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Consolidated Salt Company sells table salt to both retail grocery chains and commercial users (e.g., bakeries, snack food makers, etc.). The demand function for each of these markets is:

Retail grocery chains: P1 = 180 - 8Q1
Commercial users: P2 = 100 - 4Q2

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 salt is:
TC = 20(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 Summary

The total profit and price charges are examined.

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a) total profit = total revenue from market 1 + total revenue from market 2 - total cost

total profit = (180 - 8Q1)Q1 + (100 - 4Q2)Q2 - 20(Q1 + Q2)

rearrange to make it look nicer

total profit = -4Q2^2 + 80Q2 - 8Q1^2 + 160Q1

b) First you should note that the marginal cost of producing each good is 20. (This is obtained by taking ...

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