北京大学CCER-中级微观经济学-期中考试试题
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2010 年秋季学期中级微观经济学期中考试 Intermediate Microeconomics Midterm Exam, 2010 Fall
考试说明： 1、本次考试为闭卷考试。考试能用简单计算器，请勿将其他电子设备带入考场。 2、试卷共四题，每题 25 分，总计 100 分。 3、所有答案请一律写在答题纸上，否则不能计分。 4、试卷为中英文两个版本，答题可以使用中文或者英文。除作图外，请勿使用 铅笔或红笔。请注意保持答题纸整洁。
1.
Two
TAs,
Xu
and
Chen’s
utility
functions
are U ( x, y) x5 y
and
V ( x, y) 2( x0.5 y 0.5 ) respectively, both of which are only know by themselves but
not by others. After graduation, they have independently chosen a city to work, either
3/3
level was I B 100 . They are both rational. 1) Please derive their Marshall Demand functions for x and y; 2) Please derive their Compensated Demand functions for x and y; 3) Given the information above, can you infer who is the guy that has chosen to work in City A? (Hint: 2.5 1.58 )
2/3
Hale Waihona Puke Baidu
2. Assume that Alice needs two spoons of sugar (S) for each cup of coffee (C) and she feels better the more she drinks this kind of mixed coffee. She feels indifferent if more than two spoons of sugar are mixed with one cup of coffee, but feels as if she drinks nothing if fewer than two spoons are used. Prices for a cup of coffee and a spoon of sugar are Pc=2 and Ps=1 respectively. Alice’s income is 120. 1) Please graph Alice’s indifference curves. What is her optimal consumption bundle in this case? 2) Now suppose the price of coffee declines from 2 to 1. Please figure out the gross effect of this price change to Alice’s demand of coffee and sugar respectively. Could you please graphically demonstrate how these two gross effects are respectively decomposed into substitution and income effects, according to the Hicks compensation? Furthermore, can you calculate the values of substitution and income effects for coffee and sugar due to this price change? 3. A perfectly competitive industry has 80 firms in the short run. Each firm has an identical short-run cost function C (q) 0.1q3 2q 2 15q 150 . Total market demand is given by Q 1650 20 p . 1) Derive an individual firm’s supply function. 2) Calculate each firm’s output in the short run, the short-run equilibrium price and total industry output. 3) Calculate each firm’s short-run profit. 4) Express an individual firm’s producer surplus as a function of price ( P ). 4. Suppose the demand curve of one good is P 10 Q , and the supply curve is
1. 徐 助 教 的 效 用 函 数 方 程 是 U ( x, y) x5 y 。 陈 助 教 的 效 用 函 数 是
V ( x, y) 2( x0.5 y 0.5 ) 。他们知道自己的效用函数，但别人无法直接观察。毕
业以后，他俩分别决定去 A 城市或 B 城市中的一个工作。A 城市的物价水平
P Q4.
1） What are the equilibrium price and quantity? 2） Suppose the government provides a subsidy of $0.5 per unit. What would be the new equilibrium quantity? What would be the effective buying price and selling price? What would be the change in welfare of each participant in this society, as well as that of the whole country? 3） Suppose the country is now open to the world and the world price of this good, Pw=1, what would be the change in the social welfare of this country? 4） If the government imposes an import quota of 2 on this good, how much would be the change in social welfare of this country?
Notes: 1. This is a closed-book exam. Simple Calculators are allowed. Please do not bring any other electronic equipment with you. 2. There are four questions, each worth 25 points, totaled 100 points. 3. Please make sure that all answers are on the answer sheet. No scores will be given otherwise. 4. There are two versions of the exam, and you can answer either in Chinese or in English. Please do not use pencils or red pens unless for graphing. Please keep your answer sheet clean.
