Question

A small biotech company develops a new treatment for a rare disease. The new treatment is patented and the company is the sole monopolist in its market. The company can sell the treatment to private pharmacies and public hospitals. Pharmacies’ demand for the treatment is QPD = 84 – 0.4PP while public hospitals’ demand for the treatment is QHD = 116 – 0.6PH. The marginal cost of the new treatment is MC = 20 +2Q.

The legislature passes a new Health Costs Relief Act (HCRA) that allows biotech companies to price discriminate.

a) Once the law is enacted, does the biotech company charge the same price to pharmacies and to hospitals? Why?

b) How many doses does the company sell to hospitals? How many does it sell to pharmacies?

c) What price do hospitals pay for a dose of the new treatment? What price do pharmacies pay for a dose of the new treatment?

d) Who gains and who looses from the enactment of the HCRA?

Answer 1

a) Once the law is enacted, the biotech company will charge much more from the pharmacies than the public hospital owing to its hihger monopoly power with the pharmacies. The same has been worked out below.

b)

Pharmacies’ demand for the treatment is QPD = 84 – 0.4PP

Public hospitals’ demand for the treatment is QHD = 116 – 0.6PH

marginal cost of the new treatment is MC = 20 +2Q.

Revenue= Price x Demand

R= P x Q

Pharmacies:

R = P x Q = (84-Q) x Q/0.4

0.4 R= 84Q-Q²

Marginal Revenue, MR = dR/dQ = (84-2Q)/0.4

MR = MC

(84-2Q)/0.4 = 20 + 2Q

5(84-2Q) = 2(20+2Q)

420-10Q=40+4Q

14Q= 380

Q= 27.14

Thus, doses sold to pharmacies = 27.14

Public hospitals:

R = P x Q = (116-Q) x Q/0.6

0.6 R= 116Q-Q²

Marginal Revenue, MR = dR/dQ = (116-2Q)/0.6

MR = MC

(116-2Q)/0.6 = 20 + 2Q

10(116-2Q) = 6(20+2Q)

1160-20Q=120+12Q

32Q= 1040

Q= 32.50

Thus, doses sold to public hospitals = 32.50

c)

Pharmacies:

P= (84-Q)/0.4

P= (84-27.14)/0.4 = 142.15

Price paid by pharmacies= 142.15

Public hospitals:

P= (116-Q)/0.6

P= (116-32.50)/0.6 = 139.17

Price paid by pharmacies= 139.17

d)

Monopoly power of the firm = (P=MC)/P

Pharmacies= (142.15-74.28)/142.15 = 0.48

Public hospitals= (139.17-85)/139.17 = 0.39

Thus, the monopoly power of firm defined by the coefficient µ is 0.48 in case of pharmacies and 0.39 in case of public hospitals. Thus, the company will be able to charge more from the pharmacies to increase its profit.

Pharmacies lose from the enactments of HCRA.