作者Eleen8651 (Eleen)
看板Economics
标题[作业] profit maximization
时间Tue Oct 9 11:00:43 2012
科目: Methematical microecon
题目:
Consider the production function for pottery (P) as:
P=C^(1/3)*L^(2/3)
Where C is the amount of clay and L is the amount of labor. If the price of
pottery is $3 per unit and clay cost $2 per unit and labor $4 per unit, the:
1.what is the formula for the profit of the firm?
2.what are the first order conditions for profit maximization? What do they
mean intuitively?
3. show this is a maximum
4. what are the optimal facto demand curves? Intuitively explain what happens
as the three prices change.
5. what is the optimal level of production? why is this the case?
我的想法:
1. π=3P-2C-4L
=3C^(1/3)*L^(2/3)-2C-4L
2. FOC
dπ/dC=C^(-2/3)*L^(2/3)-2=0
dπ/dL=2C^(1/3)*L^(-1/3)-4=0
3. 我本来是想用 A. Chang SOC in relation to concavity and convexity 证明
其为严格凸函数，但是 α<1,β<1, ^f11<0 f11f22-f12f12=0
@_@ 请问这个部份要用什麽理论证明是maximum?
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1F：推 goodcar:半负定 10/10 15:31
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