精选-中级微观经济学作业及答案
中级微观经济学习题答案
第一部分 消费者理论1. 当11xx 时，加数量税t,画出预算集并写出预算线预算集：).....(. (1)12211x x m x p x p).........(..........)(1112211x x x t m x p x t p2. 如果同样多的钱可以买（4，6）或（12，2），写出预算线。
mx p x p 2211 则有mp p 2164，mp p 21212不妨假设12 p ，则可解得：8,211 m p 。
预算线为82121 x x 3．(1)0.4100x y(2)0.2100.............300.4106.............30x y if x x y if x(3)0.4106x y4. 证明：设两条无差异曲线对应的效用分别为21,uu ，由曲线的单调性假设，若21uu ，则实为一条曲线。
若21uu ，假设两曲线相交，设交点为x，则21)(,)(ux u u x u ，可推出21uu ，存在矛盾，不可能相交。
5. -5(把一元纸币放在纵轴上)或者-1/5(把一元纸币放在横轴上),6. 中性商品是指消费者不关心它的多少有无的商品商品2 如果也是中性商品那么该题就无所谓无差异曲线,也无所谓边际替代率了. 商品2如果不是中性商品:边际替代率是0(把中性商品放在横轴上)或者 (把中性商品放在纵轴上)7. (1)x1 is indefinitely the substitution of x2, and five units of x1 can bring the same utility as that one unit of x2 can do. With the most simple form of the utilityfunction,125u x x x , and assume that the prices of those two goods are p1 and p2 respectively and the total wealth of the consumer is m, the problem can be writtenas121112max ,..u x xst p x p x m③ Because 5p1=p2, any bundle 12,x x which satisfies the budget constraint, is thesolution of such problem.(2) A cup of coffee is absolutely the complement of two spoons of sugar. Let x1 and x2 represent these two kinds of goods, then we can write the utility function as12121,min ,2u x x x xThe problem of the consumer is121112max ,..u x xst p x p x mAny solution should satisfies the rule that 1212x x , and the budget constraint.So replace x1 with (1/2)(x2) in the budget constraint and we can get 1122mx p p,and 21222mx p p.8. (1) Because the preference is Cobb-Douglas utility, we can simplify thecomputation by the formula that the standardized parameter of one commodity means its share of total expenditure.So directly, the answer is 1123m x p , 213mx p.（详细方法见8(2)）. （2）库恩-塔克定理。
中级微观经济学题库及参考答案
一、名词辨析1.规范分析与实证分析；实证分析方法：实证分析不涉及价值判断，只讲经济运行的内在规律，也就是回答“是什么”的问题；实证分析方法的一个基本特征它提出的问题是可以测试真伪的，如果一个命题站得住脚，它必须符合逻辑并能接受经验数据的检验。
规范分析方法：规范分析以价值判断为基础，以某种标准为分析处理经济问题的出发点，回答经济现象“应当是什么”以及“应当如何解决”的问题，其命题无法证明真伪。
2.无差异曲线与等产量线；无差异曲线是指这样一条曲线，尽管它上面的每一点所代表的商品组合是不同的，但消费者从中得到的满足程度却是相同的。
等产量线表示曲线上每一点的产量都相等，是由生产出同一产量的不同投入品组合所形成的曲线。
3.希克斯补偿与斯卢茨基补偿;希克斯补偿是指当商品价格发生变化后，要维持原有效用水平所需补偿的货币数量。
斯卢茨基补偿是指当商品价格发生变化后，要维持原有消费水平所需补偿的货币数量。
4.边际替代率与边际技术替代率；边际替代率是指，消费者在增加额外一单位商品X之后，若要保持满足水平不变而必须放弃的商品Y 的数量。
边际替代率就等于无差异曲线在该点的斜率的绝对值。
边际技术替代率是指，当只有一种投入品可变时，要增加产量，企业必须投入更多的另一种投入品；当两种投入品都可变时，企业往往会考虑用一种投入品来替代另一种投入品。
等产量线斜率的绝对值就是两种投入品的边际技术替代率。
5.边际产出与边际收益产出边际产出，就是指在其他生产资源的投入量不变的条件下,由于增加某种生产资源一个单位的投入,相应增加的产出量。
当产出以产量表示时,即为边际产量;当产出以产值表示时,即为边际产值。
边际收益产出是指，额外单位劳动给企业带来的额外收益是劳动的边际产品与产品的边际收益的乘积。
6.显性成本与隐性成本；显性成本：是指厂商在生产要素市场上购买或租用所需要的生产要素的实际支出；隐性成本：是指厂商本身所拥有的且被用于该企业生产过程的那些生产要素的总价格。
中级微观经济学第五次作业+答案
中级微观经济学第 20 至 23 章作业
7、（刘）LAC 曲线（A）。 A.当 LMC＜LAC 时下降，而当 LMC＞LAC 时上升； B.通过 LMC 曲线的最低点； C. 随着 LMC 曲线下降而下降； D. 随着 LMC 曲线上升而上升。
说明：由长期供给曲线性质可知 8、（刘）短期条件下，厂商不能根据产量的要求调整固定的生产要素的投入量，所以短期成 本函数中就有总成本、（D）等区分。
解：（1）厂商的成本函数为TC Q3 6Q2 30Q 40
则 MC 3Q2 12Q2 30 ，又知 P=66 元。
根据利润极大化的条件 P=MC，有： 66 3Q2 12Q2 30 ，
解得：Q=6，Q=－2（舍去）。
最大利润为： TR TC PQ (Q3 6Q2 30Q 40) 176 （元）
中级微观经济学48题及答案【考研考博专用,必备48题!!】
第一部分 消费者选择理论1.有两种商品，x1和x2，价格分别为p1和p2，收入为m 。
当11x x ≥时，政府加数量税t,画出预算集并写出预算线2. 消费者消费两种商品（x1，x2），如果花同样多的钱可以买（4，6）或（12，2），写出预算线的表达式。
3．重新描述中国粮价改革（1）假设没有任何市场干预，中国的粮价为每斤0。
4元，每人收入为100元。
把粮食消费量计为x ，在其它商品上的开支为y ，写出预算线，并画图。
（2）假设每人得到30斤粮票，可以凭票以0。
2元的价格买粮食，再写预算约束，画图。
（3）假设取消粮票，补贴每人6元钱，写预算约束并画图。
4． 证两条无差异曲线不能相交5． 一元纸币（x1）和五元纸币（x2）的边际替代率是多少？6．若商品1为中性商品，则它对商品2的边际替代率？ 7. 写出下列情形的效用函数，画出无差异曲线，并在给定价格（p 1，p 2）和收入（m ）的情形下求最优解。
（1）x 1=一元纸币，x 2=五元纸币。
（2）x 1=一杯咖啡，x 2=一勺糖, 消费者喜欢在每杯咖啡加两勺糖。
8. 解最优选择（1） 21212(,)u x x x x =⋅（2）2u x =9. 对下列效用函数推导对商品1的需求函数，反需求函数，恩格尔曲线；在图上大致画出价格提供曲线，收入提供曲线；说明商品一是否正常品、劣质品、一般商品、吉芬商品，商品二与商品一是替代还是互补关系。
（1）212x x u +=（2）()212,m in x x u =（3）b a x x u 21⋅=（4） 12ln u x x =+,10.当偏好为完全替代时，计算当价格变化时的收入效用和替代效用（注意分情况讨论）。
11. 给定效用函数 (,)x y xy =，p x =3，p y =4，m=60，求当p y 降为3时价格变化引起的替代效应和收入效应。
12. 用显示偏好的弱公理说明为什么Slutsky 替代效应为负。
中级微观经济学45道题(含答案)
中级微观经济学期末考试复习题（版权归13企业管理班所有，翻版必究,哈哈！）1.实现委托代理最优合约设计的两个约束条件是什么?答：一种是代理人的个人理性约束，即委托人得保证让代理人不跳槽，安于经理岗位。
另一种是对代理人的激励相容约束，即让代理人自己去选择行动值a，使其期望的边际效用值达到最大.2、为何需求的价格弹性大于1时,降价能增加收益，而需求的价格弹性小于1时，涨价能增加收益,请给出数学证明。
答:需求的价格弹性公式为：由公式可知，当|e｜>1，即富于弹性时，MR<0，边际收益为负,即提高价格，收益降低，相反,降低价格则收益升高.当|e|<1，即缺乏弹性时,MR>0，边际收益为正，即提高价格，收益升高，相反，降低价格，收益变少。
3。
简述公共产品与私人产品的差异。
(微观经济学十八讲P352）答：公共品是指由公共部门提供用来满足社会公共需要的商品和服务。
公共品具有不可分割性、非竞争性和非排他性。
但是必须明确并不是全部的公共品都应由公共部门提供。
私人品是指那些具有效用上的可分割性，消费上的竞争性和受益上的排他性的产品。
公共品和私人品的区别在于，公共品是可以让一群人同时消费的物品,而私人品在任何时候只能为一个使用者提供效用。
4、毕加索油画的供给价格弹性是多少，为什么？答:弹性0,因为供给的价格弹性反映价格变动对供给数量变动的影响。
毕加索的油画是唯一的,因此，不管价格如何变动，供给为1，即供给不随价格变动而变动，弹性为0.5、完全竞争市场条件下，为什么行业中所有厂商的经济利润在长期均衡时都会为零?这是否意味着厂商的生产变得没有意义？西方经济学中所谓长期均衡时利润为零，是指经济利润为零,并不是会计利润为零。
所谓经济利润，通常也叫超额利润,就是一个厂商赚取了较之一般利润水平更高的利润。
之所以如此，这是因为，在西方经济学理论上，会计利润被计入厂商投入自有要素所应获得的报酬，是产品的隐含成本。
中级微观经济学习题解答最终版5精选全文完整版
