Question

Suppose a monopolist practices price discrimination in selling his product, charging different prices in two separate markets. In the market A the demand function is P_A = 100-q_A and in B it is P_B = 84-q_B, where q_A and q_B are the quantities sold per week of A and B, P_A and P_B  are the respective prices per unit . If the cost function of the monopolist is c = 600 + 4 (q_A + q_B)

A.How much should be sold in each market to maximize the benefit?

B. What selling prices give the maximum benefit? Find the maximum benefit.

Answer 1

A)

PA = 100 -Q

TR = 100Q - Q ^2

On differentiating TR

MR = 100 - 2Q

TC = 600 +4(QA+QB)

On differentiating TC

MC = 4

Equilibrium MR=MC

100 -2Q =4

96 = 2Q

Q = 96/2

= 48

Profit maximizing Q for market A = 48

Market B:

PB = 84-Q

TR = 84Q - Q^2

MR = 84 - 2Q

MR = MC

84 - 2Q = 4

Q = 40

Profit maximizing Q of B = 40

B)

Selling Price of Market A = 84 - 48

=$52

Selling Price of Market B = 84 - 40

= $ 44

Profit = TR - TC ( TC = 600 +4(QA+QB)

=48*52 +44*40 - 600 - 4*88

=2496+1766 - 600 -352

=$3310