1. Firms and markets (25 points).PharmaCorp has a patent on Medicine, making it the only seller the drug. The more Medicine the monopoly wants to sell, the less it can charge its customers. The demand for Medicine is given by the equation WTP = $90 - $10Q. Meanwhile, PharmaCorp's costs are described the equation TC = $50 + $10Q, where it costs $50 to invent Medicine and $10 to produce each dose. The monopolist's costs are shown below as well as its Total Revenue, Marginal Revenue, and Profit, assuming it charges all customers the same rate.

Q	TC	AC	MC	WTP	TR	MR	Profit
0	$50				$0
1	$60	$60.00	$10	$80	$80	$80	$20
2	$70	$35.00	$10	$70	$140	$60	$70
3	$80	$26.67	$10	$60	$180	$40	$100
4	$90	$22.50	$10	$50	$200	$20	$110
5	$100	$20.00	$10	$40	$200	$0	$100
6	$110	$18.33	$10	$30	$180	-$20	$70
7	$120	$17.14	$10	$20	$140	-$40	$20
8	$130	$16.25	$10	$10	$80	-$60	-$50

a. (5 pts) The equations above for WTP and TCcan be used to calculate the AC, MC, TR, MR, or Profit as a function of Q. Provide equations for 2 out of 5 of these terms. (Note: your equations should produce the same values for Q= 1, 2, ..., 8 as shown in the above table.)

b. (5 pts.) Using what you know about PharmaCorp, what quantity of Medicine will it produce and at what price will it sell? Explain your answer.

c. (5 pts.) Is the equilibrium price and quantity you found in (b) efficient? Why or why not?

d. (5 pts.) What is the consumer surplus at the equilibrium you identified in (b)?

e. (5 pts.) Suppose that the patent for Medicine was made freely available to all pharmaceutical companies, so that each company's costs would be given by the equation TC = 10Q. In a perfectly competitive market, what would be the new equilibrium price and quantity? What is the consumer surplus in perfect competition? Would consumers be better off if they had to purchase the patent from PharmaCorp for $50?