可编辑修改精选全文完整版2、假设某消费者的效用函数为U XY =，X 和Y 表示两种商品，当效用为20单位、X 商品的消费量为5时，Y 商品的消费量是多少？这一商品消费组合对应的边际替代率是多少？如果这时的组合是达到消费者均衡的组合，那么X 和Y 两种商品的价格之比应为多少？① ∵U XY =当错误!未找到引用源。
=20时，由X=5得：错误!未找到引用源。
=80。
② 边际替代率Y X MU MU错误!未找到引用源。
11221=2X MU X Y -③ 达到均衡时，故：错误!未找到引用源。
. 3、已知效用函数为1U X Y αα-=，求商品的边际替代率MRS XY 和MRS YX ，并求当X 和Y 的数量分别为4和12时的边际替代率。
解：11113(1)(1)(1)(1)(1)(1)3X XY Y Y YX X MU X Y Y MRS MU X Y X MU X Y X MRS MU X Y Y αααααααααααααααααααα------====------====4、假设某消费者的效用函数为22(,)U U X Y X Y ==，消费者的预算线是X Y I P X P Y =+，试求该约束条件下的最优化问题，并推导出消费者均衡的一阶条件，再推导出用参数表示的X 和Y 的需求函数。
解：22max ..X YU X Y s t I P X P Y ⎧=⎨=+⎩ 22()X Y L X Y I P X P Y λ=+--220X L XY P Xλ∂=-=∂……（1） 220Y L X Y P Yλ∂=-=∂……（2） 0X Y L I P X P Y λ∂=--=∂……（3） （1）除于（2）可得：X YP Y X P =……（4） 由（4）得：X YP Y X P =……（5） 将（5）代入（3）得：2XI X P =……（6） 将（6）代入（5）得： 2Y I Y P =……（7） 答：（4）式为一阶条件，（6）、（7）式为需求函数。
中级微观经济学习题及答案
ANSWERS1 The Market1. Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. What would the demand curve look like?1.1. It would be constant at $500 for 25 apartments and then drop to $200.2. In the above example, what would the equilibrium price be if there were 24 apartments to rent? What if there were 26 apartments to rent?What if there were 25 apartments to rent?1.2. In the first case, $500, and in the second case, $200. In the third case, the equilibrium price would be any price between $200 and $500.3. If people have different reservation prices, why does the market demand curve slope down?1.3. Because if we want to rent one more apartment, we have to offer a lower price. The number of people who have reservation prices greater than p must always increase as p decreases.4. In the text we assumed that the condominium purchasers came from the inner-ring people—people who were already rentingapartments. What would happen to the price of inner-ring apartments if all of the condominium purchasers were outer-ring people—the people who were not currently renting apartments in the inner ring? 1.4. The price of apartments in the inner ring would go up since demand for apartments would not change but supply would decrease.5. Suppose now that the condominium purchasers were all inner-ring people, but that each condominium was constructed from two apartments. What would happen to the price of apartments?1.5. The price of apartments in the inner ring would rise.6. What do you suppose the effect of a tax would be on the number of apartments that would be built in the long run?1.6. A tax would undoubtedly reduce the number of apartments supplied in the long run.7. Suppose the demand curve is D(p) = 100−2p. What price would the monopolist set if he had 60 apartments? How many would he rent? What price would he set if he had 40 apartments? How many would he rent?1.7. He would set a price of 25 and rent 50 apartments. In the second case he would rent all 40 apartments at the maximum price the marketwould bear. This would be given by the solution to D(p) = 100−2p = 40, which is p∗ = 30.8. If our model of rent control allowed for unrestricted subletting, who would end up getting apartments in the inner circle? Would the outcome be Pareto efficient?1.8. Everyone who had a reservation price higher than the equilibrium price in the competitive market, so that the final outcome would be Pareto efficient.(Of course in the long run there would probably be fewer new apartments built, which would lead to another kind of inefficiency.)2 Budget Constraint1. Originally the consumer faces the budget line p1x1 + p2x2 = m. Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write down an equation for the new budget line in terms of the original prices and income.2.1. The new budget line is given by 2p1x1 +8p2x2 =4m.2. What happens to the budget line if the price of good 2 increases, but the price of good 1 and income remain constant?2.2. The vertical intercept (axis) decreases and the horizontalx2intercept (axis) stays the same. Thus the budget line becomes flatter.x13. If the price of good 1 doubles and the price of good 2 triples, does the budget line become flatter or steeper?2.3. Flatter. The slope is −2/3.p1p24. What is the definition of a numeraire good?2.4. A good whose price has been set to 1; all other goods’ prices are measured relative to the numeraire good’s price.5. Suppose that the government puts a tax of 15 cents a gallon on gasoline and then later decides to put a subsidy on gasoline at a rate of 7 cents a gallon. What net tax is this combination equivalent to?2.5. A tax of 8 cents a gallon.6. Suppose that a budget equation is given by += m. Thep1x1p2x2 government decides to impose a lump-sum tax of u, a quantity tax on good 1 of t, and a quantity subsidy on good 2 of s. What is the