中级微观经济学习题及答案

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中级微观经济学习题答案

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48题及答案【考研考博专用,必备48题!!】

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45道题(含答案)

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。

中级微观经济学复习题及答案

中级微观经济学复习题及答案

一、简述题1.如果我们看到在(1y ,2y )可以同时得到的情况下,消费者却选择了(1x ,2x ),那么,(1x ,2x ) (1y ,2y )的结论是否正确?(第二章,题1) 答:不正确,因为也可能是消费者恰好在这两个消费束之间无差异。

也就是说,根据题目的已知条件我们只能断定(1x ,2x ) (1y ,2y ),这是弱偏好。

对本题加上什么样的假设前提,题目中的断定就是正确的?如果加上消费者的偏好是严格凸的这一限制条件,断定(1x ,2x ) (1y ,2y )就是正确的。

因为严格凸性条件下,最优解若存在则只有一个。

2.若某个消费者的偏好可以由效用函数22121122(,)10(2)50u x x x x x x =++-来描述,那么对消费者而言,商品1和商品2是完全替代的吗?为什么?(第二章,题5)答:两种商品完全替代即它们的边际替代率为常数。

边际替代率是在消费者保证效用相等的条件下,用一种商品替代另一种商品的比率。

因此有: 商品1的边际效用为MU 1=du /dx 1=10(2x 1 +2 x 2)商品2的边际 效用为MU 2= du /dx 2=10(2x 1 +2 x 2)商品1对商品2的边际替代率MRS 12= MU 1 / MU 2 =1。

满足完全替代品的效用函数特征,因此这个说法是正确的。

3.假定消费者购买x 和y 两种商品,起初,x x y yMU P MU P =,若x P 下降,y P 保持不变,再假定x 的需求价格弹性大于1,则y 的购买量会不会发生变化?(第三章,题3)答:原来消费处于均衡状态。

设消费者花在x 商品上的支出为1m ,则1x m p x =。

对该式求x p 的导数有,11x x x x x p dm dx dx p x x dp dp dp x ⎡⎤=+=+⎢⎥⎣⎦,因x 的需求价格弹性大于1(绝对值),所以有10x dm dp <,即随着价格下降,消费者花在x 商品上的支出会增加。

中级微观经济学习题及部分答案

中级微观经济学习题及部分答案

中级微观经济学习题及部分答案一、单项选择题(每题0.5分,共15分,将正确答案填入答题纸上)1.有下列因素除哪一种外都会使需求曲线移动?(B)a消费者收入变化;b商品价格变化;c消费者偏好变化;d其他相关商品价格变化。

2.假定某耐用消费品的需求函数Qd=400-5P时的均衡价格为50,当需求函数变为Qd=600-5P时,(供给不变)均衡价格将(B)a低于50b高于50c等于50d不变3.下列命题中哪个是规范经济学的命题?(A)a.征税对中等收入家庭是不公平的c.1982年8月政府把贴现率降到10%b.1981年失业率超过9%d.社会保险税的课税依据现已超过30000美元4.当供求力量自由作用时,一次谷物歉收通过什么显示在市场上?(B)a.政府规定的购买量限制b.谷物价格上涨c.劝说人们减少购买量的广告d.谷物贸易量的增加5.某月内,X商品的替代品的价格上升和互补品的价格上升,分别引起X商品的需求变动量为50单位和80单位,则在它们共同作用下该月X商品需求数量:(B)。

a.增加30单位b.减少30单位c.增加130单位d.减少130单位6.在完全竞争市场中,(C)。

a.消费者是价格接受者,而企业不是b.消费者和企业都不是价格接受者c.消费者和企业都是价格接受者d.企业是价格接受者,而消费者不是/doc/3914130.html,C曲线(A)。

a.当LMC<LAC时下降,而当LMC>LAC时上升b.随LMC曲线下降而下降c.随LMC曲线上升而上升 d.通过LMC曲线的最低点8.一个企业在以下哪种情况下应该关闭?(A)a.P<A VCb.P<SACc.发生亏损时d.SMC>MR9.寡头垄断和垄断竞争之间的主要区别是(C)。

a.厂商的广告开支不同b.非价格竞争的种类不同c.厂商之间相互影响的程度不同d.以上都不对10.短期内,完全竞争厂商只能通过对(D)调整来实现最大利润。

a.生产规模b.价格c.全部生产要素d.产量11.不完全竞争市场中出现低效率的资源配置是因为产品价格(A)边际成本a.大于b.小于c.等于d.大于或等于12.当市场处于长期均衡状态时,向右下方倾斜的需求曲线相切于长期平均成本的最低点的左边,产品的价格等于生产的平均成本,产品产量较高但存在多余的生产能力,则该市场属于下列哪一类(B)。

