Question

2. Suppose that there is a drug that was shown to be effective at treating the novel coronavirus. Only two firms can produce this drug. The (inverse) demand function for the drug is given by P = 200 − 2Q where Q is the quantity of the drug available in the market and P is the market price. Firm 1 produces the drug with a constant marginal cost of 8 USD (total costs are equal to 8Q for firm 1) while firm 2 produces the drug with a constant marginal cost of 10 USD (total costs are equal to 10Q for firm 2).

a) Define the best response functions of each firm.

b) Find the equilibrium quantities of each firm and find the market price at the equilibrium.

c) Now assume a third firm has figured out how to produce the drug. What do you think will happen to equilibrium quantity and price (answer verbally)?

Answer 1

P = 200 - 2Q1 - 2Q2 [as Q = Q1 + Q2]

(a)

For firm 1,

TR1 = P x Q1 = 200Q1 - 2Q12 - 2Q1Q2

MR1 = TR1/Q1 = 200 - 4Q1 - 2Q2

Setting MR1 = MC1,

200 - 4Q1 - 2Q2 = 8

4Q1 + 2Q2 = 192

2Q1 + Q2 = 96............(1) [best response, firm 1]

For firm 2,

TR2 = P x Q2 = 200Q2 - 2Q1Q2 - 2Q22

MR2 = TR2/Q2 = 200 - 2Q1 - 4Q2

Setting MR2 = MC2,

200 - 2Q1 - 4Q2 = 10

2Q1 + 4Q2 = 190

Q1 + 2Q2 = 95............(2) [best response, firm 2]

(b)

Multiplying (2) by 2,

2Q1 + 4Q2 = 190........(3)

2Q1 + Q2 = 96..........(1)

(3) - (1) yields: 3Q2 = 94

Q2 = 31.33

Q1 = 95 - 2Q2 [from (2)] = 95 - (2 x 31.33) = 95 - 62.66 = 32.34

Q = 32.34 + 31.33 = 63.67

P = 200 - (2 x 73.67) = 200 - 127.34 = 72.66

(c)

The higher the number of firms, the higher the market output and the lower the market price. So if a third firm joins, price will be less than 72.66 and quantity will be higher than 63.67.