formula for the new budget line?2.6. (+ t)+(−s)= m−u.p1x1p2x27. If the income of the consumer increases and one of the prices decreases at the same time, will the consumer necessarily be at leastas well-off?2.7. Yes, since all of the bundles the consumer could afford before are affordable at the new prices and income.3 Preferences1. If we observe a consumer choosing (,) when (,) is availablex1x2y1y2one time, are we justified in concluding that (,)>(,)?x1x2y1y23.1. No. It might be that the consumer was indifferent between the two bundles. All we are justified in concluding is that (,)> (,).x1x2y1y22. Consider a group of people A, B, C and the relation “at least as tall as,” as in “A is at least as tall as B.” Is this relation transitive? Is it complete?3.2. Yes to both.3. Take the same group of people and consider the relation “strictly taller than.” Is this relation transitive? Is it reflexive? Is it complete? 3.3. It is transitive, but it is not complete—two people might be the same height. It is not reflexive since it is false that a person is strictly taller than himself.4. A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preferencerelation transitive? Is it complete?3.4. It is transitive, but not complete. What if A were bigger but slower than B? Which one would he prefer?5. Can an indifference curve cross itself? For example, could Figure 3.2 depict a single indifference curve?3.5. Yes. An indifference curve can cross itself, it just can’t cross another distinct indifference curve.6. Could Figure 3.2 be a single indifference curve if preferences are monotonic?3.6. No, because there are bundles on the indifference curve that have strictly more of both goods than other bundles on the (alleged) indifference curve.7. If both pepperoni and anchovies are bads, will the indifference curve have a positive or a negative slope?3.7. A negative slope. If you give the consumer more anchovies, you’ve made him worse off, so you have to take away some pepperoni to get him back on his indifference curve. In this case the direction of increasing utility is toward the origin.8. Explain why convex preferences means that “averages are preferred to extremes.”3.8. Because the consumer weakly prefers the weighted average of two bundles to either bundle.9. What is your marginal rate of substitution of $1 bills for $5 bills?3.9. If you give up one $5 bill, how many $1 bills do you need to compensate you? Five $1 bills will do nicely. Hence the answer is −5 or−1/5, depending on which good you put on the horizontal axis.10. If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?3.10. Zero—if you take away some of good 1, the consumer needs zero units of good 2 to compensate him for his loss.ANSWERS A1311. Think of some other goods for which your preferences might be concave.3.11. Anchovies and peanut butter, scotch and Kool Aid, and other similar repulsive combinations.4 Utility1. The text said that raising a number to an odd power was amonotonic transformation. What about raising a number to an even power? Is this a monotonic transformation? (Hint: consider the case f(u)=u^2.)4.1. The function f(u)=u^2 is a monotonic transformation for positive u, but not for negative u.2. Which of the following are monotonic transformations?(1) u =2 v−13;(2) u = −1/v^2;(3)u =1/v^2; (4)u = ln v; (5)u = −e^−v; (6)u = v^2; (7) u = v^2 for v>0; (8) u = v^2 for v<0.4.2. (1) Yes. (2) No (works for v positive). (3) No (works for v negative).(4) Yes (only defined for v positive). (5) Yes. (6) No. (7) Yes. (8) No.3. We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?)4.3. Suppose that the diagonal intersected a given indifference curve at two points, say (x,x) and (y,y). Then either x>y or y>x, which means that one of the bundles has more of both goods. But if preferences are monotonic, then one of the bundles would have to be preferred to the other.4. What kind of preferences are represented by a utility function of thex1+x2form u(x1,x2)=? What about the utility function v(x1,x2)= 13x1 + 13x2?4.4. Both represent perfect substitutes.5. What kind of preferences are represented by a utility function of thex2x2 form u(x1,x2)=x1 +? Is the utility function v(x1,x2)=x2 1 +2x1+x2 a monotonic transformation of u(x1,x2)?4.5. Quasilinear preferences. Yes.x1x26. Consider the utility function u(x1,x2)=. What kind of pref- erences does it represent? Is the function v(,)= ax1x2x12x22 monotonic transformation of u(,)? Is the function w(,) =x1x2x1x2x12a monotonic transformation of u(,)?x22x1x24.6. The utility function represents Cobb-Douglas preferences. No. Yes.7. Can you explain why taking a monotonic transformation of a utility function doesn’t change the marginal rate of substitution?4.7. Because the MRS is measured along an indifference curve, and utility remains constant along an indifference curve.5 Choice1. If two goods are perfect substitutes, what is the demand function forgood 2?5.1.