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1、Chapter 1 NAMEThe MarketIntroduction. The problems in this chapter examine some variations on the apartment market described in the text. In most of the problems we work with the true demand curve constructed from the re
2、servation prices of the consumers rather than the “smoothed” demand curve that we used in the text. Remember that the reservation price of a consumer is that price where he is just indifferent between renting or not rent
3、ing the apartment. At any price below the reservation price the consumer will demand one apartment, at any price above the reservation price the consumer will de- mand zero apartments, and exactly at the reservation pric
4、e the consumer will be indifferent between having zero or one apartment. You should also observe that when demand curves have the “stair- case” shape used here, there will typically be a range of prices where supply equa
5、ls demand. Thus we will ask for the the highest and lowest price in the range.1.1 (3) Suppose that we have 8 people who want to rent an apartment. Their reservation prices are given below. (To keep the numbers small, thi
6、nk of these numbers as being daily rent payments.)Person = A B C D E F G H Price = 40 25 30 35 10 18 15 5(a) Plot the market demand curve in the following graph. (Hint: When the market price is equal to some consumer i’s
7、 reservation price, there will be two different quantities of apartments demanded, since consumer i will be indifferent between having or not having an apartment.)2 THE MARKET (Ch. 1)0 1 2 3 4 5 6 7 8102030406050PriceApa
8、rtments(b) Suppose the supply of apartments is fixed at 5 units. In this case there is a whole range of prices that will be equilibrium prices. What is the highest price that would make the demand for apartments equal to
9、 5units? $18.(c) What is the lowest price that would make the market demand equalto 5 units? $15.(d) With a supply of 4 apartments, which of the people A–H end upgetting apartments? A, B, C, D.(e) What if the supply of a
10、partments increases to 6 units. What is therange of equilibrium prices? $10 to $15.1.2 (3) Suppose that there are originally 5 units in the market and that 1 of them is turned into a condominium.(a) Suppose that person A
11、 decides to buy the condominium. What will be the highest price at which the demand for apartments will equal the supply of apartments? What will be the lowest price? Enter your an- swers in column A, in the table. Then
12、calculate the equilibrium prices of apartments if B, C, . . . , decide to buy the condominium.NAME 3Person A B C D E F G HHigh price 18 18 18 18 25 25 25 25Low price 15 15 15 15 18 15 18 18(b) Suppose that there were two
13、 people at each reservation price and 10 apartments. What is the highest price at which demand equals supply?18. Suppose that one of the apartments was turned into a condo-minium. Is that price still an equilibrium price
14、? Yes.1.3 (2) Suppose now that a monopolist owns all the apartments and that he is trying to determine which price and quantity maximize his revenues.(a) Fill in the box with the maximum price and revenue that the monop-
15、 olist can make if he rents 1, 2, . . ., 8 apartments. (Assume that he must charge one price for all apartments.)Number 1 2 3 4 5 6 7 8Price 40 35 30 25 18 15 10 5Revenue 40 70 90 100 90 90 70 40(b) Which of the people A
16、–F would get apartments? A, B, C, D.(c) If the monopolist were required by law to rent exactly 5 apartments,what price would he charge to maximize his revenue? $18.(d) Who would get apartments? A, B, C, D, F.(e) If this
17、landlord could charge each individual a different price, and he knew the reservation prices of all the individuals, what is the maximumrevenue he could make if he rented all 5 apartments? $148.(f) If 5 apartments were re
18、nted, which individuals would get the apart-ments? A, B, C, D, F.1.4 (2) Suppose that there are 5 apartments to be rented and that the city rent-control board sets a maximum rent of $9. Further suppose that people A, B,
19、C, D, and E manage to get an apartment, while F, G, and H are frozen out.4 THE MARKET (Ch. 1)(a) If subletting is legal—or, at least, practiced—who will sublet to whom in equilibrium? (Assume that people who sublet can e
20、vade the city rent-control restrictions.) E, who is willing to pay only$10 for an apartment would sublet to F,who is willing to pay $18.(b) What will be the maximum amount that can be charged for the subletpayment? $18.(
21、c) If you have rent control with unlimited subletting allowed, which ofthe consumers described above will end up in the 5 apartments? A,B, C, D, F.(d) How does this compare to the market outcome? It’s thesame.1.5 (2) In
22、the text we argued that a tax on landlords would not get passed along to the renters. What would happen if instead the tax was imposed on renters?(a) To answer this question, consider the group of people in Problem 1.1.
23、What is the maximum that they would be willing to pay to the landlord if they each had to pay a $5 tax on apartments to the city? Fill in the box below with these reservation prices.Person A B C D E F G HReservation Pric
24、e 35 20 25 30 5 13 10 0(b) Using this information determine the maximum equilibrium price ifthere are 5 apartments to be rented. $13.(c) Of course, the total price a renter pays consists of his or her rent plusthe tax. T
25、his amount is $18.(d) How does this compare to what happens if the tax is levied on thelandlords? It’s the same.NAME 9(b) What is the ratio of the price of x to the price of y? 1/2.(c) If you spent all of your income on
26、x, how much x could you buy?16.(d) If you spent all of your income on y, how much y could you buy? 8.(e) Write a budget equation that gives you this budget line, where theprice of x is 1. x + 2y = 16.(f) Write another bu
27、dget equation that gives you the same budget line,but where the price of x is 3. 3x + 6y = 48.2.4 (1) Murphy was consuming 100 units of X and 50 units of Y . The price of X rose from 2 to 3. The price of Y remained at 4.
