关于微观经济学的几道题，不大会，求大神们讲解

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①A’s endowment is composed of 30 unites of good 1 and40 unites of good 2. and the price of good 1 and good 2 are p1 and p2.A has no income and her unility function is U(x1, x2)=(X1-3)(X2-4)

1.    what is A’s budget constraint.

2.    write out the Lagrangian function for theutility-maximization problem.

3.    find her ordinary demand function?

②G’s income is 200 per month, and her utility functionis U(x1,x2)=x12(x2)3

1. write out the Lagrangian function.

2. Find her ordinary demand function.

3. Is good 1 normal or inferior? Is good 2 normal orinferior?

4. what is the price elasticity of demand for good 1and good 2?

③Consider the following utility function:U(x1, x2)=5x2+15x1-(x1)2/6

1. find the ordinary demand function for good 1. Isquantity demanded dependent on income?

2. Find the compensated demand function for good 1.

3. Comnpare the two demand functions, and explain theresult in terms of the absence of income effect on the demand for good 1.

④A firm owns two plants that produce the same good. Themarginal cost function for the two plants are : SMC1=3y1    SMC2=7y2

Where y1 and y2 are quantitiesof output produced in each plant.

1.    if the firm wants to produce 20 unites ofoutput at minimum cost, how much should it produce in each plant?

2.    Now consider an arbitrary quantity ofoutput y. To minimize costs, what function of the total output should the firmproduce in each plant?

⑤A perfectly competitive market has demand curveP=18-0.05Y. If every firm in the industry has an average cost functionAC=9/y+y.

1. what is the equilibrium price and qunatity in themarket?

2. What is the long-run equilibrium number if firms?

3. find the market supply function

4. calculate the producer and consumer surplus forthis competitive equilibrium.

                          

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关键词：微观经济学 微观经济 经济学 maximization equilibrium 经济学

①1、A的预算线为p1x1+p2x2=30p1+40p2
   2、效用最大化的拉格朗日函数为L=（x1-3)(x2-4)+μ（p1x1+p2x2-30p1-40p2）
   3、通过求解上面的拉格朗日方程，可以得到需求函数为：x1=33/2+18p2/p1；x2=22+27p1/2p2
②你的效用函数是((x1)^2)((x2)^3)吧:
   1、拉格朗日函数为L=((x1)^2)((x2)^3)+μ(p1x1+p2x2-200)
   2、效用函数为x1=80/p1，x2=120/p2
   3、商品1和商品2均为正常品
   4、商品1和商品2的需求弹性均为1
③这个需求函数就看不出来了，请你把格式调一下
④1、又y1+y2=20以及SMC1=SMC2可知，y1=14,y2=6
   2、同样，由y1+y2=y以及SMC1=SMC2可知y1=7y/10,y2=3y/10
⑤1、在完全竞争市场中，企业在平均成本最低点进行生产，又AC=9/y+y可知，此时y=3，价格p=6
   2、当价格p=6时，市场需求量Y=240，故厂商数量n=Y/y=80
   3、单个厂商的供给函数为边际成本函数在品均成本最低点以上的部分。由AC=9/y+y可知，总成本TC=y^2+9，边际成本MC=2y。所以整个市场的供给函数为P=160Y
   4、将供给函数与需求函数放在同一张图里，可以看到在价格线之上需求函数之下的部分为消费者剩余，计算得1440；价格线之下供给函数之上的部分为生产者剩余，计算得720。