Chapter problems EC6150 LP5.docx - Chapter problems 3 The...

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Chapter problems 3. The Bramwell Corporation has estimated its demand function and total cost function to be as follows: Q = 25 – 0.05P TC = 700 + 200Q Answer the following questions either by developing demand and cost schedules (hint: Use quantities from 1 to 14) or by solving the equations a. What will be the price and quantity if Bramwell wants to 1. Maximize profits? Q = 7.5 P = 350 2. Maximize revenue? Q = 12.105 P = 250 3. Maximize revenue but require the profit to be a minimum of $300? With Q at 7.5 the profit is $425 (500(7.5)-20(7.5)^-700-20(7.5)) = 3750-1125- 700+1500 = 425 b. Now assume the cost function is TC = 780 + 200Q while the demand function remains the same, What will the price and quantity be if Bramwell wants to 1. Maximize profits? Q = 7.5 P = 350 2. Maximize revenue? Q = 11.65 P = 267
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Chapter problems 3. Maximize revenue but require the profit to be a minimum of $300? 500(7.5)-20(7.5)^-780-20(7.5) = 3750-1125-780+1500 = $345 c. Why are the answers the same in a(1) and b(1) but different in a(3) and b(3)? The reason that they are the same in a1 and b1 is because the MR and MC are the same. The reason that a3 and b3 are different is because the AC was different in both. 8. The Prestige Office Equipment Company produces and sells different types of office  furniture. One of the important items it sells is a high-quality desk. During the past year,  Prestige sold 5,000 of these at a price of $500 each. The contribution profit for this line of furniture last year was $700,000. A consultant suggests that Prestige decrease the price of each desk by $30. In his  opinion, another 500 desks could then be sold, and the total profit would be maintained.  A trade publication that employs an economist has estimated price elasticity of office  furniture (including desks) to be about  1.8.  Assume the variable unit cost per desk in the coming year will remain the same.  Evaluate the consultant’s proposal. Be sure to include in your answer the price elasticity  assumed by the consultant, as well as the published elasticity estimate.  Looking at the information provided and calculating the numbers, it would be in the best  interest of Prestige not to take advice from either the consultant or the economist as both  will lead to losses.
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