Microeconomics Questions

EC489.03 – Bo?azi?i University

Summer 2011 by Arhan Ertan

Study Questions

1.For each of the following production functions, draw a diagram showing the

general shape of its corresponding isoquant. Comment on the ease at which labor and capital can be substituted for one another relative to the other two production functions.

a. Q = K + L.

b. Q = K0.5L0.5.

c. Q = min(K, L).

Answer:

a. Isoquants are straight lines from the horizontal axis to the vertical axis. Perfect substitutability.

b. Isoquants are curves with slope -1 in the middle and asymptotically approaching both the vertical and horizontal axes. Limited substitutability.

c. Isoquants are L-shape

d. No substitutability.

2. A firm uses 3 factors to produce its output. Its production function is f(x, y, z) =

min{x3/y, y2, (z4 - x4)/y2}. If the amount of each input is multiplied by 2, by which factor will its output be multiplied?

Answer: 4.

3.Which of the following production functions exhibit constant returns to scale?

Explain. In each case y is output and K and L are inputs.

(1) y = K1/2L2/3. (2) y = 3K1/2L1/2. (3) y = K1/2 + L1/2. (4) y = 2K + 3L.

Answer: 2 and 4

4. A competitive firm has a production function described as follows. “Weekly

output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week.” Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely.

a. Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.)

b. If the wage is w = $1 and the price of output is p = $4, how much labor will the firm demand in the short run?

c. What if w = $1 and p = $10?

d. Write down an equation for the firm’s short-run demand for labor as a function of w and p.

Answer:

a. MP = 1/(2L1/2) if L < 16, MP = 0 if L > 16.

b. 4.

c. 16.

d. L = (p/2w)2.

5. A firm has the production function Q = X1/21X2. In the short run it must use exactly

15 units of factor 2. The price of factor 1 is $75 per unit and the price of factor 2 is

$2 per unit. Write down the firm’s short-run marginal cost function

Answer:MC(Q) = 10Q/15

6.Mr. X’s total costs are 2s2 + 40s + 40. If he repairs 10 cars, what will be his

average variable costs?

Answer: $60

7.Miss Z’s production function for comic books is 0.1J1/2L3/4, where J is the number

of jokes and L is the number of hours of cartoonists labor that he uses. If she can vary both jokes and cartoonists’ labor and if old jokes cost $2 each and

cartoonists’ labor costs $18 per hour, then the cheapest way to produce comics books requires using jokes and labor in which ratio of J/L?

Answer: 6

8.The snow removal business in East Icicle, Minnesota, is a competitive industry.

All snowplow operators have the cost function C = Q2 + 4, where Q is the number of driveways cleared. Demand for snow removal in the town is given by Q d = 120 - P. What is the long-run equilibrium number of firms in this industry? Answer: In LR, P = minAC = 4 (Q i = 2). Then Qtotal = 120 – 4 = 116 and n=58

9.Merih produces plastic dog dishes using a process that requires only labor and

plastic as inputs and has constant returns to scale. With the process she is

currently using, a laborer can turn out 30 dog dishes an hour. The wage rate is $9 per hour. The plastic in a dog dish costs Merih $0.10. She has no other costs

besides labor and plastic. Merih faces a perfectly competitive market for plastic dog dishes, and she decides that she is maximizing profits when she makes 300 dog dishes an hour. What is the market price of dog dishes?

Answer: $0.40

10.A competitive firm has a single factory with the cost function c(y) = 4y2 + 89 and

produces 28 units in order to maximize profits. Although the price of output does not change, the firm decides to build a second factory with the cost function c(y) = 8y2 + 39. To maximize its profits, how many units should it produce in the second factory?

Answer: Equate MCs in both factories: Y1=28, Y2=14

11.A competitive firm has a long-run total cost function c(y) = 5y2 + 1.125 for y > 0

and c(0) = 0. Write down its long-run supply function.

Answer:y = p/10 if p > 150, y = 0 if p < 150

12.The bicycle industry is made up of 100 firms with the long-run cost curve c(y) = 2

+ (y2/2) and 60 firms with the long-run cost curve c(y) = y2/10. No new firms can enter the industry. What is the LR industry supply curve at prices greater than $2? Answer:y = 400p

13.On a tropical island there are 100 potential boat builders, numbered 1 through

100. Each can build up to 20 boats a year, but anyone who goes into the boat-

building business has to pay a fixed cost of $19. Marginal costs differ from person to person. Where y denotes the number of boats built per year, boat builder 1 has a total cost function c(y) = 19 + y. Boat builder 2 has a total cost function c(y)= 19 + 2y, and more generally, for each i, from 1 to 100, boat builder i has a cost

function c(y) = 19 + iy. If the price of boats is 25, how many boats will be built per year?

