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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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    https://brainmass.com/economics/pricing-output-decisions/maximizing-profit-with-without-price-discrimination-215508

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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 Summary

    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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