中级微观经济学习题答案

中级微观经济学习题答案

中级微观经济学习题答案第⼀部分消费者理论1. 当11x x ≥时,加数量税t,画出预算集并写出预算线预算集:).....(..........112211x x m x p x p ≤≤+).........(..........)(1112211x x x t m x p x t p ≥+≤++ 2. 如果同样多的钱可以买(4,6)或(12,2),写出预算线。

m x p x p≤+2211 则有 m p p =+2164,m p p =+21212不妨假设12=p ,则可解得:8,211==m p 。

预算线为82121=+x x3.(1)0.4100x y +=(2)0.2100.............300.4106.............30x y if x x y if x +=≤??+=>?(3)0.4106x y +=4. 证明:设两条⽆差异曲线对应的效⽤分别为21,u u ,由曲线的单调性假设,若21u u =,则实为⼀条曲线。

若21u u ≠,假设两曲线相交,设交点为x ,则21)(,)(u x u u x u ==,可推出21u u =,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 utility function, ()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 written as()121112max ,..u x x s t p x p x m+≤③ Because 5p1=p2, any bundle ()12,x x which satisfies the budget constraint, is the solution 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 as()12121,min ,2u x x x x ??=The problem of the consumer is()121112max ,..u x x s t p x p x m+≤Any solution should satisfies the rule that 1212, 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。

中级微观经济学习题及答案

中级微观经济学习题及答案

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 ?rst 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 di?erent reservation prices, why does the market demand curve slope down?1.3. Because if we want to rent one more apartment, we have to o?er 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 e?ect 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 e?cient?1.8. Everyone who had a reservation price higher than the equilibrium price in the competitive market, so that the ?nal outcome would be Pareto e?cient.(Of course in the long run there would probably be fewer new apartments built, which would lead to another kind of ine?ciency.)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 ?atter.x13. If the price of good 1 doubles and the price of good 2 triples, does the budget line become ?atter or steeper?2.3. Flatter. The slope is ?2/3.p1p24. What is the de?nition 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-o??2.7. Yes, since all of the bundles the consumer could a?ord before are a?ordable at the new prices and income.3 Preferences1. If we observe a consumer choosing (,) when (,) is availablex1x2y1y2one time, are we justi?ed in concluding that (,)>(,)?x1x2y1y23.1. No. It might be that the consumer was indi?erent between the two bundles. All we are justi?ed 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 re?exive? Is it complete? 3.3. It is transitive, but it is not complete—two people might be the same height. It is not re?exive 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 indi?erence curve cross itself? For example, could Figure 3.2 depict a single indi?erence curve?3.5. Yes. An indi?erence curve can cross itself, it just can’t cross another distinct indi?erence curve.6. Could Figure 3.2 be a single indi?erence curve if preferences are monotonic?3.6. No, because there are bundles on the indi?erence curve that have strictly more of both goods than other bundles on the (alleged) indi?erence curve.7. If both pepperoni and anchovies are bads, will the indi?erence 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 o?, so you have to take away some pepperoni to get him back on his indi?erence 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 de?ned 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 indi?erence curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indi?erence curve twice?)4.3. Suppose that the diagonal intersected a given indi?erence 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 indi?erence curve, and utility remains constant along an indi?erence 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 indi?erence 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, 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 co?ee. If the price of sugar is p1 per spoonful and the price of co?ee is p2 per cup and the consumer has m dollars to spend on co?ee and sugar, how much will he or she want to purchase?5.3. Let z be the number of cups of co?ee 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-o?facing 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 o?er curve is to the Engel curve as the price o?er 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.。

《中级微观经济学》试题与答案

《中级微观经济学》试题与答案

《中级微观经济学》试题与答案一、名词解释(5道题)1. 消费者剩余-解释:消费者愿意支付的最高价格与实际支付价格之间的差额,是消费者获得的净收益。

2. 边际替代率-解释:消费者在维持同一效用水平的情况下,愿意用一种商品替代另一种商品的比率。

3. 规模经济-解释:当企业的生产规模扩大时,平均成本随着产量的增加而下降的现象。

4. 纳什均衡-解释:在博弈论中,每个参与者在给定其他参与者策略的情况下,所选择的最佳策略组合。

5. 帕累托最优-解释:资源配置的一种状态,无法在不使任何人变得更差的情况下,使某些人变得更好。

二、填空题(5道题)1. 在短期生产函数中,边际产量递减规律是指(在其他投入固定时,增加一个单位可变投入,产量的增加量递减)。

2. 供给弹性大于1表示(供给是弹性的)。

3. 无差异曲线上的点表示(消费者获得相同效用的不同商品组合)。

4. 在完全竞争市场中,长期均衡时,企业的经济利润是(零)。

5. 价格上限政策可能导致的直接结果是(商品短缺)。

三、单项选择题(5道题)1. 下列哪一项不是完全竞争市场的特征?()。

- A. 大量的买者和卖者- B. 同质产品- C. 自由进入和退出市场- D. 厂商具有定价权-答案:D2. 在长期,完全竞争市场中的企业会选择生产在()。

- A. 平均成本最低的产量- B. 边际成本最低的产量- C. 平均总成本等于价格的产量- D. 边际成本等于价格的产量-答案:D3. 如果一种商品的需求是价格无弹性的,那么价格上升10%将导致需求量()。

