求经济学大神！微观经济的一点内容！

豆豆龙

Find the Marshallian demand functions, indirect utility functions, Hicksian demand functions and expenditure functions for each of the following utility functions:
a) U(X,Y,Z)=  X② YZ  （这里是x的平方）
b) U(X,Y,Z) = 2X +Y +3Z
c) U(X,Y,Z) = min(X,Y,Z)
d) U(X,Y)  = max(X,Y)

II. Explain whether each of the following statements is TRUE or FALSE.
1. If the utility function is homothetic, then the income consumption curves are linear (and pass
through the origin).
2. A night club that has an admission or cover charge in addition to the price of food and drink
cannot be maximizing its income.
3. Other things being equal, higher interest rate will lead to a lower price of gold.
4. If utility is held constant, the change in the number of oranges consumed with respect to a small
change in the price of apples would equal the change in the number of apples consumed with
respect to a small change in the price of oranges.
5. In a duopoly model, the total output under the collusion equilibrium is always bigger than the
total output under the Nash equilibrium.


Consider a consumer with a utility function U = X1X2 . Let his income and the prices of the
goods be  M = $240,P1 = $8 and P2 = $12. For each of the following cases find a numerical
solution for the consumer’s utility-maximizing consumption levels.
a) There are no further constraints on his behavior.
b) A rationing system goes into effect. The consumer is allocated 32 ration points, one of
which must be given for each unit of good 1 purchased and 2 for each unit of good 2
purchased.
[Note: Both ration points and money must be paid for each unit of each good purchased.
Ration points cannot be transferred among individuals.]
c) The same situation as (b) except that a legal market arises in which ration points may be
bought or sold for $4 each.


有没有会的同学， 帮忙做一下！万分感谢！急！！