=0 when>, = m/when <, and anything betweenx2 p2p1x2p2p2p10 and m/p2 when = .p1p22. Suppose that indifference curves are described by straight lines witha slope of −b. Given arbitrary prices and money income p1, p2, and m, what will the consumer’s optimal choices look like?5.2. The optimal choices will be x1 = m/p1 and x2 = 0 ifp1/p2 <b , x1 = 0 andx2 = m/p2 if p1/p2 >b, and any amount on the budget line if p1/p2 = b.3. Suppose that a consumer always consumes 2 spoons of sugar with each cup of coffee. If the price of sugar is p1 per spoonful and the price of coffee is p2 per cup and the consumer has m dollars to spend on coffee and sugar, how much will he or she want to purchase?5.3. Let z be the number of cups of coffee the consumer buys. Then we know that 2z is the number of teaspoons of sugar he or she buys. We must satisfy the budget constraint2z + z = m.p1p2Solving for z we havez =m2p1+ p2.4. Suppose that you have highly nonconvex preferences for ice cream and olives, like those given in the text, and that you face prices p1, p2 and have m dollars to spend. List the choices for the optimal consumption bundles.5.4. We know that you’ll either consume all ice cream or all olives. Thus the two choices for the optimal consumption bundles will be x1 = m/,p1 x2 = 0, or x1 = 0, x2 = m/.p25. If a consumer has a utility function u(x1,x2)=x1x4 2, what fraction of her income will she spend on good 2?5.5. This is a Cobb-Douglas utility function, so she will spend 4/(1 + 4) = 4/5 of her income on good 2.6. For what kind of preferences will the consumer be just as well-offfacing a quantity tax as an income tax?5.6. For kinked preferences, such as perfect complements, where the change in price doesn’t induce any change in demand.6 Demand1. If the consumer is consuming exactly two goods, and she is always spending all of her money, can both of them be inferior goods?6.1. No. If her income increases, and she spends it all, she must be purchasing more of at least one good.2. Show that perfect substitutes are an example of homotheticpreferences.6.2. The utility function for perfect substitutes is u(,)=+ .x1 x2 x1 x2Thus if u(,) >u (,), we have + >+ . It follows x1 x2 y1 y2 x1 x2 y1y2that t+ t> t+ t, so that u(t,t) >u (t, t).x1 x2 y1y2 x1 x2 y1y23. Show that Cobb-Douglas preferences are homothetic preferences.6.3. The Cobb-Douglas utility function has the property that u(t,t)=x1 x2= 2 = t 2 = t*u(x1,). ( t x1)a( t x2)1‒a t a t1‒a x1a x21‒a x1a x21‒a x2Thus if u(,) >u (,), we know that u(t,t) >u (t,), so x1 x2 y1 y2 x1 x2 y1t y2that Cobb-Douglas preferences are indeed homothetic.4. The income offer curve is to the Engel curve as the price offer curveis to ...?6.4. The demand curve.5. If the preferences are concave will the consumer ever consume bothof the goods together?6.5. No. Concave preferences can only give rise to optimal consumptionbundles that involve zero consumption of one of the goods.6. Are hamburgers and buns complements or substitutes?6.6. Normally they would be complements, at least for non-vegetarians.7. What is the form of the inverse demand function for good 1 in the case of perfect complements?6.7. We know that x1 = m/(p1 + p2). Solving for p1 as a function of the other variables, we have p1 = m x1 −p2.8. True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.6.8. False.7 Revealed Preference1. When prices are (p1,p2) = (1 ,2) a consumer demands (x1,x2) = (1 ,2), and when prices are ( q1,q2) = (2 ,1) the consumer demands (y1,y2) = (2 ,1). Is this behavior consistent with the model of maximizing behavior?7.1. No. This consumer violates the Weak Axiom of Revealed Preference since when he bought (x1,x2) he could have bought (y1,y2) and vice versa. In symbols:p1x1 + p2x2 =1×1+2×2=5> 4=1×2+2×1=p1y1 + p2y2andq1y1 + q2y2 =2×2+1×1=5> 4=2×1+1×2=q1x1 + q2x2.2. When prices are (p1,p2) = (2 ,1) a consumer demands (x1,x2) = (1 ,2), and when prices are ( q1,q2) = (1 ,2) the consumer demands (y1,y2) = (2 ,1). Is this behavior consistent with the model of maximizing behavior?7.2. Yes. No violations of WARP are present, since the y-bundle is not affordable when the x-bundle was purchased and vice versa.3. In the preceding exercise, which bundle is preferred by the consumer, the x-bundle or the y-bundle?7.3. Since the y-bundle was more expensive than the x-bundle when the x-bundle was purchased and vice versa, there is no way to tell which bundle is preferred.4. We saw that the Social