Answer: 24 boat builders, each will produce 20 (to minimize AC) = 480 boats

14.In the absence of government interference, there is a constant marginal cost of $4

per ounce for growing marijuana and delivering it to buyers. Suppose that

government authorities seize shipments whenever they find them and resell the marijuana that they seize on the open market. The probability that any shipment of marijuana is seized is 0.50. If a shipment is seized, there is no other punishment besides loss of the marijuana that is seized. What is the effect of the government action on the equilibrium price of marijuana?

Answer: It raises the equilibrium price by $4.

15.In a certain industry, the supply curve of any firm is S i(p) = p/2. If a firm produces

5 units of output, what are its total variable costs?

Answer: $25.

16.The demand for a monopolist’s output is 7,000 divided by the square of the price

in dollars that it charges per unit. The firm has constant marginal costs equal to 1 dollar per unit. At what level of output is his total revenue maximized and at what level of output is his profit maximized?

Answer: It should charge a price of 2 dollars to maximize profits.

17.A profit-maximizing monopolist faces a downward-sloping demand curve that has

a constant elasticity of -3. The firm finds it optimal to charge a price of $12 for its

output. What is its marginal cost at this level of output?

Answer: $8.

18.A monopolist produces at a point where the price elasticity of demand is -0.7 and

the marginal cost is $2. If you were hired to advise this monopolist on how to

increase his profits, would you recommend to increase or to decrease its output? Answer: Decrease its output.

19.A major software developer has estimated the demand for its new personal finance

software package to be Q = 1,000,000P-2 while the total cost of the package is C = 100,000 + 25Q. If this firm wishes to maximize profit, what percentage markup should it place on this product?

Answer: 100%.

20.A monopolist sells in two markets. The demand curve for her product is given by

p1 = 122 - 2x1 in the first market and p2 = 306 - 5x2 in the second market, where x i is the quantity sold in market i and p i is the price charged in market i. She has a constant marginal cost of production, c = 6, and no fixed costs. She can charge different prices in the two markets. What is the profit-maximizing combination of quantities for this monopolist?

Answer: Make MR = 6 in both markets. Then: x1 = 29 and x2 = 30

21.A careful analysis of demand for bubble-gums reveals a strange segmentation in

the market. It is produced by the process Q = min{R/3, W}, where R and W are the only inputs needed to produce bubble-gums and P R = $1, P W = $5. If demand for bubble-gums by senior citizens is described by Q0 = 500P-3/2 while demand by those under 65 years old is Q y= 50P-5, how should bubble-gums to be priced to maximize profits?

Answer: Optimal production: Use 3R and 1W. So, MC = 3 + 5 = 8. Make MR = 8 in both markets: Therefore price = $24 for senior citizens and = $10 for those younger

22.Suppose that the demand curve for mineral water is given by p = 40 - 12q, where

p is the price per bottle paid by consumers and q is the number of bottles

purchased by consumers. Mineral water is supplied to consumers by a

monopolistic distributor who buys from a monopolistic producer, who is able to produce mineral water at zero cost. The producer charges the distributor a price of

c per bottle. Given his marginal cost of c per unit, the distributor chooses an

output to maximize his own profits. Knowing that this is what the distributor will do, the producer sets his price c so as to maximize his revenue. The price paid by consumers under this arrangement is

Answer: $30.

23.Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Its

production function is Q = 40L, where L is the amount of labor it uses and Q is the number of meals produced. In order to hire L units of labor, Rabelaisian

Restaurants must pay a wage of 40 + .1L per unit of labor. The demand curve for meals at Rabelaisian Restaurants is given by P = 5.25 - Q/1,000. The profit-

maximizing output for Rabelaisian Restaurants is

Answer: 2,000 meals.

24.An industry has two firms each of which produces output at a constant unit cost of

$10 per unit. The demand function for the industry is q = 1,000,000/p. The

Cournot equilibrium price for this industry is

Answer: $20.

25.An industry has two firms producing at a constant unit cost of $10 per unit. The

inverse demand curve for the industry is p = 110 - .5q. Suppose that firm 1 is a Stackelberg leader in choosing its quantity (i.e., firm 1 chooses it’s quantity first, knowing that firm 2 will observe firm 1’s quantity when it chooses its own

output.) How much output will firm 2, the follower, produce?.

Answer: 50 units.

26.The demand for y is given by y = 256/p2. Only two firms produce y. They have

identical costs c(y) = y2. If they agree to collude and maximize their joint profits, how much output will each firm produce?

