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solution_PS1_spring2006

# solution_PS1_spring2006 - d The existence of pollution if...

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d) The existence of pollution, if there is no government intervention, some level of market power is socially preferable to none. Uncertain:

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2) You run the only bookstore dealing in used textbooks on a college campus. You know that a lot of students took Econ 1, and although the class was very exciting it’s likely that some will want to sell back their textbooks at the end of the semester. The number of students who sell it back to you is likely to vary by the amount of money you’re willing to pay for it. You decide that you don’t want to be too fancy in your estimation so you’ll keep it linear, and you guess that if you offer \$15 you will get 20 books, and if you offer \$30 you’ll get about 40. Next you have to figure out how many you think you can sell. Let’s say that the students are cheap, and you know that when you go to sell the books to the next class, the higher you price your textbook the more likely they are to buy it online. Again you decide that you don’t want to be more complicated than making a linear estimation of how many you can sell, and you suppose that if you sell the book for \$80 you will sell just 40 copies, but if you sell it for \$50 then 100 of them will buy it. I. Describe mathematically and show graphically the supply and demand “curves” (actually straight lines). The supply curve information is given first, so let’s deal with that. The line rises 15 over a run of 20, so the slope of the line is 15/20, or ¾. To find the p-intercept, we solve p = ¾ q + b at either point; try (p=15, q = 20) to get b = 0. Thus the supply curve is p = ¾ q . Do the same for demand; the slope is -½ , so p = -½ q + b. Put in the first point (p = 80, q = 40) to get p = -½ q + 100.
II. Consider the case of a perfectly competitive market for buying the book. a) How much would you (the bookstore owner) have to pay to buy the book back from students? In the perfectly competitive market, supply equals demand, so p = ¾ q and p = -½ q + 100. Solving, ¾ q = -½ q + 100 or q = 80. Since p = ¾ q, p = 60. The owner would have to pay \$60 to buy the book back from students. b) How much could you charge when you sold it to the next class? In a perfectly competitive market, no one has any control over the price, so no one can manipulate it. The owner can’t charge any more than \$60 when she sells it, because if she does the students will buy the book from someone else. c) About how many copies would you expect to sell, and what would be your total revenue? If the owner charges the competitive price of 60, we saw in part a) that she will sell 80 books. Her total revenue will therefore be 60 * 80 = \$4800. d) If buying the books is your only cost, what would your profit be?

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solution_PS1_spring2006 - d The existence of pollution if...

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