Security adjustment for changing prices would typically make recipients at least as well-off as they were at the base year. What kind of price changes would leave them just as well-off, no matter what kind of preferences they had?7.4. If both prices changed by the same amount. Then the base-year bundle would still be optimal.5. In the same framework as the above question, what kind ofpreferences would leave the consumer just as well-off as he was in the base year, for all price changes?7.5. Perfect complements.8 Slutsky Equation1. Suppose a consumer has preferences between two goods that are perfect substitutes. Can you change prices in such a way that the entire demand response is due to the income effect?8.1. Yes. To see this, use our favorite example of red pencils and blue pencils. Suppose red pencils cost 10 cents a piece, and blue pencils cost 5 cents a piece, and the consumer spends $1 on pencils. She would then consume 20 blue pencils. If the price of blue pencils falls to 4 cents a piece, she would consume 25 blue pencils, a change which is entirely due to the income effect.2. Suppose that preferences are concave. Is it still the case that the substitution effect is negative?8.2. Yes.3. In the case of the gasoline tax, what would happen if the rebate to the consumers were based on their original consumption of gasoline, x, rather than on their final consumption of gasoline, x’?8.3. Then the income effect would cancel out. All that would be leftwould be the pure substitution effect,which would automatically be negative.4. In the case described in the preceding question, would the government be paying out more or less than it received in tax revenues?8.4. They are receiving tx’ in revenues and paying out tx, so they are losing money.5. In this case would the consumers be better off or worse off if the tax with rebate based on original consumption were in effect?8.5. Since their old consumption is affordable,the consumers would have to be at least as well-off. This happens because the government is giving them back more money than they are losing due to the higher price of gasoline.9 Buying and Selling1. If a consumer’s net demands are (5,−3) and her endowment is (4,4), what are her gross demands?9.1. Her gross demands are (9,1).2. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). There is a perfect market for the two goods in which they can be bought and sold costlessly. Will the consumernecessarily prefer consuming the bundle (y1,y2) = (3 ,5)? Will she necessarily prefer having the bundle (y1,y2)?9.2. The bundle (y1,y2) = (3 ,5) costs more than the bundle (4,4) at the current prices. The consumer will not necessarily prefer consuming this bundle, but would certainly prefer to own it, since she could sell it and purchase a bundle that she would prefer.3. The prices are (p1,p2) = (2 ,3), and the consumer is currently consuming (x1,x2) = (4 ,4). Now the prices change to (q1,q2) = (2 ,4). Could the consumer be better off under these new prices?9.3. Sure. It depends on whether she was a net buyer or a net seller of the good that became more expensive.4. The U.S. currently imports about half of the petroleum that it uses. The rest of its needs are met by domestic production. Could the price of oil rise so much that the U.S. would be made better off?9.4. Yes, but only if the U.S. switched to being a net exporter of oil.5. Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours (with luck this would happen shortly before exam week). How would this affect the budget constraint?9.5. The new budget line would shift outward and remain parallel to theold one, since the increase in the number of hours in the day is a pure endowment effect.6. If leisure is an inferior good, what can you say about the slope of the labor supply curve?9.6. The slope will be positive.10 Intertemporal Choice1. How much is $1 million to be delivered 20 years in the future worth today if the interest rate is 20 percent?10.1. According to Table 10.1, $1 20 years from now is worth 3 cents today at a 20 percent interest rate. Thus $1 million is worth .03×1,000,000 = $30,000 today.2. As the interest rate rises, does the intertemporal budget constraint be- come steeper or flatter?10.2. The slope of the intertemporal budget constraint is equal to −(1+r). Thus as r increases the slope becomes more negative (steeper).3. Would the assumption that goods are perfect substitutes be valid ina study of intertemporal food purchases?10.3. If goods are perfect substitutes, then consumers will only purchase the cheaper good. In the case of intertemporal food purchases, thisimplies that consumers only buy food in one period, which may not be very