Economic 251 Problem Set 10
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ECO251 Problem Set 10
Maximizing Profit
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1. The table below shows the hourly output and cost structure for a small-town pizza shop. Calculate Marginal Revenue and Marginal Cost to determine the pizza shop’s profit-maximizing rate of output. Assume that the price of a pizza in this town is $10.
Hourly Output of Pizzas Total Hourly Cost ($)
0 5
1 9
2 11
3 12
4 14
5 18
6 24
7 32
8 42
9 54
10 68
2. Consider the business whose Total Cost and Total Revenue for various quantities of a particular product are shown in the table below.
Quantity
Total Cost
Total Revenue
0
100
0
1
250
500
2
350
950
3
500
1350
4
725
1700
5
1000
2000
6
1400
2250
Use the Profit-Maximizing Rule to explain the quantity that this business should produce to maximize its profits. To receive any credit, your answer must both state the number to produce and an explanation of how you used the profit-maximizing rule to arrive at that number.
3. Daniel Jones thought he was getting his girlfriend the best surprise Valentine’s Day gift ever. He bought two airline tickets for the couple to fly from their home in Cambridge, England to Belfast, Northern Ireland to see her favorite band, the Red Hot Chili Peppers. With over 80 million records sold worldwide, Red Hot Chili Peppers are one of the best-selling bands of all time. Jones’ girlfriend had always wanted to see the band perform live, and Jones thought nothing could be better than a romantic trip to see the band play live on Valentine’s Day. Jones managed to keep the concert tickets a surprise until they landed in Belfast – in their hotel room she opened the envelope in which he had placed the concert tickets for her favorite band. Jones was surprised when his girlfriend, rather than jumping for joy, simply turned to him with a puzzled look on her face. It was then that Jones looked more carefully at the tickets, to realize that he had purchased two seats for a performance by the Red Hot Chili Pipers, the self-proclaimed “most famous bagpipe band in the world.” Jones later admitted that he was surprised at what a good deal he’d gotten on the tickets.
Here is the question: Having spent the equivalent of a thousand dollars or so on the airline tickets, hotel room, and concert tickets, should the couple actually go to the Red Hot Chili Pipers concert? Use sound economic reasoning to explain your answer. In particular, identify the concept that is the basis for your answer; explain that concept in general; and then apply that concept to this particular situation.
4. The Lead Zeppelin Company produces powered and steerable lighter-than-air craft. The company’s airships are specially lined and are therefore safer than normal dirigibles. The table below shows the weekly production of dirigibles, along with the associated Average Cost and Total Revenue figures (the Average Cost and Total Revenue figures are actually in thousands of dollars, so the $15 represents $15,000, but we have left off the zeros to save space).
Quantity
Average Cost
Total Cost
Total Revenue
0
—
0
$0
1
$15
15
$10
2
$9
18
$20
3
$8
24
$30
4
$8.50
34
$40
5
$9
45
$50
6
$10
60
$60
7
$12
84
$70
The Lead Zeppelin Company has decided that it will produce at least 1 dirigible. Now the question becomes, How many more dirigibles should it produce to make as much profit as possible?
Use the profit-maximizing rule to explain how many dirigibles the Lead Zeppelin Company should produce to maximize its weekly profit. Your answer should include a statement of the profit-maximizing rule and the calculations that apply it. To receive any credit on this question, you must use the profit-maximizing rule. To receive full credit on this question, you must show all of your work in the calculations.
5. People who commit bank robberies must make the decision to rob banks. That decision comes with a built-in dilemma: every minute a robber stays in the bank increases the amount of money the robber will get, but every minute in the bank also increases the likelihood that the robber will get caught.
A study of more than 5000 bank robberies between 2005 and 2007 found that the average bank robbery lasted 4 minutes and 16 seconds and yielded about $20,000. The study also found that each additional minute that robbers spent in the bank increased their haul by about $2,000.
Explain how an economically rational bank robber should determine how many minutes to spend in the bank committing the robbery. Be sure to explain the principle that a rational bank robber would apply to this decision, and how that principle would be applied.
6. Your company has invested $5 million in developing a new product, but the development process isn’t quite complete. You have just learned from your marketing team that other companies have introduced similar products. As a result of this competition, the expected sales of your new product once you have completed development and actually begun production is now just $3 million. Your production team tells you that it will cost another $1 million to finish development and make your product. The decision is now yours: should you give the go-ahead to complete development of the product? Why or why not? In the event that your production team’s cost estimate is inaccurate, what is the most that your company should pay to complete development? Why? Be sure to incorporate (and define) the relevant concept into your answer.