28、(a) How much would Murphy’s income have to rise so that he can stillexactly afford 100 units of X and 50 units of Y ? $100.2.5 (1) If Amy spent her entire allowance, she could afford 8 candy bars and 8 comic books a week
29、. She could also just afford 10 candy bars and 4 comic books a week. The price of a candy bar is 50 cents. Draw herbudget line in the box below. What is Amy’s weekly allowance? $6.0 8 16 24 3281624Candy barsComic books32
30、1210 BUDGET CONSTRAINT (Ch. 2)2.6 (0) In a small country near the Baltic Sea, there are only three commodities: potatoes, meatballs, and jam. Prices have been remark- ably stable for the last 50 years or so. Potatoes cos
31、t 2 crowns per sack, meatballs cost 4 crowns per crock, and jam costs 6 crowns per jar.(a) Write down a budget equation for a citizen named Gunnar who has an income of 360 crowns per year. Let P stand for the number of s
32、acks of potatoes, M for the number of crocks of meatballs, and J for the numberof jars of jam consumed by Gunnar in a year. 2P + 4M + 6J =360.(b) The citizens of this country are in general very clever people, but they a
33、re not good at multiplying by 2. This made shopping for potatoes excru- ciatingly difficult for many citizens. Therefore it was decided to introduce a new unit of currency, such that potatoes would be the numeraire. A sa
34、ck of potatoes costs one unit of the new currency while the same rel- ative prices apply as in the past. In terms of the new currency, what isthe price of meatballs? 2 crowns.(c) In terms of the new currency, what is the
35、 price of jam? 3crowns.(d) What would Gunnar’s income in the new currency have to be for him to be exactly able to afford the same commodity bundles that he couldafford before the change? 180 crowns.(e) Write down Gunnar
36、’s new budget equation. P + 2M + 3J =180. Is Gunnar’s budget set any different than it was before the change?No.2.7 (0) Edmund Stench consumes two commodities, namely garbage and punk rock video cassettes. He doesn’t act
37、ually eat the former but keeps it in his backyard where it is eaten by billy goats and assorted vermin. The reason that he accepts the garbage is that people pay him $2 per sack for taking it. Edmund can accept as much g
38、arbage as he wishes at that price. He has no other source of income. Video cassettes cost him $6 each.(a) If Edmund accepts zero sacks of garbage, how many video cassettescan he buy? 0.NAME 11(b) If he accepts 15 sacks o
39、f garbage, how many video cassettes can hebuy? 5.(c) Write down an equation for his budget line. 6C ? 2G = 0.(d) Draw Edmund’s budget line and shade in his budget set.0 5 10 15 2051015Video cassettesGarbage20Budget LineB
40、udget Set???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
41、?????2.8 (0) If you think Edmund is odd, consider his brother Emmett. Emmett consumes speeches by politicians and university administrators. He is paid $1 per hour for listening to politicians and $2 per hour for listeni
42、ng to university administrators. (Emmett is in great demand to help fill empty chairs at public lectures because of his distinguished appearance and his ability to refrain from making rude noises.) Emmett consumes one go
43、od for which he must pay. We have agreed not to disclose what that good is, but we can tell you that it costs $15 per unit and we shall call it Good X. In addition to what he is paid for consuming speeches, Emmett receiv
44、es a pension of $50 per week.0 25 50 75 100255075Politician speechesAdministrator speeches10012 BUDGET CONSTRAINT (Ch. 2)(a) Write down a budget equation stating those combinations of the three commodities, Good X, hours
45、 of speeches by politicians (P), and hours of speeches by university administrators (A) that Emmett could afford toconsume per week. 15X ? 1P ? 2A = 50.(b) On the graph above, draw a two-dimensional diagram showing the l
46、ocus of consumptions of the two kinds of speeches that would be possible for Emmett if he consumed 10 units of Good X per week.2.9 (0) Jonathan Livingstone Yuppie is a prosperous lawyer. He has, in his own words, “outgro
47、wn those confining two-commodity lim- its.” Jonathan consumes three goods, unblended Scotch whiskey, de- signer tennis shoes, and meals in French gourmet restaurants. The price of Jonathan’s brand of whiskey is $20 per b
48、ottle, the price of designer tennis shoes is $80 per pair, and the price of gourmet restaurant meals is $50 per meal. After he has paid his taxes and alimony, Jonathan has $400 a week to spend.(a) Write down a budget equ
49、ation for Jonathan, where W stands for the number of bottles of whiskey, T stands for the number of pairs of tennis shoes, and M for the number of gourmet restaurant meals that heconsumes. 20W + 80T + 50M = 400.(b) Draw
50、a three-dimensional diagram to show his budget set. Label the intersections of the budget set with each axis.MT W8520(c) Suppose that he determines that he will buy one pair of designer tennis shoes per week. What equati
51、on must be satisfied by the combinations ofrestaurant meals and whiskey that he could afford? 20W +50M =320.2.10 (0) Martha is preparing for exams in economics and sociology. She has time to read 40 pages of economics an
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