Adrug 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

a) 400 million

b) loss of 100 million

Explanation:

Given:

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

Here,

various costs of production , TC = 100 + 5Q

ATC =

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 = = 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 = = 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

there's 11 people for the 1st position. then, no matter who gets it, there's only 10 left for the second, and then 9 left for the third. 11 x 10 x 9 = 990.   the answer is there are 990 different ways the positions can be filled by these applicants