realistic.4. A consumer, who is initially a lender, remains a lender even after a decline in interest rates. Is this consumer better off or worse off after the change in interest rates? If the consumer becomes a borrower after the change is he better off or worse off?10.4. In order to remain a lender after the change in interest rates, the consumer must be choosing a point that he could have chosen under the old interest rates, but decided not to. Thus the consumer must be worse off.If the consumer becomes a borrower after the change, then he is choosing a previously unavailable point that cannot be compared to the initial point (since the initial point is no longer available under the new budget constraint), and therefore the change in the consumer’s welfare is unknown.5. What is the present value of $100 one year from now if the interest rate is 10%? What is the present value if the interest rate is 5%?10.5. At an interest rate of 10%, the present value of $100 is $90.91. At a rate of 5% the present value is $95.24.11 Asset Markets1. Suppose asset A can be sold for $11 next period. If assets similar to Aare paying a rate of return of 10%, what must be asset A’s current price?11.1. Asset A must be selling for 11/(1 + 0.10) = $10.2. A house, which you could rent for $10,000 a year and sell for $110,000 a year from now, can be purchased for $100,000. What is the rate of return on this house?11.2. The rate of return is equal to (10,000 + 10,000)/100,000 = 20%.3. The payments of certain types of bonds (e.g., municipal bonds) are not taxable. If similar taxable bonds are paying 10% and everyone faces a marginal tax rate of 40%, what rate of return must the nontaxable bonds pay?11.3. We know that the rate of return on the nontaxable bonds, r, must be such that (1−t)= r, therefore (1−0.40)*0.10 =0 .06 = r.r t4. Suppose that a scarce resource, facing a constant demand, will be exhausted in 10 years. If an alternative resource will be available at a price of $40 and if the interest rate is 10%, what must the price of the scarce resource be today?11.4. The price today must be 40/(1 +0 .10)^10 = $15.42.12 Uncertainty1. How can one reach the consumption points to the left of the endowment in Figure 12.1?12.1. We need a way to reduce consumption in the bad state and increase consumption in the good state. To do this you would have to sell insurance against the loss rather than buy it.2. Which of the following utility functions have the expected utility property? (a) u(c1,c2,π1,π2)=a(π1c1 + π2c2), (b) u(c1,c2,π1,π2)=π1c1 + π2c2 2, (c)u(c1,c2,π1,π2)=π1 lnc1 + π2 lnc2 + 17.12.2. Functions (a) and (c) have the expected utility property (they are affine transformations of the functions discussed in the chapter), while (b) does not.3. A risk-averse individual is offered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payment of $325. Which would he choose?12.3. Since he is risk-averse, he prefers the expected value of the gamble, $325, to the gamble itself, and therefore he would take the payment.4. What if the payment was $320?12.4. If the payment is $320 the decision will depend on the form of theutility function; we can’t say anything in general.5. Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles.12.5. Your picture should show a function that is initially convex, but then becomes concave.6. Why might a neighborhood group have a harder time self insuring for flood damage versus fire damage?12.6. In order to self-insure, the risks must be independent. However, this does not hold in the case of flood damage. If one house in the neighborhood is damaged by a flood it is likely that all of the houses will be damaged.13 Risky Assets1. If the risk-free rate of return is 6%, and if a risky asset is available with a return of 9% and a standard deviation of 3%, what is the maximum rate of return you can achieve if you are willing to accept a standard deviation of 2%? What percentage of your wealth would have to be invested in the risky asset?13.1. To achieve a standard deviation of 2% you will need to invest x = σx/σm =2 /3 of your wealth in the risky asset. This will result in a rate of return equal to (2/3)0.09 + (1−2/3)0.06 = 8%.2. What is the price of risk in the above exercise?13.2. The price of risk is equal to (rm −rf)/σm = (9− 6)/3 = 1. That is, for every additional percent of standard deviation you can gain 1% of return.3. If a stock has a β of 1.5, the return on the market is 10%, and the risk- free rate of return is 5%, what expected rate of return should this stock offer according to the Capital Asset Pricing Model? If the expected value of the stock is $100, what price should the stock be selling for