辽宁大学西方经济学真题14.

经济学习题1

一（20分）

,1，某消费者拥有货币收入180元,他想用这些收入购买商品A和商品B,商品A和商品B的价格分别是2元和六元,在其效用函数为:U=AB时，消费者为了实现效用最大化，应该购买两种商品的数量是多少？总效用是多少？

2，在消费者的收入和商品的价格既定的条件下，消费者试图使自身的效用最大，请结合无差异曲线分析方法来说明消费者的均衡条件。

答: 1，消费者的预算方程式为:

两种商品的边际效用函数分别为:,

消费者实现效用最大化需满足的条件是:

根据这一条件,可知在效用最大化时,

代入预算方程式中,可得:

总效用为:

2，消费者要实现自身效用最大化,需要不断地在预算线上对两种商品的消费数量做出调整,这就需要分析预算线同无差异曲线相交、相切、和相离三种情况。然后由预算线和无差异曲线相切得出均衡条件。（省略分析三种情况和图）

二（15）

已知生产函数,假定厂商目前处于短期生产，且。

1，写出在短期生产中该厂商关于劳动的总产量函数，劳动的平均产量函数和劳动的边际产量函数。

2，分别计算当劳动的总产量，劳动的平均产量和劳动的边际产量各自达到最大值时厂商的劳动投入量。

3，短期生产的三个阶段的产量曲线的特征是什么？为什么在第II 阶段是生产者进行短期生产的决策区间？

答：1，把代入生产函数可得总产量；；

2，当,即时，总产量最大。

当时，平均产量最大，代入有关参数可得，求解可得。

由劳动的边际产量函数可知，当，边际产量最大。

3，根据短期生产的总产量曲线、平均产量曲线和边际产量曲线之间的关系，可将短期生产划分为三个阶段（图见课本）理性的生产者既不会将生产停留在第I阶段，也不会将生产扩张到第III阶段，所以，生产只能在第II阶段进行。在生产的第II阶段，生产者可以得到由于第I阶段增加可变要素投入所带来的全部好处，又可以避

免将可变要素增加到第III阶段带来的不利影响。因此第II阶段是生产者的决策区间。

三（20）

1，假设某产品的边际成本函数为，若生产5单位产品时，总成本是595，求总成本函数，平均成本函数，可变成本函数和平均可变成本函数。

2，分析边际成本曲线与平均可变成本，平均成本曲线，总成本曲线间的关系。

答：1，根据边际成本函数可知总成本函数：

。

因为生产5单位产品时，总成本是595，所以，，可得a=70 2，（1）在边际报酬递减规律的作用下，边际成本曲线先下降后上升，边际成本曲线呈U型。因此，平均可变成本曲线和平均成本曲线也呈U型。边际成本曲线与平均可变成本曲线和平均成本曲线在平均可变成本曲线和平均成本曲线的最低点相交。在平均成本曲线的下降段，边际成本小于平均成本，在平均成本的上升段，边际成本大于平均成本。在平均可变成本曲线的下降段，边际成本曲线低于平均可变成本曲线，在平均可变成本的上升段，边际成本曲线高于平均可变成本曲线。（2）每一产量上的边际成本值是相应的总成本曲线的斜率。由于边际成本曲线呈U型，所以总成本曲线的斜率有递减转为递增，边际成本曲线的最低点与总成本曲线上的拐点相对应。（3）平均可变成本曲线低于平均成本曲线，两条曲线间的距离由不同产量上的平均固定成本决定。随着产量的增加，；两条曲线逐渐接近，但不会相交。

