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Maximizing Net Revenues

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The rule for maximizing net revenue (total revenue minus total cost) is: Take any action if, but only if, the expected marginal revenue exceeds the expected marginal cost. What is marginal revenue? How is it related to demand? You can test your grasp of this key concept by examining the case of Maureen Supplize, who runs a yacht dealership. She has five potential customers, and she knows how much each would be willing to pay for one of her yachts.

See the attachment for the full problem and related tables.

(a) Fill in the blanks in the second column to complete the demand schedule implied by these data.
(b) Fill in the blanks in the third column to show Maureen s total receipts from yacht sales at the various prices listed.
(c) Fill in the blanks in the fourth column to show the extra revenue obtained by Maureen from each additional yacht she manages to sell when she lowers her selling price.
(d) How many yachts will she want to sell if her goal is to maximize total revenue? (Don't start thinking yet about selling to different people at different prices. We'll take that up later. Assume for now that she can't get away with charging one buyer more than another.) What price will she want to set?
(e) Now assume that her goal is to maximize net revenue and that the marginal cost to her of selling a yacht is $6 million. In other words, each additional yacht she sells adds $6 million to her total costs. How many yachts will she now want to sell? What price will she want to set?
(f) If you have proceeded correctly, you should now be able to experience something of Maureen's frustration. Ewing and Penney are both willing to pay more for a yacht than it costs Maureen to sell one to them. Yet she can't sell to either without reducing her net revenue. Why?
(g) Suppose now that none of her customers is acquainted with any of the others and that she can consequently get away with charging each one the maximum he is willing to pay. Under such an arrangement, which we shall call "perfect" price discrimination, what is Maureen's marginal-revenue schedule? Fill in the blanks in the fifth column.
(h) How many yachts will Maureen now want to sell?
(i) Fill in her total revenue schedule under "perfect" price discrimination.

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Solution Summary

This solution looks at maximizing net revenues with an applied problem (yacht sales). In addition it looks at the difference in maximizing net revenues with and without price discrimination.

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Excel Solver Product Mix Maximizes Revenues

Stanley Furniture produces two types of china cabinets, First Provincial (FP) and Deluxe Modern (DM). Each cabinet goes through 3 departments: carpentry, painting and finishing. The following table contains relevant information on production times per cabinet produced, daily production capacities for each department and net revenue per cabinet produced. Woodstock has a contract with its distributor to supply at least 60 units of each type of cabinet per day. The company would like to determine a product mix to maximize daily net revenue.

Department

Carpentry Painting Finishing Net Revenue
hrs/cabinet hrs./cabinet hrs./cabinet $'s /cabinet
Cabinet type
FP 3 1.5 0.75 28
DM 2 1 0.75 25
Dept. capacity (hrs.) 360 200 125

Using Excel and the Excel Solver:

(a) What product mix maximizes daily net revenue, and what is daily net revenue?

(b) Stanley Furniture can purchase 30 additional hours of carpentry time for $20 per hour. Should the company purchase the additional time? Explain.

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