- A. 增加10%- B. 减少10%- C. 减少少于10%- D. 减少多于10%-答案:C4. 在垄断市场中,垄断者的利润最大化产量是()。

- A. 边际成本等于价格- B. 边际收益等于价格- C. 边际收益等于边际成本- D. 平均成本等于边际成本-答案:C5. 在短期内,完全竞争企业的供给曲线是()。

- A. 平均总成本曲线- B. 平均可变成本曲线- C. 边际成本曲线- D. 边际成本曲线位于平均可变成本曲线之上的部分-答案:D四、多项选择题(5道题)1. 影响需求的主要因素有()。

中级微观经济学复习题与答案

中级微观经济学复习题与答案

一、简述题1.如果我们看到在(1y ,2y )可以同时得到的情况下,消费者却选择了(1x ,2x ),那么,(1x ,2x )(1y ,2y )的结论是否正确?(第二章,题1)答:不正确,因为也可能是消费者恰好在这两个消费束之间无差异。

也就是说,根据题目的已知条件我们只能断定(1x ,2x )(1y ,2y ),这是弱偏好。

对本题加上什么样的假设前提,题目中的断定就是正确的?如果加上消费者的偏好是严格凸的这一限制条件,断定(1x ,2x )(1y ,2y )就是正确的。

因为严格凸性条件下,最优解若存在则只有一个。

2.若某个消费者的偏好可以由效用函数22121122(,)10(2)50u x x x x x x =++-来描述,那么对消费者而言,商品1和商品2是完全替代的吗?为什么?(第二章,题5)答:两种商品完全替代即它们的边际替代率为常数。

边际替代率是在消费者保证效用相等的条件下,用一种商品替代另一种商品的比率。

因此有:商品1的边际效用为MU 1=du /dx 1=10(2x 1 +2 x 2)商品2的边际 效用为MU 2= du /dx 2=10(2x 1 +2 x 2)商品1对商品2的边际替代率MRS 12= MU 1 / MU 2 =1。

满足完全替代品的效用函数特征,因此这个说法是正确的。

3.假定消费者购买x 和y 两种商品,起初,x x y yMU P MU P =,若x P 下降,y P 保持不变,再假定x 的需求价格弹性大于1,则y 的购买量会不会发生变化?(第三章,题3)答:原来消费处于均衡状态。

设消费者花在x 商品上的支出为1m ,则1x m p x =。

对该式求x p 的导数有,11x x x x x p dm dx dx p x x dp dp dp x ⎡⎤=+=+⎢⎥⎣⎦,因x 的需求价格弹性大于1(绝对值),所以有10xdm dp <,即随着价格下降,消费者花在x 商品上的支出会增加。

中级微观经济学习题答案

中级微观经济学习题答案

第一部分 消费者理论1. 当11x x ≥时,加数量税t,画出预算集并写出预算线 预算集:).....(..........112211x x m x p x p ≤≤+).........(..........)(1112211x x x t m x p x t p ≥+≤++ 2. 如果同样多的钱可以买(4,6)或(12,2),写出预算线。

m x p x p ≤+2211 则有 m p p =+2164,m p p =+21212不妨假设12=p ,则可解得:8,211==m p 。

预算线为82121=+x x3.(1)0.4100x y +=(2)0.2100.............300.4106.............30x y if x x y if x +=≤⎧⎨+=>⎩(3)0.4106x y +=4. 证明:设两条无差异曲线对应的效用分别为21,u u ,由曲线的单调性假设,若21u u =,则实为一条曲线。

若21u u ≠,假设两曲线相交,设交点为x ,则21)(,)(u x u u x u ==,可推出21u u =,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 utility function, ()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 written as()121112max ,..u x x s t p x p x m+≤③ Because 5p1=p2, any bundle ()12,x x which satisfies the budget constraint, is the solution 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 as()12121,min ,2u x x x x ⎧⎫=⎨⎬⎩⎭The problem of the consumer is()121112max ,..u x x s t p x p x m+≤Any 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。

中级微观经济学习题与答案

中级微观经济学习题与答案
1 The Market 1. 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.
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. 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.

中级微观经济学考试试题答案完整版

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。

中级微观经济学例题及答案

中级微观经济学例题及答案
1 ,q=4 12
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时的消费者剩余。
11
解: (1)
MU
U 1 0.5 U q , 3 Q 2 M
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=(180-160)/(100-80)×(80+100)/(160+180)=0.53
3、 假定下表是供给函数 Qs=-3+2P 在一定价格范围内 的供给表。 某商品的供给表 价格 (元) 供给量 性。 (2) 根据给出的供给函数,求 P=4 是的供给的价格 点弹性。 (3) 根据该供给函数或供给表作出相应的几何图 形,利用几何方法求出 P=4 时的供给的价格点 弹性。它与(2)的结果相同吗? 解:(1) (2)
7
(3)若某工会愿意接纳张某为会员,会费为 100 元,但张某可以 50%的价格购买 X,则张某是否应该 加入该工会? 解:(1)由效用函数 U=X2Y2 可得 MUX=2XY2,MUY =2YX2 消费者均衡条件为 MUX/MUY =2XY2/2YX2 =Y/X=Px/Py =2/5 500=2·X+5·Y 可得 X=125 者均衡。 (2)消费者可以原价格的 50%购买 X,意味着商品 X 的价格发生变动,预算约束线随之变动。消费者均 衡条件成为: Y/X=1/5 500=1·X+5·Y 可得 X=250 Y=50 张某将消费 250 单位 X,50 单位 Y。 (3)张某收入发生变动,预算约束线也发生变动。 消费者均衡条件成为:

