Reference no: EM133126228

Assume that a competitive firm sells it's output for a price of 16 dollars per unit and producing q units of output costs the firm 1/3 q3 dollars. The firm's production process pollutes a nearby river and total environmental damage caused is e = 3q - a where a is the amount of pollution abatement effort. The firm's cost of abating a units of pollution is 1/3a3.

(a) Find the firm's profit maximizing output quantity and the resulting amount of environmental damage in the absence of any regulation.

(b) If the firm must pay a tax of $7 per unit of output produced, find the new profit maximizing output quantity and amount of environmental damage.

(c) Assume there is public backlash to the tax on output, so the government needs to determine what subsidy per-unit of abatement effort would replace the tax and yield the same environmental damage. What subsidy on abatement effort should the government set?

(tip: First find the firm's profit maximizing choices of q and a as a func- tion of some unknown subsidy s per unit of abatement. Then combine with the environmental damage function to find s.)