profit maximization - 經濟

科目: Methematical microecon

題目:
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. 我本來是想用 A. Chang SOC in relation to concavity and convexity 證明
其為嚴格凸函數，但是 α<1,β<1, ^f11<0 f11f22-f12f12=0

@_@ 請問這個部份要用什麼理論證明是maximum?

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