A 20 , and the City A or City B. In City A, prices for the two goods were pxA 10, p y B B 20, py 20 , and the income income level was I A 60 . In City B, prices were px
C (q) 0.1q3 2q 2 15q 150 ，行业的市场需求函数为 Q 1650 20 p 。
1) 2) 3) 4) 求厂商的供给函数。 求短期内每个厂商的产量、行业的短期均衡价格与总产量。 求每个厂商的短期利润。 写出厂商短期生产者剩余关于价格 P 的表达式。
4. 假定某国某种商品的需求曲线为 P 10 Q ，供给曲线为 P Q 4 。 1) 商品的均衡价格和销售量是多少？ 2) 假定政府对每单位出售的商品提供 0.5 元的补贴，问：新的均衡销售量 是多少？消费者购买一单位商品需要支付多少钱？销售者出售一单位商 品获得多少钱？社会中各主体的福利变化分别是多少？社会福利的总变 化是多少？ 3) 假定该国现在对国际市场开放，国际市场价格为 Pw=1。请问该国开放带 来的社会福利变化是多少？ 4) 如果该国限制其进口量最多为 2，由此带来的福利变化为多少？
2. 假设爱丽丝喝一杯咖啡 C 就得加两勺糖 S，而且这样的咖啡喝得越多她越满 意。如果一杯咖啡加多于两勺糖，她会觉得和加两勺没什么两样；如果一杯 咖啡没有糖或者只加了一勺，她会觉得和没喝一样。每杯咖啡和每勺糖的价 格分别为 Pc=2 和 PS=1。假设爱丽丝的收入为 120。
1/3
1) 请画出无差异曲线的形状。并求爱丽丝的最优消费组。 2) 现在，假设咖啡的价格从 2 降低到 1。请问这一价格变化对爱丽丝咖啡 和糖需求的总效应各是多少？你能作图说明如何根据希克斯补偿法，将 这两个总效应分别拆分成替代效应和收入效应么？进而，你能说出对咖 啡和糖而言，这一价格变化所带来的替代效应和收入效应各为多少么？ 3. 一个完全竞争的行业短期内有 80 个厂商，每个厂商有相同的短期成本函数
A B B 20 ，收入是 I A 60 ；B 城市的物价水平是 px 20, py 20 ， 是 pxA 10, p y
收入 I B 100 。已知他俩都是理性人。 1) 求出两位助教的马歇尔需求函数； 2) 求出两位助教的补偿需求函数； 3) 已知他俩中有一个人在 A 城市工作，给定以上两城市的具体信息，你能 推断出他是谁吗？ （提示： 2.5 1.58 ）
考试说明： 1、本次考试为闭卷考试。考试能用简单计算器，请勿将其他电子设备带入考场。 2、试卷共四题，每题 25 分，总计 100 分。 3、所有答案请一律写在答题纸上，否则不能计分。 4、试卷为中英文两个版本，答题可以使用中文或者英文。除作图外，请勿使用 铅笔或红笔。请注意保持答题纸整洁。
1.
Two
TAs,
Xu
and
Chen’s
utility
functions
are U ( x, y) x5 y
and
V ( x, y) 2( x0.5 y 0.5 ) respectively, both of which are only know by themselves but
not by others. After graduation, they have independently chosen a city to work, either
3/3
level was I B 100 . They are both rational. 1) Please derive their Marshall Demand functions for x and y; 2) Please derive their Compensated Demand functions for x and y; 3) Given the information above, can you infer who is the guy that has chosen to work in City A? (Hint: 2.5 1.58 )
2/3
Hale Waihona Puke Baidu
2. Assume that Alice needs two spoons of sugar (S) for each cup of coffee (C) and she feels better the more she drinks this kind of mixed coffee. She feels indifferent if more than two spoons of sugar are mixed with one cup of coffee, but feels as if she drinks nothing if fewer than two spoons are used. Prices for a cup of coffee and a spoon of sugar are Pc=2 and Ps=1 respectively. Alice’s income is 120. 1) Please graph Alice’s indifference curves. What is her optimal consumption bundle in this case? 2) Now suppose the price of coffee declines from 2 to 1. Please figure out the gross effect of this price change to Alice’s demand of coffee and sugar respectively. Could you please graphically demonstrate how these two gross effects are respectively decomposed into substitution and income effects, according to the Hicks compensation? Furthermore, can you calculate the values of substitution and income effects for coffee and sugar due to this price change? 3. A perfectly competitive industry has 80 firms in the short run. Each firm has an identical short-run cost function C (q) 0.1q3 2q 2 15q 150 . Total market demand is given by Q 1650 20 p . 1) Derive an individual firm’s supply function. 2) Calculate each firm’s output in the short run, the short-run equilibrium price and total industry output. 3) Calculate each firm’s short-run profit. 4) Express an individual firm’s producer surplus as a function of price ( P ). 4. Suppose the demand curve of one good is P 10 Q , and the supply curve is
1. 徐 助 教 的 效 用 函 数 方 程 是 U ( x, y) x5 y 。 陈 助 教 的 效 用 函 数 是
V ( x, y) 2( x0.5 y 0.5 ) 。他们知道自己的效用函数，但别人无法直接观察。毕
业以后，他俩分别决定去 A 城市或 B 城市中的一个工作。A 城市的物价水平
P Q4.
