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9. The Zinger Company manufactures and sells a line of sewing machines. Demand per period (Q) for a particular model is given by the following relationship:
Q = 400 - .5P
where P is price. Total costs (including a "normal" return to the owners) of producing Q units per period are:
TC = 20,000 + 50Q + 3Q2
(a) Express total profits () in terms of Q. This should be an equation.
(b) At what level of output are total profits maximized? What price will be charged? What are total profits at this output level?

10. 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 = 50 + 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?

11. Two Grocery Stores serve a defined market provided market research, the two firms have determined that their profit potential is served by either developing a product mix directed at one of three possibilities. The first is the general grocery products that are discounted and attempt for volume. The second is to sell high end meats and produce. The third is to feature organic products.

The following matrix depicts the payoffs to these two stores, when they develop different combination of appeals toward different customer bases. This is an oligopoly market with full information.

Firm 2
High Volume High End Meats and Produce Organic

High Volume  = 0 = 0  = 1 = 2  = 2 = 1
Firm 1
High End Meats and Produce  = 4 = 2  = 2 = 3  = 4 = 2

Organic  = 5 = 1  = 3 = 2  = 3 = 0

a. Given the attached matrix, which choice would each Firm make?

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