Answer: 2

27.A game has two players. Each player has two possible strategies. One strategy is

Cooperate, the other is Defect. Each player writes on a piece of paper either a C for cooperate or a D for defect. If both players write C, they each get a payoff of $100. If both players write D, they each get a payoff of 0. If one player writes C and the other player writes D, the cooperating player gets a payoff of S and the defecting player gets a payoff of T. To defect will be a dominant strategy for both players if

Answer:S < 0 and T > 100

高级英语写作黄金句型和新词

1) With the rapid improvement in.../growing awareness of..., more and more.../sth.... 1 随着…的飞速发展/越来越多的关注，越来越… (e.g. With the considerable improvement in building industry, more and more structures are being erected to set the people's minds at ease.) 例：随着建筑业的大力推进，人们对建立越来越多的房屋建筑感到宽心。 2) Recently, sth./the problem of...has been brought to popular attention/ has become the focus of public concern. 2 近来，某事/某问题引起了人们的普遍关注/成了公众关注的焦点。 (e.g. Recently, the problem of unemployment has been brought to such popular attention that governments at all levels place it on the agenda as the first matter.) 例：近来失业问题引起了人们的普遍关注，各级政府已把它列为首要议程。 3) One of the universal issues we are faced with/that cause increasing concern is that... 3 我们面临的一个普遍问题是… /一个越来越引人关注的普遍问题 是… (e.g. One of the universal issues that draw (cause) growing concern is whether it is wise of man to have invented the automobile.) 例：一个越来越引人关注的普遍问题是，发明汽车是否为人 4) In the past few years, there has been a boom/sharp growth/decline in.. . 4 在过去的几年里，…经历了突飞猛进/迅猛增长/下降。 (e.g. In the past ten years, there has been a sharp decline in the number of species.) 例：在过去的几年里，物种数量骤然下降。 5) Nowadays, more/most important/dangerous for our society is... 5 如今对我们社会更（最）为重要的（危险的）事情是… (e.g. Nowadays, most dangerous for our society is the tendency to take advantage of each other in political circles.) 例：对我们社会最为危险的事情是政界倾向于互相利用。 6) According to the information given in the table/graph, we can find that... 6 根据图表资料，我们可以发现… 7) As can be seen from the table/graph/figure, there is a marked increase /decline/favorable (an unfavorable) change in... 7 根据图表（数字）显示，…明显增长（下降）/发生了有利（不利）变化。 8) As we can see from the table/graph/figure above, drastic/considerable/ great changes have taken place in...over the period of time from...(年份)to...( 年份) 8 据上面图表（数字）所示，从某年到某年某方面发生了剧烈的（相当大的；巨大的）变化。