1） What are the equilibrium price and quantity? 2） Suppose the government provides a subsidy of $0.5 per unit. What would be the new equilibrium quantity? What would be the effective buying price and selling price? What would be the change in welfare of each participant in this society, as well as that of the whole country? 3） Suppose the country is now open to the world and the world price of this good, Pw=1, what would be the change in the social welfare of this country? 4） If the government imposes an import quota of 2 on this good, how much would be the change in social welfare of this country?
Notes: 1. This is a closed-book exam. Simple Calculators are allowed. Please do not bring any other electronic equipment with you. 2. There are four questions, each worth 25 points, totaled 100 points. 3. Please make sure that all answers are on the answer sheet. No scores will be given otherwise. 4. There are two versions of the exam, and you can answer either in Chinese or in English. Please do not use pencils or red pens unless for graphing. Please keep your answer sheet clean.
A 20 , and the City A or City B. In City A, prices for the two goods were pxA 10, p y B B 20, py 20 , and the income income level was I A 60 . In City B, prices were px
C (q) 0.1q3 2q 2 15q 150 ，行业的市场需求函数为 Q 1650 20 p 。
1) 2) 3) 4) 求厂商的供给函数。 求短期内每个厂商的产量、行业的短期均衡价格与总产量。 求每个厂商的短期利润。 写出厂商短期生产者剩余关于价格 P 的表达式。
4. 假定某国某种商品的需求曲线为 P 10 Q ，供给曲线为 P Q 4 。 1) 商品的均衡价格和销售量是多少？ 2) 假定政府对每单位出售的商品提供 0.5 元的补贴，问：新的均衡销售量 是多少？消费者购买一单位商品需要支付多少钱？销售者出售一单位商 品获得多少钱？社会中各主体的福利变化分别是多少？社会福利的总变 化是多少？ 3) 假定该国现在对国际市场开放，国际市场价格为 Pw=1。请问该国开放带 来的社会福利变化是多少？ 4) 如果该国限制其进口量最多为 2，由此带来的福利变化为多少？
2. 假设爱丽丝喝一杯咖啡 C 就得加两勺糖 S，而且这样的咖啡喝得越多她越满 意。如果一杯咖啡加多于两勺糖，她会觉得和加两勺没什么两样；如果一杯 咖啡没有糖或者只加了一勺，她会觉得和没喝一样。每杯咖啡和每勺糖的价 格分别为 Pc=2 和 PS=1。假设爱丽丝的收入为 120。
1/3
1) 请画出无差异曲线的形状。并求爱丽丝的最优消费组。 2) 现在，假设咖啡的价格从 2 降低到 1。请问这一价格变化对爱丽丝咖啡 和糖需求的总效应各是多少？你能作图说明如何根据希克斯补偿法，将 这两个总效应分别拆分成替代效应和收入效应么？进而，你能说出对咖 啡和糖而言，这一价格变化所带来的替代效应和收入效应各为多少么？ 3. 一个完全竞争的行业短期内有 80 个厂商，每个厂商有相同的短期成本函数
A B B 20 ，收入是 I A 60 ；B 城市的物价水平是 px 20, py 20 ， 是 pxA 10, p y
收入 I B 100 。已知他俩都是理性人。 1) 求出两位助教的马歇尔需求函数； 2) 求出两位助教的补偿需求函数； 3) 已知他俩中有一个人在 A 城市工作，给定以上两城市的具体信息，你能 推断出他是谁吗？ （提示： 2.5 1.58 ）