Question

Question 5 Consider a firm that is a monopolist and sells in two distinct markets. The demand curves in the two markets are: P1 = 160 -8Q1 P2 = 80-2Q2 The marginal cost curves is 5+ Q where Q is the firms entire output destined for either market. What pricing policy would you suggest? How many units of output should it sell in each market?

Answer 1

Answer: market one:

P1 = 160-8Q1

Output/ quantity = Q

TR = Price * quantity

     = (160 – 8Q1 )* Q

TR = 160Q – 8Q^2

We will find MR by 1^st order derivation of TR

MR = 160- 16Q

Equilibrium condition is : MR = MC

MC = 5 + Q

160 – 16Q = 5 + Q

-16Q – Q = 5 – 160

-17 Q = - 155

Q = - 155 / -17

Q = 9.12

P1 = 160 – 8Q

       = 160 – 8 * 9.12

   P = 87.04

So , price is 87.04 in market 1 and monopolist will sell 9.12 units of output there      

Market 2:

P2 = 80 – 2Q2

Quantity = Q

TR = (80 – 2Q ) * Q

TR = 80Q – 2Q^2

MR will be 1^st order differentiation of TR

MR = 80 – 4Q

Equilibrium is MR = MC

80 – 4Q = 5 + Q

80 -5 = Q + 4Q

5Q = 75

Q = 75 / 5

Q = 15

P2 = 80 – 2Q­2

      = 80 – 2 (15)

      = 80 – 30

P = 50

So, price will be 50 in market 2 and the output sell at this price will be 12 units