Question

Suppose a stream is discovered whose water has remarkable healing powers. You decide to bottle the liquid and sell it. The market demand curve is linear and is given as follows:

P = 30 - Q
The marginal cost to produce this new drink is $3.


12. What price would this new drink sell for if it sold in a competitive market?

    A) 0
    B) $3
    C) $13.50 D) $16.50

13. What will be the price of this new drink in the long run if the firms in the industry collude with one another to maximize joint profit?
    A) 0
    B) $3

    C) $13.50

    D) $16.50

14. What will be the price of this new drink in the long run if the industry is a Cournot duopoly?

    A) $3
    B) $9
    C) $12 D) $13.50

15. What will be the price of this new drink in the long run if the industry is a Bertrand duopoly? A) $3 B) $9 C) $12 D) $13.50

Answer 1

Answer : 1) The answer is option B.

In competitive market at equilibrium P = MC.

=> 30 - Q = 3

=> 30 - 3 = Q

=> Q = 27

Now, P = 30 - 27 = $3. Therefore, option B is correct.

2) The answer is option D.
In collude the firm act like a monopolist.

Given, P = 30 - Q

TR (Total Revenue) = P * Q = (30 - Q) * Q

=> TR = 30Q - Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 30 - 2Q

At equilibrium in collude, MR = MC

=> 30 - 2Q = 3

=> 30 - 3 = 2Q

=> 27 = 2Q

=> Q = 27 / 2

=> Q = 13.5

Now, P = 30 - 13.5 = $16.5 . Therefore, option D is correct.

3) The answer is option C.

In Cournot duopoly Q = Q1 + Q2.

So, P = 30 - (Q1 + Q2)

=> P = 30 - Q1 - Q2

TR1 = P * Q1 = (30 - Q1 - Q2) * Q1

=> TR1 = 30Q1 - Q1^2 - Q1Q2

MR1 = TR1 / Q1

=> MR1 = 30 - 2Q1 - Q2

TR2 = P * Q2 = (30 - Q1 - Q2) * Q2

=> TR2 = 30Q2 - Q1Q2 - Q2^2

MR2 = TR2 / Q2

=> MR2 = 30 - Q1 - 2Q2

At equilibrium for first firm, MR1 = MC

=> 30 - 2Q1 - Q2 = 3

=> 30 - 3 - Q2 = 2Q1

=> 27 - Q2 = 2Q1

=> Q1 = (27 - Q2) / 2

=> Q1 = 13.5 - 0.5Q2

At equilibrium for second firm, MR2 = MC

=> 30 - Q1 - 2Q2 = 3

=> 30 - 3 - Q1 = 2Q2

=> 27 - Q1 = 2Q2

=> Q2 = (27 - Q1) / 2

=> Q2 = 13.5 - 0.5Q1

Now by putting the value of  Q1 in Q2, we get,

Q2 = 13.5 - 0.5 (13.5 - 0.5Q2)

=> Q2 = 13.5 - 6.75 + 0.25Q2

=> Q2 - 0.25Q2 = 6.75

=> 0.75Q2 = 6.75

=> Q2 = 6.75 / 0.75

=> Q2 = 9

From Q1 equation we get,

Q1 = 13.5 - 0.5Q2

=> Q1 = 13.5 - (0.5 * 9)

=> Q1 = 9

Now, Q = Q1 + Q2 = 9 + 9

=> Q = 18

P = 30 - 18

=> P = $12
Therefore, option C is correct.

4) The answer is option A.

In case of Bertrand duopoly for all firms at equilibrium, P (Price) = MC (Marginal Cost). As here MC = $3 hence P = $3. Therefore, option A is correct.