Question

Suppose that the demand function of a pharmaceutical firm is p = 20 – 0.5x, where p is the price of a prescription drug and x is the number of prescription drugs demanded by patients. For simplicity, assume that the pharmaceutical firm can produce an extra pill at a constant cost, and hence the marginal cost function is

MC = 4.

a. Compute the optimal price and quantity for the pharmaceutical firm if the firm receives patent protection from the government. (2pt)

b. Assuming that generic competition will drive down the price to marginal cost, compute the quantity of this product demanded when the patent expires. (2pt)

c. Based on your answer, calculate the welfare loss that the patent system imposes on this product. (2pt)

Answer 1

The patent system here facilitates the creation of monopoly

a. In presence of patent, profit maximization would be that of a monopolist

Hence, the firm would first equate MC = MR

Here, p = 20-x/2

Total Revenue = TR = p*x = 20x - x²/2

Marginal Revenue = MR = d(TR)/dx = 20 - x

MC = 4(given)

Equating MC and MR,

20-x = 4, implies x = 16, substituting this quantity into the demand curve

p = 20 - 16/2 = 12

Hence, optimal price = 12, optimal quantity = 16

b. When patent expires, firm will maximize profits in a competitive market

Hence, P = MC will be the profit max condition

20- x/2 = 4

x = 32, and p = MC = 4

So, Optimal price = 4, optimal quantity = 32

c. Welfare loss from patent system = reduction in total surplus due to patent

Total Surplus = Consumer Surplus + Producer Surplus

Since, monopoly charges a higher price, less people can afford that product which reduces the quantity traded. This reduction in trade results in a welfare loss to both consumers and producers.

The green area denotes dead weight loss due to monopoly which is equivalent to the welfare loss

As clear from the diagram, it is the area of triangle, whose base is the difference between competitive quantity and monopoly quantity, and height is the difference between the corresponding prices,

Area of traingle = 1/2*b*h = 1/2*(32-16)*(12-4)

= 1/2*16*8 = 64

Therefore, welfare loss due to patent = $64