Question

Suppose that the pharmaceutical rm Merck is deciding whether to develop a new diagnostic procedure that can detect early-stage Alzheimer's disease more accurately than existing tests. Developing this technology would require an up-front fixed cost FC > 0. If Merck develops the technology, it can screen Q patients for Alzheimer's at the variable cost VC(Q) = 20Q. Merck estimates that market demand for the procedure would be p(Q) = 80 - (1/10)Q

a. Suppose that other companies can quickly copy Merck's procedure as soon as it is developed so that the market for medical tests will become perfectly competitive. If Merck develops the procedure, what are the equilibrium price pc and quantity Qc? If FC = 5000, will Merck develop the procedure? What about if FC = 10,000?

b. Now suppose that, if Merck develops the procedure, it will receive a patent that allows it to operate as a uniform-pricing monopolist. In this case, if Merck develops the procedure, how many patients will it screen (Qm), and what will it charge (pm)? If FC = 5000, will Merck develop the procedure? What about if FC = 10,000?

c. Now suppose that, if Merck develops the procedure, it is legally permitted (and able) to engage in perfect price discrimination. If Merck develops the procedure, what are its optimal quantity Qppd , revenue R(Qppd ), and variable costs VC(Qppd )? If FC = 5000, will Merck develop the procedure? What about if FC = 10,000?

d. Suppose that FC = 5000. Using your answers above, compute consumer surplus, producer surplus, and total surplus under each of the following policies:

i. No patent protecting Merck's innovation (as in part a).

ii. A patent letting Merck operate as a uniform-pricing monopolist (as in b).

iii. Legal permission for Merck to engage in perfect price discrimination (as in c).

(If Merck develops the procedure, make sure to subtract FC from the producer surplus.)

If we are trying to maximize total surplus, which of these policies is best? If we are instead trying to maximize consumer surplus, which policy is best?

Answer 1

Schedule representing revenues and cost :-

Quantity	AR	TR	MR	VC	TC	MC
100	70	7000	7000	2000	7000	2000
200	60	12000	5000	4000	9000	2000
300	50	15000	3000	6000	11000	2000
400	40	16000	1000	8000	13000	2000
500	30	15000	(1000)	10000	15000	2000
600	20	12000	(3000)	12000	17000	2000
700	10	7000	(5000)	14000	19000	2000
800	0	0	(7000)	16000	21000	2000

Answer a :-

In perfect competitive market the marginal cost curve intersects the marginal revenue curve at 350 units and the price charged is Dollar 20.

Answer b :-

In Monopoly market the marginal cost curve intersects the marginal revenue curve at 350 units therefore the quantity sold is 350 units while the demand curve that is the average revenue curve intersect the marginal cost curve at $45 therefore the price charged for 350 units is $45.

Answer c :-

Under perfect price discrimination the marginal cost curves intersect the average revenue curve at dollar 20 e at 600 units therefore 600 units are sold at dollar 20.

Answer d :-

Under perfect competition :-

Consumer surplus -((80-20)*350/2)=10500

Producer surplus = (20*350)-5000=2000

Total surplus = 10500+2000=12500

For monopoly :-

Consumer surplus = ((80-45)*350)/2)=6125

Producer surplus = (350*45)-5000=10750

Total surplus = 6125+10750=16875

Perfect price discrimination :-

Consumer surplus = 0

Producer surplus = (600*(80-20)/2)-5000=13000

1) For maximum total surplus monopoly is the best option .

2) For maximum consumer surplus perfect competitive market is the best option.