中级微观经济学期末考试及答案

中级微观经济学期末考试及答案

中级微观经济学期末考试及答案一、选择题(每题2分,共20分)1、当某消费者对商品W的消费达到饱和点时,则边际效用MUₓ为( C )A、正值B、负值C、零D、不确定2、当吉芬商品的价格上升时,应该有( B )A、替代效应为正值,收入效应为负值,且前者的作用大于后者B、替代效应为负值,收入效应为正值,且前者的作用小于后者C、替代效应为负值,收入效应为正值,且前者的作用大于后者D、替代效应为正值,收入效应为负值,且前者的作用小于后者3、对于生产函数Q=F(L,K)和成本方程C=WL+RK来说,在最优的生产要素组合点上应该有( ABC )A、等产量曲线和成本线相切B、 MRTSᴋʟ=W/RC、MP ʟ/W=MP ᴋ/RD、MP ʟ=MP ᴋ4、在短期成本曲线图形中,从原点出发的射线与TC曲线相切的点上,必有( BCD )A、MC曲线处于下降阶段B、AC最小C、AC=MCD、MC曲线处于上升阶段5、对于完全竞争厂商,如果在厂商的短期产量是,AR小于SAC但大于AVC,则厂商( B )A、亏损,立即停产B、亏损,但继续生产C、亏损,生产或不生产都行D、获得正常利润,继续生产6、垄断厂商实现利润最大化的均衡条件是( C )A、MR=ACB、AR=ACC、MR=MCD、AR=MC7、在垄断厂商的长期均衡点上,不可能出现的情形是( B )A、价格P大于LACB、价格P等于最小的LACC、价格P小于LACD、AR大于MR8、市场失灵的表现是( ABCD )A、信息不完全B、存在垄断C、公共物品生产D、外部性9、在非完全竞争的产品市场,企业的边际收益线( A )A.向右下方倾斜,在AR的下方B.向右上方倾斜,在AR的下方C.平行于横轴,在AR的上方D.不能确定10、当边际产量大于平均产量时,平均产量( C )A.递减 B不变 C.递增 D先增后减二、判断题(每题1分,共10分)1、西方经济学所说的吉芬商品是一种劣等品。

中级微观经济学题库及答案

中级微观经济学题库及答案

中级微观经济学题库及答案一、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。

7.机会成本与会计成本;会计成本:是指企业财务人员记载的、企业运行过程中所发生的每一笔成本和费用;机会成本:是指生产者所放弃的使用相同要素在其他生产用途上所能得到的最高收入;8.生产者剩余与消费者剩余;生产者剩余:所有生产单位商品的市场价格和边际成本之间的差额。

消费者剩余:指消费者愿意为某一物品支付的最高价格与它的市场价格之间的差额。

9.规模经济与规模报酬;规模经济指的是企业在生产过程中能够以低于双倍的成本获得双倍产出。

规模报酬是指在其他条件不变的情况下,企业内部各种生产要素按相同比例变化时所带来的产量变化。

规模经济与规模报酬的区别在于,规模报酬是指所有投入品增加一倍,产出增加量超过一倍;规模经济所指是成本增加一倍,产出增加超过一倍。

也就是说,规模经济不一定是所有投入同比例增加,但它包括了所有投入品同比例增加一倍的情形。

中级微观经济学考题及答案

中级微观经济学考题及答案

中级微观经济学考题及答案
1. 何为微观经济学?
微观经济学是研究个体之间的经济行为的学科,旨在了解单个人、家庭、公司和其他组织如何做出经济决定,以及如何受到政府政策和
其他因素的影响。

该学科利用统计技术和模型,以及涉及决策行为的
理论分析,来分析经济活动。

它也研究如何应用经济政策来影响经济
绩效和人民生活。

2. 市场均衡与价格敏感
市场均衡是指市场中购买者和销售者都在一定价格下能获得最大
利益的一种经济状态。

价格敏感性是指消费者在价格的变动性的程度,也就是说,当价格上升时,消费者购买的量会减少。

市场均衡和价格
敏感性之间存在直接关系,当价格敏感性增大时,消费者对价格变化
会有密切关注,进而影响市场均衡。

3. 动态效用和信息不对称
动态效用指的是由于消费者向高效用的货物和服务偏爱的行为,
使其短期的满意度增加而长期的满意度降低的状态。

信息不对称指的
是消费者在购买时无法获得完整的可靠信息,导致其在决策过程中受到巨大的影响的状况。

动态效用和信息不对称之间存在联系,当消费者在购买中缺乏信息时,他们会关注动态效用,从而做出更糟糕的决策。

4. 最优消费艺术和最优生产艺术
最优消费艺术是指消费者以最大限度满足他们欲望的最有效价格分配货物和服务的方式,可以以最少成本实现最大收益。

最优生产艺术指的是采取最有效的生产方式和技术,以最小的成本获得最大的收益。

最优消费艺术和最优生产艺术的实现都受到道德和法律的限制,二者之间也存在着联系,一方面,最优生产需要有效的资源配置,来满足消费需求;另一方面,最优消费除了遵循经济模型外,还需考虑在效用函数中考虑善恶和道德行为等因素。