today?13.3. According to the CAPM pricing equation, the stock should offer an expected rate of return of rf + β(rm−rf)=0.05 + 1.5(0.10−0.05) =0 .125 or 12.5%. The stock should be selling for its expected present value, which is equal to 100/1.125 = $88.89.14 Consumer’s Surplus1. A good can be produced in a competitive industry at a cost of $10 per unit. There are 100 consumers are each willing to pay $12 each to consume a single unit of the good (additional units have no value to them.) What is the equilibrium price and quantity sold? The government imposes a tax of $1 on the good. What is the deadweight loss of this tax?14.1. The equilibrium price is $10 and the quantity sold is 100 units. If the tax is imposed, the price rises to $11, but 100 units of the good will still be sold, so there is no deadweight loss.2. Suppose that the demand curve is given by D(p) = 10−p. What is the gross benefit from consuming 6 units of the good?14.2. We want to compute the area under the demand curve to the left of the quantity 6. Break this up into the area of a triangle with a base of 6 and a height of 6 and a rectangle with base 6 and height 4. Applying the formulas from high school geometry, the triangle has area 18 and the rectangle has area 24. Thus gross benefit is 42.3. In the above example, if the price changes from 4 to 6, what is the change in consumer’s surplus?14.3. When the price is 4, the consumer’s surplus is given by the area ofa triangle with a base of 6 and a height of 6; i.e., the consumer’s surplus is 18. When the price is 6, the triangle has a base of 4 and a height of 4, giving an area of 8. Thus the price change has reduced consumer’s surplus by $10.4. Suppose that a consumer is consuming 10 units of a discrete good and the price increases from $5 per unit to $6. However, after the pricechange the consumer continues to consume 10 units of the discrete good. What is the loss in the consumer’s surplus from this price change?14.4. Ten dollars. Since the demand for the discrete good hasn’t changed, all that has happened is that the consumer has had to reduce his expenditure on other goods by ten dollars.15 Market Demand1. If the market demand curve is D(p) = 100 − .5p, what is the inverse demand curve?15.1. The inverse demand curve is P(q) = 200−2q.2. An addict’s demand function for a drug may be very inelastic, but the market demand function might be quite elastic. How can this be?15.2. The decision about whether to consume the drug at all could well be price sensitive, so the adjustment of market demand on the extensive margin would contribute to the elasticity of the market demand.3. If D(p) = 12−2p, what price will maximize revenue?15.3. Revenue is R(p) = 12 p−2p2, which is maximized at p = 3.4. Suppose that the demand curve for a good is given by D(p) = 100/p. What price will maximize revenue?15.4. Revenue is pD(p) = 100, regardless of the price, so all prices maximize revenue.5. True or false? In a two good model if one good is an inferior good the other good must be a luxury good.15.5. True. The weighted average of the income elasticities must be 1, so if one good has a negative income elasticity, the other good must have an elasticity greater than 1 to get the average to be 1.16 Equilibrium1. What is the effect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?16.1. The entire subsidy gets passed along to the consumers if the supply curve is flat, but the subsidy is totally received by the producers when the supply curve is vertical.2. Suppose that the demand curve is vertical while the supply curve slopes upward. If a tax is imposed in this market who ends up paying it?16.2. The consumer.3. Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is。
中级微观经济学考试试题答案完整版
一．简答题1.机会成本相关答：是指为了得到某种东西而所要放弃另一些东西的最大价值。
在稀缺性的世界中选择一种东西意味着放弃其他东西。
一项选择的机会成本，也就是所放弃的物品或劳务的价值。
机会成本是指在资源有限条件下，当把一定资源用于某种产品生产时所放弃的用于其他可能得到的最大收益。
2.劣等品和低档品的逻辑推导（P78）答：低档品或劣等品（inferior goods）：指消费量随收入的上升而下降的物品。
对于正常商品，替代效应与价格呈反方向变动，收入效应也与价格成反方向变动，所以总效应与价格成反方向变动，因此正常商品的需求曲线向右下方倾斜。
对于低档品来说，替代效应与价格成反方向变动，收入效应与价格同向变动，但替代效应大于收入效应的作用，总效应与价格反方向变动，需求曲线向右下方倾斜。
吉芬商品，替代效应与价格反方向变动，收入效应与价格通向变动，收入效应极大地大于替代效应，使总效应与价格同向变动，其需求线向右上方倾斜。
二．计算题1.生产理论：已知企业的生产函数要素价格需求函数企业生产量求：市场长期均衡的产品价格和企业数量EG A: 已知生产函数为Q=KL-0.5L2—0.32K2，其中Q表示产量，K表示资本，L表示劳动，若K=10，求：（1）写出劳动的平均产量函数和边际产量函数。
（2）分别计算出当总产量、平均产量和边际产量达到极大值时，厂商雇佣的劳动量。
（3）证明当APL达到最大值时，APL=MPL=2AN A:（1）TP=Q=10L-0.5L^2-30 把K=10带进去边际产量（MPL ）函数 就是上式对L 求导。
MPL=10-L平均产量（APL ）函数 就是总产量除以投入的劳动。
APL=TP/L=10-0.5L-30/L（2）当TP 最大时，MPL=0。
令MPL=10-L=0 ，解得L=10，所以当劳动投入量L=10时，劳动的总产量TP 达到极大值。
当APL 最大时，是APL 与MPL 相交的时候。
令APL 的导数=0，解得L=2倍根号15（负值舍去），所以当劳动投入量L=2倍根号15 时，劳动的平均产量达到极大值。
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则拉格朗日辅助函数为：
s.t.
