电大西方经济学计算题小抄参考.doc

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1、专业好文档1、已知某商品的需求方程和供给方程分别为：Qd=14-3P，Qs=2+6P，试求：该商品的均衡价格，以及均衡时的需求价格弹性和供给价格弹性。解：（1）均衡时，供给量等于需求量，即QD=QS，也就是 14-3P=2+6P解得 P=4/3 ，Q=10 。 （2）需求价格弹性：ED=-Qd/QP/P=-Qd/PP/Q=-(-3) 4/3/10= 4/10 = 0.4 需求供给弹性：ED=Qs/QP/P=Qs/PP/Q=6 4/3/10 = 4/5=0.8 2、若消费者张某的收入为270元，他在商品X和Y的无差异曲线上斜率为dY/dX=-20/Y的点上实现均衡。已知X和Y的价格分别为PX=2

2、，PY=5，那么此时张某将消费X和Y各多少?解:消费者均衡条件为：- dY/dX = MRS = PX/PY，所以-(-20/Y)= 2/5，Y = 50。根据收入I= XPx+YPY，可以得出：270=X2 + 505，X=10，则消费者消费10单位X和50单位Y。 3、若消费者张某消费X和Y两种商品的效用函数U=X2Y2，张某收入为500元，X和Y的价格分别为Px =2元，PY=5元，求: (1)张某的消费均衡组合点。解:由效用函数U=X2Y2，可得M Ux= 2XY2，M UY = 2X2Y，消费者均衡条件为：M UX / M UY =2 XY2/ 2X2Y =Y/X=PX/PY= 2/

3、5，500 = 2X+5Y，可得，X=125，Y=50，即张某消费125单位X和50单位Y时，达到消费者均衡。 (2)若政府给予消费者消费X以价格补贴，即消费者可以原价格的50%购买X，则张某将消费X和Y各多少?解: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=lX+5Y，可得X=250，Y=50，张某将消费250单位X，50单位Y。 (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: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：Y/X

4、= 1/5 400 = lX+5Y，可得X= 200，Y = 40，比较一下张某参加工会前后的效用。参加工会前:U=X2Y2 = 1252502=39062500，参加工会后:U=X2Y2 = 2002 402=64000000，可见，参加工会以后所获得的总数效用较大，所以张某应加入工会。 4、假定某完全竞争的行业中有500家完全相同的厂商，每个厂商的成本函数为STC=0.5q2 + q + 10。(1)求市场的供给函数。 (2)假定市场需求函数为QD= 4000 - 400P，求市场均衡价格。解: (1)根据STC = 0.5 q2 + q +10，得AVC = 0.5q + 1，则P =

5、q+1为单个厂商的供给函数，由此可得市场的供给函数QS = 500P 500。 (2)当QD= QS时，市场处于均衡，由4000 - 400P = 500P - 500，得市场均衡价格为P=5。5、设有如下简单经济模型：C=80+0.75Yd，Yd=Y-T，T=-20+0.2Y，I=50+0.1Y，G=200，试求：收入、消费、投资与税收的均衡值及综合乘数。解：Y = C+I+G = 80+0.75Y-（-20+0.2Y）+50+0.1Y+200得到Y=1150，C = 80+0.75Yd = 785，I = 50+0.1Y = 165， T = -20+0.2Y = 210，已知C=80+0

6、.75Yd，得到b=0.75, 已知T=-20+0.2Y，得到 t=0.2, 已知I=50+0.1Y，得到边际储蓄倾向=0.1 ，K=1/1-（0.750.8+0.1）= 3.3 。 由简单的国民收入决定模型可知，均衡时有：Y=C+I+G=80+0.75Yd+50+0.1Y+200,因为Yd=Y-T=Y-(-20+0.2Y)=0.8Y+20,所以Y=80+0.75(0.8y+20)+50+0.1Y+200，0.3Y=345,均衡的国民收入为：Y=1150。当Y=1150时有：C=80+0.75Yd=80+0.75（0.8Y+20）=80+0.75(0.8*1150+20)=785。I=50+0

7、.1Y=50+0.1*1150=165，T=-20+0.2Y=-20+0.2*1150=210，K=1/1-b(1-t)-i=1/1-0.75(1-0.2)-0.1=3.3。6、设完全竞争市场中的代表性厂商的短期成本函数是,若该产品的市场价格时315元，试问：(1)该厂商利润最大时的产量和利润；(2)该厂商的不变成本和可变成本曲线及图形。 解：（1）因为MC= 240 40Q + 3Q2, MR = 315， 得Q=15,利润 =TR-TC = 2250。 （2）不变成本FC=20,可变成本VC = 240Q 20Q2 + Q3 ,依据两个方程画出不变成本和可变成本曲线： （3）停止营业点应该