四（10）

完全竞争行业中某厂商的成本函数为，假设产品价格为66元。

1，求利润最大时的产量及其利润总额。

2，由于竞争市场发生供求变化，由此决定的新的价格为30元，在新的价格下，厂商是否会发生亏损？如果会，最小的亏损额为多

少？

3，该厂商在什么情况下才会退出该行业？

答：1，由，可得

，又知。根据利润最大化的条件：，则可得：

解之得。根据利润最大化的充分条件来判断，可以保证利润最大化。

此时，利润最大值为：

2，由于市场供求发生变化，新的价格为,又根据,即：

解之得(没有经济意义，舍去)。

当时，利润是：

可见，当价格为30元时，厂商会发生亏损，最小亏损额为8元。

3，厂商推出行业的条件是的最小值。

由可得：

所以

要求的最小值，须使，即：解之得。

当时，，可见，只要，厂商就会停止生产。

五（15）

用图说明垄断厂商短期均衡和长期均衡的形成及其条件。

答：（1）垄断厂商的短期均衡的形成：a.垄断厂商面对着一条向右下方倾斜的需求曲线，这条需求曲线和厂商的平均收益曲线重合。b.垄断厂商的边际收益曲线可以通过平均收益曲线求得。边际收益曲线位于平均收益曲线下方，同样向右下方倾斜，但是其斜率的绝对值是平均收益曲线的两倍。C.垄断厂商为了获得最大利润也必须遵循利润最大化原则。当时，垄断厂商获得了最大利润。此时确定的价格和产量为短期均衡产量和均衡价格。d.在短期均衡时，垄断厂商可能获得正常利润、超额利润或亏损。只要，厂商即使在亏损的情况下也比继续生产。e.短期均衡条件是：。

（2）垄断厂商的长期均衡：a.厂商在长期内可以调整全部生产要素的数量，从而实现最大利润。垄断厂商在长期内对生产的调整一般可以有三种可能的结果：第一种结果，垄断厂商在短期内亏损的，但是在长期内无论怎样调整生产规模，厂商都不可能亏损。面对这种情况厂商将推出。第二种结果，垄断厂商在短期内是亏损的，但是在长期内通过生产规模的调整可以摆脱亏损局面。第三种结果，厂商在短期内获得了利润，在长期内通过对生产规模的调整使得利润进一步增大。b.长期内厂商要获得最大利润必须使。c.在的时候，厂商实现了最大利润，此时确定的价格和产量就是长期均衡价格和产量。厂商在长期内不会由亏损的存在。垄断厂商的长期均衡条件是：

六（15）

1，解释帕累托最优状态必须满足的三个条件。

2，垄断是如何造成市场失灵的？

答：1，实现帕累托最优状态所需要满足的三个条件包括：交换的最优条件、生产的最优条件和生产与交换的最优条件。

交换的最优条件要求，对于任意两种商品而言，两个消费者的边际替代率必须相等。如果边际替代率不同，两个消费者之间进行交换，至

少可以使一个消费者满足不变，另外一个消费者满足程度提高，这意味着存在着帕累托改进余地。

生产的最优条件要求两个生产者之间使用的两种要素的边际技术替代率相等。如果边际替代率不同，则通过要素的重新分配，至少可以使一个生产者的产量不变，另外一个生产者的产量增加。这同样意味着帕累托改进的存在。

生产和交换的最优条件要求：边际替代率等于边际转换率。如果二者不等，通过重新安排产品的组合，消费者的福利将会增进，这种情况表明存在着帕累托改进的可能。

2，垄断厂商根据利润最大化原则确定其产品的价格和产量。由于垄断厂商面对向下倾斜的需求曲线，因此，垄断厂商确定的价格高于边际成本。这表明，同帕累托最优状态相比，垄断厂商的价格较高，产量较低。同完全竞争市场相比，一方面，消费者剩余较少，这造成了社会福利损失；另一方面，较少的产量意味着垄断厂商所使用的资源低于社会最优水平。价格高于边际成本意味着消费者愿意为增加额外一单位产量所支付的价格超过了生产该单位产量所引起的成本，因此存在着帕累托改进的余地。但是由于垄断厂商和消费者之间以及消费者之间难以达成相互满意的的一致意见，因此垄断市场条件下，价格和产量难以达到帕累托最优状态所要求的水平。

