求解两道EV和CV的题目

1、某消费者效用函数为u(x,y)=2x+y，x,y表示每周消费商品的数量。该消费者每周的收入为200元，x的价格为4元/单位，但目前该消费者不消费y。现在该消费者收到了一个俱乐部的邀请，如果他参加俱乐部，购买y 可以享受1元/单位的折扣价格，那么他愿意花多少钱参加该俱乐部？
2、某消费者的效用函数为u(x,y)=max(x,y)。x,y表示消费的商品量。若初始他的收入为600元，x的价格为0.5元/单位，y的价格为1元/单位，如果x的 价格上升到2元/单位，则相当于他的收入减少了多少呢？

最好能有计算过程啊！谢谢坛友啊！

1、
(1) x and y are perfect substitutes.
   The consumer will always consume the good that has the relatively cheaper price, or any quantities of x and y when the price of x*2  equals the price of y.
(2) Originally,the consumer consumes 200/4=50 units of x,the utility u=2*50=100.
     If the consumer has the incentive to enter the club , it means that the consumer will better off from the original consumption of x because of the price discount but paying for the right of discount.
     Let t represents the payment for the right of discount,and p denotes the price of y before discount.Then, we get the amount of y that the consumer will consume after discount
    y'=(200-t)/(p-1)
so as that p>2 and p-1<2.
Then , the utility u'=2*0+y'=(200-t)/(p-1).
From u'>u,we can conclude
      (200-t)/(p-1)>100
      t<300-100p   (2<p<3)
So,we get
      0<t<100.
That is to say, the consumer will pay no more than 100 yuan to enter the club .

2.
(1)
When p'(x,y)=(2,1) and m remains unchanged ,
the consumer will consume only y',and y'=600; the utility u'=600.
(2)Considering in order to obtain the equal utility 600 in the situation before ---- p(x,y) =(0.5,1)----the consumer would have owned income m=300.
    So it is equivalent that the income decreases by 300 yuan.

Right?

解答第二题：刚开始时消费者全部消费X，消费者的效用为600/0.5=1200,当x的价格上升到2时，消费者全部消费Y,此时，消费者的效用为600/1=600，为了维持消费者的效用不变，消费者需增加收入1200-600=600，相当于消费者的收入减少了600.

steventung 发表于 2013-1-5 22:30
Right?

为什么p要大于2，p-1要小于2，价格不能为小数吗，也就是为什么不是前者大于1，后者小于1呢

侯国鑫 发表于 2013-1-6 09:17
解答第二题：刚开始时消费者全部消费X，消费者的效用为600/0.5=1200,当x的价格上升到2时，消费者全部消费Y, ...

这个是解CV吧