The Market Supply and Demand Functions for a Good Traded

Essay

The market supply and demand functions for a good traded on a perfectly competitive market are:
Qd = 50 - 0.5P and Qs = 10 + 1.5P
(i) What is the equilibrium price and quantity on this market?
(ii) If the production of each unit of this good gives rise to a social cost of $4, what is the socially optimal equilibrium quantity and price? Assume that producers pay a tax of $4 per unit.
(iii) If the production of each unit of this good gives rise to a social benefit of $8, what is the socially optimal equilibrium quantity and price? Assume that producers receive a subsidy of $8 per unit.