help

以下四道题目,请各位高手指点,万分感谢(刚刚接到的样题,自己工作十来年了,以前的东西全部忘光了,马上就要考试,没时间准备了):

1.Consider the following macroeconomic model:

C=15+0.8(Y-T)

T=-25+0.25Y

I=65-R

G=94

L=5Y-50R

M=1500

where C denotes aggregate consumtpion, T tax revenue, I investment, G government expeditures, Y aggregate output, R interest rate, L demand for money, and M supply of money.

a) Simplify this model by deviving the IS and LM curves into a model with two equations and two endogenous variables

b) solve for Y and r

2.A monopolist faces the inverse demand curve p=200-x. Its cost function is C=x＊x(注C等于x的平方). Find the output which maximises the monopolist's profits.

3.Consider a competitive firm that produces a given output using labour and capital according to the production function f(K,L)=L的0.25次方乘以K的0.5次方(不好意思,数学表达式写不出来),Let p denote the price of the output, w the wage rate, and r the price of capital. Assume further that p=64, w=2 and r=4. Find the optimal use of labour and capital.

4. Two cards are drawn without replacement from a standard deck of cards. Find the probability that the followings:

a) Both cards are red.

b) At least one card is red.

前三题是西方经济学方面的内容,第四题是概率方面的内容(好像题目不明确,a standard deck of cards为一幅标准牌,一般有红黑方草四中颜色,但是大小王也应该算).

第一题好像是用宏观经济学的IS-LM曲线求,我基本忘记了IS-LM的内容.

第二题是垄断经济条件下厂商利润最大化的题目,怎么解我不太清楚.

第三题好像关于微观经济学的生产成本理论.给出生产函数,求劳动和资本的最佳组合,好像是这个意思.