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Maximizing Profit with/without Price Discrimination

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Consolidated Sugar company sells granulated sugar to both retail grocery chains and commercial users (e.g., bakeries, candy makers, etc.). The demand function for each of these markets is:
Retail grocery chains: P1 = 90 - 4q1
Commercial users: P2 = 50 - 2q2
where P1 and P2 are the prices charged and q1 and q2 are the quantities sold in the respective markets. Consolidated's total cost function (which includes a "normal" return to the owners) for granulated sugar is
TC = 25 + 10(q1 + q2 )

(a) Determine Consolidated's total profit function.

(b) Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Consolidated's total profit under this condition?

(c) Assuming that Consolidated is required to charge the same price in each market, what are the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?

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Solution describes the steps in calculating profit maximizing output in case of price discrimination as well as in the case of without price discrimination.

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Solution:

(a) Determine Consolidated's total profit function.

Total Revenue from retail grocery chain (TR1)= P1*q1
P1 = 90-4q1
TR1=P1*q1=(90-4q1)*q1=90q1-4q12

Total Revenue from commercial users (TR2)= P2*q2
P2 = 50-2q2
TR2=P2*q2=(50-2q2)*q2=50q2-2q22

Total revenue from both markets TR = TR1+ TR2
=90q1-4q12 +50q2-2q22

TC= 25+10(q1+q2)

Consolidated Profit ( ) = TR-TC = 90q1-4q12 +50q2-2q22 -25-10(q1+q2)
...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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