效用最大化的一阶条件为：
解上述方程可得： 所以，如果消费者的收入足够高，则收入的变化不会导致该消费者对商品 1 消费的变 化。
5、一个消费者被观察到当他面临的价格为
时，购买量为
；另
一次，当他面临的价格为
时，他的购买量为
。请问他的行为符
合显示性偏好弱公理吗？请解释原因。
解：他的行为符合显示性偏好弱公理。显示偏好弱公理指的是如果（x1,x2）被直接显示
x2
，
x1
m p1 2 p2
x2
，
2m p1 2 p2
解：（1）当 p1/p2>0.2 时，x1=0, x2=m/p2；
当 p1/p2=0.2 时， 当 p1/p2<0.2 时，x1=m/p1, x2=0
（2）
解得：
,
4、假设某消费者的效用函数为：
试问：给定商品 1 和商品 2 的价格为 和 ，如果该消费者的收入 足够高，则收入的变 化是否会导致该消费者对商品 1 的消费，并解释原因。 解：该消费者追求效用最大化，则有：
中级微观经济学第一次作业答案
1、假设政府对一个每月收入 400 美元的贫困家庭进行补贴。有三种方案：第一，允许该家
庭购买 400 美元的食品券，单位美元食品券的价格为 0.5；第二，政府直接发给该家庭 200
美元的食品券补贴；第三，政府直接发给该家庭 200 美元的货币补贴。画出三种方案下该
家庭的预算线，解释该家庭的最优选择，并分析三种方案的优劣。
s.t. 效用最大化时，边际效用之比等于价格之比，则有：
解得：
，
,
则收入用于商品 1 的比例为：
收入用于商品 2 的比例为：
（2）由（1）可知两种商品各自的需求函数为：
, （3）商品 1 的需求价格弹性为：
同理，商品 2 的需求价格弹性为：
7、在下列效用函数形式里，哪些是效用函数的单调变换？
（1） u 2v 13 ；（2） u 1/ v2 ；（3） u 1/ v2 ；（4） u ln v （5） u ev ；（6） u v2 ；（7） u v2 ，对于 v 0 ；（8） u v2 ，对于 v 0
解：（1）该学生对面包的需求函数为
，当
时，该学生
对面包的需求量为：
。
当价格从 p=4 上升到 p’=5 时，让使得该学生仍然买得起原来的面包消费量 x=6，他
3*18+5*4<3*20+5*10,说明在价格为（3,5）时，消费者（20,10）是该消费者支付不起的。 所以他的行为符合显示偏好弱公理。
6、我们用 和 表示消费者对商品 和 的消费数量。现在给定消费者的效用函数为 ，两种商品的价分别为 和 ，消费者的收入为 。
（1）求该消费者将收入的多大比例分别用于消费 和 ； （2）求消费者对 和 的需求函数； （3）当消费者均衡时，两种商品的需求价格弹性是多少？ 解：（1）消费者追求效用最大化，则有：
好于（y1,y2），且（x1,x2）和（y1,y2）不相同，那么，（y1,y2）就不可能被直接显示
偏好于（x1,x2）。换句话说，假定一个消费束（x1,x2）是按价格（p1,p2）购买的，另一
个 消 费 束 是 按 价 格 （ q1,q2 ） 购 买 的 ， 只 要 有 p1x1+p2x2>=p1y1+p2y2, 就 不 可 能 再 有
2、请画出以下各位消费者对两种商品（咖啡和热茶）的无差异曲线。
（1）消费者 A 喜欢喝咖啡，对喝热茶无所谓；
（2）消费者 B 喜欢 1 杯热茶和 1 杯咖啡一起喝；
（3）消费者 C 认为，在任何情况下，1 杯热茶和 2 杯咖啡是无差异的；
（4）消费者 D 喜欢喝咖啡，讨厌喝热茶。
解：（1）
（2）
U1 U2 U3
解：
Y（美元）
A
E3
E2 C
200
E1
D
200
400
B
U3
U2 U1
F（美元）
如上图所示，横轴表示花费在食品上的货币数量，纵轴表示花费在其他商品上的货币 量，初始预算线为 CD。
第一种补贴方案下，该家庭可以用 200 美元购买 400 美元的食品券，因此预算线变为 折线 CE1B，最优选择为 E1 点，效用水平为 U1；
q1x1+q2x2>=q1y1+q2y2。
在本题中，当价格（2,6）时，20*2+10*6>18*2+4*6 说明消费者有能力购买（18,4）
这个消费束，却选择了（20,10）这个消费束。这表明，在价格为（2,6）时，（20,10）比
（18,4）更受该消费者偏好；当价格为（3,5）时，他选择了消费束（ 18,4），并且
第二种补贴方案下，政府直接发放给该家庭 200 美元食品券补贴，因此预算线变为 CE2B，最优选择为 E2 点，效用水平为 U2；
第三种补贴方案下，政府直接发放给该家庭 200 美元的货币补贴，因此预算线直接平 移到 AB，最优选择为 E3 点，效用水平为 U3。
综上所述，因为 U3>U2>U1,所以对于该家庭而言，第三种方案最好，第二种方案次之， 第一种方案最差。
解：（1）、（4）、（5）、（7）
8、某人的效用函数为
，购买 和 两种商品，月收入为 120 元，
。
（1）为获得最大的效用，应如何选择商品 和 的组合；
（2）货币的边际效用和总效用各是多少；
（3） 的价格提高 30%， 的价格不变，他必须增加多少收入才能保持原有效用不变。
解：（1）由效用最大化原则有：
拉格朗日函数为： 效用最大化的一阶条件为：
s.t.
解得：x=30,y=20 （2）总效用为：
货币的边际效用为： （3）若 的价格提高 30%，则
阶条件为：
。在新的价格之下，效用最大化的一
再加上方程： 则收入应增加：
,可解得
9、假设某个学生的月收入为 包的价格为 。
元，他对面包的需求函数为
，面
（1）当面包的价格从 上升到 时，为使该学生仍然买得起原来的面包消费量，他 的收入应该增加多少； （2）请计算面包价格上升的斯勒茨基（Slutsky）替代效应； （3）请计算收入效应。
热茶
U1
U2
U3
热茶
（3）
热茶 U3
U2 U1
咖啡
（4）
咖啡
热茶
U1
U2
U3
咖啡
咖啡
3、写出下列情形的效用函数，画出无差异曲线，并在给定价格（p1，p2）和收入（m）的 情形下求最优解。
（1）x1=一元纸币，x2=五元纸币。
（2）x1=一杯咖啡，x2=一勺糖, 消费者喜欢在每杯咖啡加两勺糖。
u
x1,