中级微观经济学作业及标准答案

中级微观经济学作业及标准答案

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。

解: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;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。

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。

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。

U (x )=x 1+5x 2(2)x1=一杯咖啡,x2=一勺糖, 消费者喜欢在每杯咖啡加两勺糖。

()12121,min ,2u x x x x ⎧⎫=⎨⎬⎩⎭,1122m x p p =+,21222m x p p =+ 解:(1)当p1/p2>0.2时,x1=0, x2=m/p2;当p1/p2=0.2时,(x 1,x 2)={(x 1,x 2)|p 1x 1+p 2x 2=m,x 1>0,x 2>0} 当p1/p2<0.2时,x1=m/p1, x2=0(2){x 1=12x 2=mp 1x 1+p 2x 2=m解得:x 1=m p 1+2p 2, x 2=2mp 1+2p 24、假设某消费者的效用函数为:U (x 1,x 2)=lnx 1+x 2试问:给定商品1和商品 2 的价格为p 1和p 2,如果该消费者的收入I 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。

中级微观经济学(1-4章习题及答案)

中级微观经济学(1-4章习题及答案)

(1) 将 1代入 CES 函数,立即得到 y A1x1 A 2x 2 ,这是线性函数。
(2)当 0 时,CES 函数成为不定式,为求其极限,对 CES 函数取对数。
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内容,参照显示偏好内容进行理解)
提示:假设现在收藏家在( M* , X* )处达到均衡,其中 M 指钱币数量, X 是所有其他消费
品(的支出)。在图中,预算线与一条无差异曲线I* 相切。如果 pM 上升, pM/pX 增大,预 算约束线较以前陡峭,但它必然还通过( M* ,X* )点,因为这点的坐标满足预算线方程[注
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中级微观经济学题库及答案