不仅如此，如果垄断厂商为了维持垄断地位而采取“寻租”活动，那么垄断厂商为此付出的代价也是资源的一种浪费。

七（15）

假定某经济中消费函数为,税率，投资函数为，政府购买G=800，货币需求为，实际货币供给,求：

1 （1）IS曲线（2）LM曲线（3）两个市场同时均衡时的利率和收

入。

2 试说明IS曲线向右下方倾斜的假定条件是什么？

答：1，（1）由Y=C+I 可知IS曲线为 Y=100+0.8Y+150-6R 即Y=1250-30r （2）由货币供给和货币需求相等：可得LM曲线为：

0.2Y-4r=150/1 即Y=750+20r

（3）当商品市场和货币市场同时均衡时，IS和LM相交于一点，该点的收入和利率可通过求IS和LM交点而得：

Y=1250-30r

Y=750+20r

解之得均衡利率r=10，均衡收入为Y=950

2，IS曲线向右下倾斜的假定条件是投资需求是利率的减函数，以及储

蓄是收入的增函数。即利率上升时，投资要减少，利率下降时，投资要增加；以及收入增加时，储蓄要随之增加，收入减少时，储蓄要随之减少。如果这些条件成立，那么，当利率下降时，投资必然增加，为了达到产品市场的均衡，或者说储蓄和投资相等；则储蓄必须增加，而储蓄又只有在收入增加时才能增加。这样，较低的利率必须和较高的收入配合，才能保证产品市场上总供给和总需求相等。于是当坐标图形上纵轴表示利率，横轴表示收入时，IS曲线就必然向右下倾斜。如果上述前提条件不存在，则IS曲线就不会向右下方倾斜。例如，当投资需求的利率弹性无限大时，即投资需求为水平状时，则IS曲线将成为一条水平线。再如，如果储蓄不随收入而增加，即边际消费倾向如果等于1，则IS曲线也成水平状。由于经济学家们一般认为投资随利率下降而增加，储蓄随收入下降而减少，因此一般可假定IS曲线为向右下倾斜的。

八（15）

1，什么是凯恩斯陷阱？

2，用模型说明为什么凯恩斯主义强调财政政策的作用。

答1，当利率降到很低水平时，一方面人们持有货币成本极低，另一方面债券极高，人们预期利率只升不跌，有价证券只跌不升，因而会将所持有的有价证券全部换成货币，即对货币投机需求无限大，这种情况被称作“流动偏好陷阱”。此时LM曲线呈水平状。

2

九（20）

1，用蒙代尔-弗莱明模型考察固定汇率下紧缩性货币政策的影响。

2，用蒙代尔-弗莱明模型考察浮动汇率下紧缩性财政政策的影响。答：1，在固定汇率制度下，一国中央银行宣布一个汇率值，并随时准备买卖本币把汇率保持在所宣传的水平上。

这时如果中央银行试图实行紧缩性的货币政策，如在公开市场上卖出债券。这种政策在开始时将使曲线左移，汇率上升，收入减少。但是由于汇率固定，套汇投资者对市场汇率上升的反应是用本国货币在外汇市场上购买外国货币，然后向中央银行兑现本国货币，以获得汇率升值部分的利差。中央银行用来收购投资者手中的外币而释放出来的本国通货说明中央银行增加了本国货币的供给。这导致曲线右移，重新回到原来位置。因此，在固定汇率制度下，中央银行的紧缩性货币政策是无效的。

2，在浮动汇率制度下，汇率由市场供求力量决定，允许汇率对经济状况的变动作出反应，自由地变动。在这种情况下，假定政府采取减少政府购买支出或增加税收等紧缩性，这将导致总需求的减少，使得IS曲

线向左移动。结果，汇率下降了，而收入水平保持不变。这是因为紧缩性财政政策使得总需求减少，资本将从国内流出，增加了外汇市场的供给，进而本币贬值。本币的贬值使得国内产品相对国外产品更便宜，从而增加了净出口。净出口的增加抵消了紧缩性财政政策对收入的影响。因此，在浮动汇率制度下，紧缩性的财政政策只会引起汇率降低，而收入水平保持不变。

十（10）

1，什么是新古典增长模型的基本公式？它有什么含义？

答：（1）离散形式的新古典增长模型的基本公式为：

其中，k为人均资本，s为储蓄率，y为人均产量，n为人口增长率，为资本折旧率。

（2）上述关系式表明，人均资本的增加等于人均储蓄sy减去项。均储蓄的一部分必须用于装备新增加的人口，每个人占有社会平均量的资本k，这一部分储蓄为nk，另一方面，人均储蓄的一部分必须用于替换折旧资本，这一用途的储蓄为，总计为的人均储蓄被用于资本的广化。人均储蓄越过的部分将导致人均资本k的上升，即，这被称为资本的深化。因此，新古典增长模型的基本公式可以表述为：

资本深化=人均储蓄—资本广化

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