function and the

supply function for the monopolist who produces these batteries is, respectively, p = 3 - q

and p = 2q

By imposing a tax on the production of batteries, the government wants to ensure that

the social optimum is reached. The government defines it

social optimum as that equilibrium outcome in which, given the market structure,

the externality is completely internalized. However, she has doubts between a specific

tax and an ad valorem tax.

Calculate both (the specific tax and the ad valorem tax) where

the monopolist produces a quantity corresponding to it

social optimum as defined by the government. Submit your

answers clearly.