人教版新目标八年级英语初二英语上册课文翻译全册

人教版新目标八年级英语初二英语上册课文翻译【全册】 一单元 SECTION A 图片周末你通常做什么？我经常去看电影。 1c她在周末做什么？她经常去看电影。 2a你多久看一次电视？每周两次。 2c 你多久看一次电视？我每天看电视。你最喜欢什么节目？《动物世界》。你多久看一次？ Grammar Focus 你周末通常做什么？我通常踢足球。他们周末做什么？他们经常去看电影。他周末做什么？他有时看电视。你多久购物一次？我每月购物一次。程多久看一次电视？他每周看两次电视。 3格林中学学生做什么？大多数学生每周锻炼三或四次。一些学生每周锻炼一两次。一些学生非常活跃，每天都锻炼。至于家庭作业，大多数学生每天都做家庭作业。一些学生每周做三或四次家庭作业。没有学生每周做一两次作业。关于“看电视”的结果很有趣。一些学生每周看一两次电视，一些学生每周看三或四次电视。但大多数学生每天都看电视。 4谁是最好的英语学生？你能做什么来提高你的英语水平？你多久读一次英语书？我每周读两次英语书。 SECTION B 1a垃圾食品牛奶水果蔬菜睡觉咖啡 1b刘芳，你多久喝一次牛奶？我每天喝牛奶。你喜欢牛奶吗？不喜欢，但我妈妈想让我喝。她说牛奶对我的健康有益。 2c你多长时间运动一次？我每天都运动。你多长时间……一次？ 3a……但是我非常健康。我每天都锻炼，通常是在我放学回家的时候，我的饮食习惯非常好。我尽量多吃蔬菜。我每天都吃水果，每天都喝牛奶。我从不喝咖啡。当然了，我也喜欢垃圾食品，我每周吃二或三次。噢，还有，我每天晚上都睡九个小时。所以你看，我爱惜我身体。我的健康的生活方式帮助我取得了好的成绩。好的食品加上运动帮助我更好地学习。 3b我认为我有点不健康。我几乎不锻炼。我每周吃两次蔬菜，但我从不吃水果。并且我不喜欢喝牛奶。啐！我喜欢垃圾食品，每周吃三到四次。我也喜欢喝咖啡。因此或许我不是很健康，尽管我拥有一个健康的习惯。我每天晚上都睡九个小时。 4 你多久吃一次蔬菜？你做什么运动？玛丽亚每天锻炼。她喜欢玩…… SELF CHECK 1妈妈想让我六点起床跟她一起打乒乓球。爷爷十分健康因为他每天都锻炼。大量的蔬菜帮助你保持健康。你必须得尽量少吃肉。你有健康的生活方式吗？ Just for fun你健康吗？噢，我很健康。你最喜欢的运动是什么？我喜欢打篮球。哇！ 二单元 SECTION A 图片怎么了？我感冒了。怎么了？我胃痛。我背痛。 1c怎么啦？我喉咙痛。 2a 1.发烧—d.多喝水2.喉咙痛—b.加蜂蜜的热茶 3.胃痛—a.躺下休息 4.牙痛——c.看牙医 2c怎么了？我牙痛。也许你应该去看牙医。好主意。 Grammar Focus 我头痛。你应当上床睡觉。我胃痛。他不应当吃东西。她牙痛。她应当看牙医。 3a怎么啦？我觉得不舒服。我感冒了。什么时候开始的？大约两天前。噢，那太糟糕了。你应当休息一下。是的，我也是这样想的。我希望你快点好起来。 4怎么啦？你喉咙痛吗？不，我不痛。你头痛吗？是的，我头痛。你应当躺下来休息一下。 SECTION B 1a疲乏的；劳累的饥饿的口渴的紧张的；有压力的1b吃个苹果。早点上床睡觉。喝些水。听音乐 2c吉娜怎么啦？她累了。噢，她应当早点上床睡觉。她不应该去参加聚会。 3a健康的生活方式，中国方式 传统中医认为我们需要阴阳食品的平衡以保持健康。例如，你经常没有力气并感到疲倦吗？这或许是因为你吃了太多的阴性食品，你应当吃含阳性较高的食品，像牛肉。吃党参和黄芪草对这方面也是有好处的。但那些太紧张和易怒的人也许吃了太多的阳性食品，中医认为他们应当多吃阴性食品，像豆腐。现在中药在很多西方国家很受欢迎。拥有一个健康的生活方式很容易，均衡饮食很重要。 3b每个人都会不时地感到疲倦。当你疲倦时，你不应当晚上外出。你应当几个晚上早儿上床睡觉，并且你应该锻炼以保持健康，你也应吃水果和其他健康的食品。你不应当在你感到疲倦时学习。

新版新目标英语八年级上册全册教案

Unit 1 Where did you go on vacation? Section A 1 (1a-2d) 一、教学目标： 1. 语言知识目标： 1) 能掌握以下单词：anyone, anywhere, wonderful, quite a few, most, something, nothing, everyone, of course, myself, yourself 能掌握以下句型： ①—Where did you go on vacation? —I went to the mountains. ②—Where did Tina to on vacation? —She went to the beach. ③—Did you go with anyone? —Yes, I did./No, I didn’t. 2) 能了解以下语法： —复合不定代词someone, anyone, something, anything等的用法。 —yourself, myself等反身代词的用法。 3）一般过去时态的特殊疑问句，一般疑问句及其肯定、否定回答。 2. 情感态度价值观目标： 学会用一般过去时进行信息交流，培养学生的环保意识，热爱大自然。 二、教学重难点 1. 教学重点： 1) 用所学的功能语言交流假期去了什么旅行。 2) 掌握本课时出现的新词汇。 2. 教学难点： 1) 复合不定代词someone, anyone, something, anything等的用法。 2) yourself, myself等反身代词的用法。 三、教学过程 Ⅰ. Lead-in 1. 看动画片来进入本课时的主题谈论上周末做了些什么事情，谈论过去发生的事情。 Ⅱ. Presentation 1. Show some pictures on the big screen. Let Ss read the expressions. 2. Focus attention on the picture. Ask: What can you see? Say: Each picture shows something a person did in the past. Name each activity and ask students to repeat: Stayed at home, Went to mountains, went to New York City 6. Went to the beach, visited my uncle, visited museums, went to summer camp 3. Now, please match each phrase with one of the pictures next to the name of the activity，point to the sample answer. 4. Check the answers. Answers: 1. f 2. b 3. g 4. e 5. c 6. a 7. d III. Listening 1. Point to the picture on the screen. Say: Look at the picture A. Where did Tina go on vacation? She went to mountains. Ask: What did the person do in each picture? 2. Play the recording the first time. 3. Play the recording a second time. Say: There are three conversations. The people talk about what did on vacation. Listen to the recording and write numbers of the names in the right boxes of the picture. 4. Check the answers. IV．Pair work 1. Point out the sample conversation. Ask two Ss to read the conversation to the class.

高级英语一

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