Question

A drug company produces a new drug to treat baldness. The inverse demand curve for the drug is P = 205 – 20Q, where Q measures the number of pills in millions. The various costs of production are given by TC = 100 + 5Q, ATC = 5 + 100/Q, and MC = 5. If the government grants this firm a patent, it will earn profits of _____. If the government revokes the patent and the firm must sell its drug at marginal cost because of competition, it will earn profits of _____.

Answer 1

a) 400 million

b) loss of 100 million

Step-by-step explanation:

Given:

The inverse demand curve for the drug is P = 205 – 20Q

Here,

various costs of production , TC = 100 + 5Q

ATC =
`5 + (100)/(Q)`

Q = Number of pills in millions

MC = 5

Now,

If the government grants the firm a patent, it became a monopoly firm

And,

For monopolist, profit maximization occurs at MR = MC

Thus,

Total Revenue (TR) = P × Q = 205Q - 20Q²

MR =
`(d(TR)/(dQ)` = 205 - 20(2)Q

= 205 - 40Q

Also,

MC = 5

Therefore,

at MR = MC

or

⇒ 205 - 40Q = 5

⇒ 40Q = 200

or

⇒ Q = 5

Hence,

the profit maximizing quantity of monopolist is 5 units

and,

Profit = TR - TC

or

Profit = ( 205Q - 20Q² ) - ( 100 + 5Q )

at Q = 5

Profit = {205(5) - 20(5)²} - {100 + 5(5)}

or

Profit = 1025 - 500 - 100 - 25

or

Profit = 400 million

b) If the government revokes the patent and the firm must sell its drug at a point where Price equals marginal cost

Thus,

MR =
`(d(TR)/(dQ)` = 205 - 20(2)Q = MC

or

205 - 20Q = 5

Q = 10

Now,

Profit = TR - TC

or

Profit = (205Q - 20Q²) - (100 + 5Q)

at Q = 10

Profit = [205(10) - 20(10)²] - [100 + 5(10)]

or

Profit =2050 - 2000 - 100 - 50

or Profit = - 100

Here, negative sign depicts the loss

Hence, loss of 100 million