中级微观经济学题库及答案

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定, 只讲经济运行的内在规律, 也就就是回答“就是什么”的问题; 实证分析方法的一个基本特点它提出的问题就是可以测试真伪的站得住脚, 它必需符合规律并能接受体会数据的检验;, 假如一个命题规范分析方法: 规范分析以价值判定为基础, 以某种标准为分析处理经济问题的动身点, 回答经济现象“应当就是什么”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;无差异曲线就是指这样一条曲线, 尽管它上面的每一点所代表的商品组合就是不同的, 但消费者从中得到的满意程度却就是相同的;等产量线表示曲线上每一点的产量都相等的曲线;, 就是由生产出同一产量的不同投入品组合所形成3,希克斯补偿与斯卢茨基补偿;希克斯补偿就是指当商品价格发生变化后斯卢茨基补偿就是指当商品价格发生变化后, 要维护原有效用水平所需补偿的货币数量;, 要维护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;边际替代率就是指, 消费者在增加额外一单位商品X之后, 如要保持满意水平不变而必需舍弃的商品Y的数量;边际替代率就等于无差异曲线在该点的斜率的肯定值;边际技术替代率就是指, 当只有一种投入品可变时, 要增加产量, 企业必需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;等产量线斜率的肯定值就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位的投入, 就就是指在其她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, 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;边际收益产出就是指际收益的乘积;, 额外单位劳动给企业带来的额外收益就是劳动的边际产品与产品的边6,显性成本与隐性成本;显性成本: 就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: 就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;; 7,机会成本与会计成本;会计成本: 就是指企业财务人员记载的,企业运行过程中所发生的每一笔成本与费用机会成本: 就是指生产者所舍弃的使用相同要素在其她生产用途上所能得到的最高收入;;8,生产者剩余与消费者剩余;生产者剩余: 全部生产单位商品的市场价格与边际成本之间的差额;消费者剩余: 指消费者情愿为某一物品支付的最高价格与它的市场价格之间的差额;9,规模经济与规模酬劳;规模经济指的就是企业在生产过程中能够以低于双倍的成本获得双倍产出;规模酬劳就是指在其她条件不变的情形下的产量变化;, 企业内部各种生产要素按相同比例变化时所带来规模经济与规模酬劳的区分在于倍; 规模经济所指就是成本增加一倍, 规模酬劳就是指全部投入品增加一倍, 产出增加超过一倍;也就就是说, 产出增加量超过一, 规模经济不肯定就是全部投入同比例增加, 但它包括了全部投入品同比例增加一倍的情形;10,纳什均衡与上策均衡 ;纳什均衡 : 在给定它的竞争者的行为以后 , 各企业均实行它所能实行的最好的策略;上策均衡 : 当全部博弈方实行的策略都就是不管其她博弈方做什么 策略时 , 博弈所实现的均衡;, 对它而言都就是最优的 11,帕累托有效与帕累托改进 ;假如商品的配置在不使另一些人境况变糟的情形下就不能使某些人的境况变好 就是帕累托有效的;, 这种配置就 假如存在一种可行的贸易 , 使交易双方能够互利 , 或者在不损害一方利益的前提下使另一方 获利 , 就称这种贸易为帕累托改进;12,福利经济学第肯定理与福利经济学其次定理福利经济学第肯定理 : 假如每个人都在竞争性市场上进行贸易 , 就全部互利的贸易都将得以 完成 , 并且其产生的均衡资源配置在经济上将就是有效率的;福利经济学其次定理 : 假如个人的偏好就是凸的 , 就每种有效配置 ( 契约曲线上的每一点 ) 对 于某些商品的初始配置来说都就是竞争性均衡;二,简述或分析题4,以下哪些生产函数具有规模酬劳不变的特性 :X 2 ) 2 ;这里 Y 2 M in { X 1, X 2} Y X 1 X ;(3) Y X 1 X 2 ;(4) Y (1 X 1 (1) ;(2) 2 Y 代表产量 , X 1 , X 2 就是两个生产要素的使用量;答 : 如 F (tK, tL) = t F (K, L), 就规模酬劳不变;1, X 2}=2Min{tX 1, tX 2} 具有规模酬劳不变的特性(1)tY=2tMin{X 5,重复博弈就是实现博弈合作均衡的充分条件不?为什么?重复博弈就是否都能实现合作的博弈均衡呢?回答就是否定的; 重复博弈要实现合作的 博弈均衡仍必需满意以下三个条件 :第一 : 博弈必需重复无穷次或者博弈双方根本不知道博弈何时终止;其次 , 博弈双方都实行“冷酷战略” ;即博弈双方从挑选合作开头 , 只要对方始终合作 , 另一方也会始终合作下去 直至永久 ;, 如发觉对方偷偷实行了不合作的策略 , 便由此实行不合作的策略 第三 , 贴现因子 1/(1+r) 足够大6,结合图形推导简要说明为个体劳动供应曲线向后弯曲的缘由;依据劳动者的最优化行为 , 对应于一个特定的工资率 , 劳动者在效用最大化点上确定最 优劳动供应量 , 从而得到劳动的供应曲线 , 在工资水平较低时 , 工资率上升对劳动所产生的替 代效应大于收入效应 , 因而人们情愿供应更多的劳动 , 削减闲暇消费 ; 而当工资水平上升到一 定程度以后 , 替代效应小于收入效应 劳动的供应曲线向后弯曲;, 因而人们增加闲暇时间的消费 , 而削减劳动时间; 因此 , 图 1图 