8、是平均变动成本的最低点，所以AVC=VC/Q=(240Q-20Q2+Q3)/Q=240-20Q+Q2，对AVC求导，得：Q=10 此时AVC=140，停止营业点时价格与平均变动成本相等，所以只要价格小于140，厂商就会停止营。(4）该厂商的供给曲线应该是产量大于10以上的边际成本曲线7、已知：边际消费倾向为0.8，边际税收倾向为0.15，政府购买支出和转移支付各增加500亿元。试求：(1)政府购买支出乘数；(2)转移支付乘数；(3)政府支出增加引起国民收入增加颤；(4)转移支付增加引起的国民收入增加额。 解：已知b=0.8 t=0.15 C500 政府转移支付，TR=500， (1)KG=1/

9、1-b(1-t)=1/1-0.8*(1-0.15）=3.1， (2)KTR=b/1-b(1-t)=0.8/1-0.8*(1-0.15)=2.5,(3)YG=GKG=5003.1=1550，(4)YTR=TRKTR=5002.5=1250， 8、已知Q=675050P，总成本函数为TC=12000+O.025Q2。 求: (1)利润最大时的产量和价格?(2)最大利润是多少?解：已知Q=675050P，总成本函数为TC=12000+O.025Q2，得到P=135-Q/50 。MC= 0.05Q ，TR=PQ=135Q-Q2/50，MR=135-Q/25，根据 MC=MR,得到 0.05Q=135-

10、Q/25 ，Q=1500，P=135-Q/50= 105，利润= TR-TC= PQ-(12000+O.025Q2)= 89250 。9、设有下列经济模型：Y=C+I+G，I=20+O.15Y，C=40+0.65Y，G=60。试求： (1)边际消费倾向及边际储蓄倾向各为多少?(2)Y，C，I的均衡值； (3)投资乘数为多少。 解：(1)由已知C=40+0.65Y，得到边际消费倾向b=0.65，边际储蓄倾向=1-边际消费倾向=1-0.65=0.35。(2) Y=C+I+G=40+0.65Y+20+0.15Y+60，得到Y=600，C=40+0.65，Y=430，I=20+0.15Y=110，(3

11、) K=1/1-(0.15+0.65)=5 。 10、某钢铁厂的生产函数为Q=5LK，其中Q为该厂的产量，L为该厂每期使用的资本数量，K为该厂每期使用的资本数量。如果每单位资本和劳动力的价格分别为2元和1元，那么每期生产40单位的产品，该如何组织生产?解:由该厂的生产函数Q=5LK可得，M PL= 5K，MPK= 5L，按照厂商组合生产的最优要素组合可得出5K/5L=1/2（1），又由厂商每期生产20单位产品的条件可知40=4LK（2），由(1)(2)可求出K=2，L=4，即生产者应该购 买资本2个单位，购买劳动力4个单位，进行生产。 11、已知货币供给量M220，货币需求方程为L0.4Y1.

12、2r，投资函数为I1952000r， 储蓄函数为S500.25Y。设价格水平P1，求均衡的收入水平和利率水平。 解:由产品市场均衡条件IS，1952000r500.25Y，0.25Y2000r245（1），由货币市场均衡条件：LMP，0.4Y1.2r220（2），由(1) (2)两式有方程组Y500，r0.06，即均衡的收入水平为500，均衡的利率水平为0.06。Winger Tuivasa-Sheck, who scored two tries in the Kiwis 20-18 semi-final win over England, has been passed fit after

13、a lower-leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh Charnleys effort in their first pool match against England on the o

14、pening day.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams who has attracted the most interest in the tournament so far.The Kiwi

15、 - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just to get across the line this weekend, said Williams.The (lack of) air

16、 up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am going to be at the match tomorrow and I have asked to meet Yaya Toure, h

17、e told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel Platini, president of European footballs governing body, has

18、also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner the disappointing news: Mission aborted.The supersonic descent could

19、happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, with capsule attached, will move through the lower level of the atmos

20、phere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. As he crosses the boundary layer

21、(called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They blew it in 2008 when they got caught cold in the final and they will n

22、ot make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening game of the tournament.That could be classed as a weakness, a team un

23、der-cooked - but I have been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. Theyve been great at all the unglam

24、orous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or Greg Inglis at full-back they have a spine that is unmatched in rugb

25、y league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.