You are a very powerful lobbyist and have convinced your client that you can make them the only legal extractor of coal in the United States and simultaneously make coal imports illegal. In essence, your client can become the coal monopoly. Currently, before the policy change, the supply and demand curves for coal are as follows:
Demand Curve: Qd = 70 − 1/2P
Supply Curve: Qs = 3/4P
Where Q is in tens of thousands of short tons and P is in dollars. Show all steps used to obtain answers.
1: What is the equilibrium price and quantity in a free market?
2: Present the supply and demand curves in the form P = f(Q) instead of the form provided Q = f(P).
3: Solve for the monopoly’s marginal revenue curve.
4: Once the coal monopoly has been implemented, what is the new equilibrium price and quantity?
(Hint, set marginal revenue curve equal to the marginal cost curve (i.e. supply curve) and solve.)
5: Using the “P, Q” graph show the supply curve, demand curve, monopolist’s marginal revenue, and P and Q observed in the market for both a free market and monopoly.