210 元提高到 从图 1 可以瞧出 , 当工资率从每小时 20 元后 , 劳动者的闲暇时间从 16 小 时每天上升到了 18 小时每天 , 也就就是说 , 劳动者每天的工作时间随着工资率的提高不仅 没有增加反而削减了;其中缘由就是工资率提高给劳动者带来的收入效应 ( 闲暇时间增加 4 小时 ) 不仅抵消了它所带来的替代效应 ( 工作时间增加 2 小时 ), 而且仍导致了工作时间削减 2 小时;因此 , 劳动的供应曲线存在一个特定的工资率 , 在此工资率之下 , 劳动的供应就是随 工资率提高而增加的 的劳动供应曲线如图 , 在此工资率之上 2;, 劳动的供应将随着工资率的提高而削减; 个别劳动者 7,简述完全竞争市场实现长期均衡的条件;第一 , 全部企业的经济利润都为零 , 没有任何新的企业会进入到该行业;当然 , 假如全部 行业都实现了长期均衡 不会退出该行业;, 也就意味着任何行业都不存在正的经济利润 , 行业中的企业自然也 其次 , 产品的市场价格就是市场供应等于市场需求的价格 第三 , 行业中的企业都实现了利润最大化;, 即市场出清的价格水平 ; 15,如通过市场机制来供应公共产品 , 它能够在竞争性市场中以有效率的方式进行生产不?消费者消费的商品中有一种就是公共品 X, 另一种就是私人物品 Y ;假定消费者 1 与 2 消 , 两个消费1 21 2费 X 的边际效用分别为 MU x 与 MU x , 消费 Y 的边际效用分别为 MU y 与 MU y ;因而 者关于 X 对 Y 的边际替代率分别为1 1 12 2 2MR S xy = MU x /MU y 与 MR S xy = MU x 假如生产就是有效率的并且市场就是完全竞争的 /MU y, 那么在市场均衡状态下将有 1MR S xy =2MR S xy = MR T xy (10)从社会的角度来瞧 , 依据公共品的特点 , 对增加一单位公共品 X 而言 , 社会由此得到的 1 2边际效用为 SMUX = MU x + MU x 因此 , 社会关于 X 对 Y 的边际替代率为 SMRS XY =SMUX /MUY1 2=MRSXY +MRSXY(11) 同样地 , 社会实现帕累托效率的条件就是两种商品的社会边际替代率等于这两种商品的边际转换率 , 即SMRS XY = SMRT XY (12)当生产处于帕累托最优状态时 率 , 即 SMRTXY = MRT XY ;故有SMRS XY = MRT XY (13), 社会关于这两种商品的边际转换率等于私人的产品转换 上式被称为“萨缪尔逊规章”;该规章具有重要的理论价值与现实意义 , 它将新古典经济学的边际分析推广到公共产品领域, 供应了公共产品供应的有效规章;但比较(10) 式与(11), 同时留意到式可知,(13) 式不行能得到满意;这说明公共品的存在使得市场缺乏效率SMRTXY < SMRS XY ,这意味着公共品的供应相对不足;三,作图分析题1,分析在企业短期生产中, 它即使亏损也将仍旧连续生产的缘由;供应函数表达的就是供应量就是就企业生产的短期而言的;Q 与产品价格P 之间的一种对应关系;短期供应曲线当然P, 企业就会挑选一回到图, 我们瞧到给定一个市场均衡价格个最优的产量水平Q(P), 以使得利润达到最大;点( P, Q( P)) 落在MC曲线上, 也就就是说企业供应量Q 与产品价格P 之间的函数关系落在MC曲线上;那么MC 曲线就是否就就是短期供给曲线呢?对此进行分析, 我们必需从企业经济行为的最基本原就利润最大化动身;4,相对于完全竞争的产品市场而言, 为什么垄断竞争的产品市场会导致经济缺乏效率?在一个完全竞争的市场上,价格等于边际成本;而垄断势力意味着价格超过边际成本, 由于垄断势力的结果就是较高的价格与较低的产量, 因此它会使消费者受损而使垄断者收益;将消费者的福利与生产者的福利瞧成就是一样重要的;那么垄断势力到底使消费者与生产者作为一个总体就是受益的仍就是受损的呢?我们通过图来但如,加以说明;在图中 , 垄断势力之下的均衡为( Pm , Q m ) ;消费者的剩余为 D , 生产者的剩余 CS = 为 PS = A + E ;而在完全竞争的市场中 , 消费者的剩余为 CS = A+B+D ; 生产者的剩余为 PS = C + E ;故垄断势力带来的剩余变化为: △ C S =- A - B ; △ PS = A -C ; 总剩余的变化为 : △CS + △ PS =- B - C ;- B - C 就就是垄断势力给社会带来的无谓缺失; 9,假定面粉的供应就是配给的, 政府商品以每公斤 1 元的价格向消费者供应面粉 , 每人顶多 可以买 5 公斤 , 不足部分可以在自由市场购买 , 价格就是每公斤 5 元;请做图画出一个货币 , 免费的市场价格为一 购买力就是 30 元的消费者的预算约束线;假定现在面粉的供应放开公斤 2 元;请在图中画出这个消费者的新的预算约束线;假如前后两种情形对这个消费者 就是无差异的 , 您怎样把这个事实在图中表现出来?10,用无差异分析方法分析免费发给消费者肯定量的实物与发给消费者按市场价格运算的 这些实物折算的现金 , 哪一种给消费者带来的效用更高?用发觉金的方法给消费者会带来更高的效用;由于发觉金, 消费者可以依据自己的偏好 , 所发的实物可能不就是消费者 挑选自己需要的商品 所需要或最需要的 , 使自己的满意程度达到最大; 而发实物 , 这时 , 消费者就难以得到最大的满意;如下图所示 , 消费者在没有获得免费实物或现金的情形下 , 会挑选 A 点消费 , 可以实现最 大满意程度 U1;在免费获得实物 ( 增加了 X —食物与 Y —衣服 ) 后 ,X 与 Y 的组合点 B 达到了 满意程度 U 2 ;假如给消费者以现金 , 在支出相同的情形下 C 点消费 , 满意程度为 (B 点的支出等于 C 点 ), 消费者会依据自己的喜好挑选消费——挑选U 3;满意程度 U 3> U 2> U 1;因此, 发给消费者以实物, 实际上损害了消费者的利益, 同时不利于经济的正常进展——一般来说, 只有那些生产消费者需要的产品的厂商才能也才应当生存下来;12,一个人买了一打鸡蛋,并肯定要把它们带回家;尽管回家的旅行就是无成本的, 但在任何一条路上所带鸡蛋被打破的概率都就是50%;这个人会考虑两种战略: 第一个战略, 走一条路带全部12 个鸡蛋; 其次个战略, 走两条路每次带 6 个鸡蛋;(1) 请列出每种战略的可能结果与每种结果的可能性;请说明在每个战略下回家之后平均都有6 个鸡蛋没有被打破;战略一: 平均打碎鸡蛋的个数战略二:=0×0,5+12×0,5=6结果( 未打碎的鸡蛋) 060,512可能性0,25 0,25平均打碎鸡蛋的个数=0×0,25+6×0,5+12×0,25=6(2) 画图表示每种战略下可获得的效用, 人们会倾向哪一个战略?假如人们就是风险规避的偏好择战略二;, 就她们个人的效用函数就是凹函数, 如下列图, 她们将选四,运算题q 1,假定某消费者的效用函数为 3M ,其中 ,q 为某商品的消费量 U ,M 为收入;求 :(1) 该消费者的需求函数 ;112 (2) 当价格 , q ;p 4 时的消费者剩余 (1) 解:MU=dU/dQ=0, 5Q^(-0 , 5)入 =dU/dM=3由于入 =MU/P3=0,5Q^(-0 ,5)/PP=0,5Q^(-0 ,5)/3所以需求函数为 Q=(6P)^(-2)(2) 消费者剩余 CS=1/3Q^(1/2)-PQ=2/3-1/3=1/37,已知某垄断者的成本函数为 极大的产量 , 利润与价格; TC=0, 5Q2+10Q,对 TC 求导 , 得 MC=Q+10;TC=0, 5Q2+10Q 产品的需求函数为 P=90-0, 5Q,运算利润为 AR=P=90-0, 5Q,就 TR=AR*Q=90Q-0, 5Q2对 TR 求导 , 得 MR=90-Q;令 MC=MR 得, Q=40,进而 P=70,L=1600答案 : 产量为 40, 价格为 70, 利润为 16002TC 5 9Q 1 Q 1 10,一个垄断厂商拥有两个工厂 , 两工厂的成本函数分别为 : 工厂 ; 工1, 2TC 4 10Q 2 2 ; 市场的需求曲线为 P 31 Q , 厂 2, 求总产量,产品价格以及各 个工厂的生产数量;答案 : 总产量为 8, 价格为 23,Q1=3,Q2=5 ;1 2 Q 24L K 3 3 4 , r 8 ;求厂 11,厂商的生产函数为 商的长期成本函数;, 生产要素 L 与 K 的价格分别为 由于 Q=24L1/3K2/3, 所以 MPL=8L-2/3K2/3,MPK=16L1/3K-1/3带入生产者均衡条件 MPL/ PL= MPk/ Pk , 得 L=KC=4L+8K=12LQ=24L1/3K2/3=24L,L=1/24 QC=12L=1/2 Q1 Q2 C 长期成本函数为14,假设某企业为其产品与要素市场上的完全垄断者 , 其生产函数为 Q=2L,其中 L 为生产中 使用的劳动力数量;如该企业的需求函数为 Q=110-P, 劳动的供应函数为 L=0,5W-20;求生 产者的产量为多少?在此产量下 , 劳动使用量 L, 商品价格 P 与工资 W 各为多少?答案 :Q=30,P=80,L=15,W=70 , 15,双寡头垄断企业的成本函数分别为Q=Q1+Q2:C1=20Q1,C2=2Q2, 市场需求曲线为 P=400-2Q, 其中 (1) 求出古诺均衡下的产量,价格与利润 ;答案 : Q 1 = 80, Q 2 30 , P 180, 12800, 3600;1 2 (2) 求出斯塔克博格模型下的产量,价格与利润280 3 80 3 39200 3 256009 Q 1 Q 2 1 2 P 160, 答案 : ;, , , u( x, y) xy ;请推导出 21,甲有 300 单位商品 x, 乙有 200 单位 y, 两人的效用函数都就是 全部满意帕累托有效的配置;两人通过交换达到帕累托有效配置 , 求出两人进行交换的价格 体系 , 并求出交换结果;(x 1 , y 1 ) (x 2 , y 2 ) ,(1) 设甲乙两人的消费束为 : 甲 , 乙 题设的约束条件为 :x 1 y 1 x 2 y 2 300200 ①帕累托有效配置的条件就是 : 甲,乙两人的无差异曲线相切 , 即MU MU MU x2x 1 MRS x , y MRS x , y 即 1 1 2 2 MU y 1 y 2y 1 x 1 y 2x 2 于就是我们有 : ②= y 1 x 1 300 = 200 y 1x 1 23 y 1 x 1联立①②得 : 23 y 1 x 1 因此 , 全部满意 Pareto 最优的状态的契约线为 ;: p ,(2) 令 x 价格为 1,y 的价格为 先求甲的效用最大化条件 :maxU 1 ( x 1, y 1) x 1 y 1300s.t. x 1 py 1 150x 1 150, y 1p 解得 : ;再求乙的效用最大化条件 :maxU 2 ( x 2 , y 2 ) x 2 y 2200 ps.t. x 2 py 2 x 2 100 p, y 2 100 ;解得 : 23 y 1 x 1 由第 (1) 问中解得的 Pareto 最优条件 : p ;可求得 : x 1 150, y 1 100 x 2 150, y 2 100此时 , 也就就是说 ,社会最终的价格体系为 :X 的价格为 Y;乙也消费 1,Y 的价格为 1,5;交换结果 为:甲消费 150 单位的 X,消费 100 单位的 150 单位的 X, 消费 100 单位的 Y ;。

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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。

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