Using Lagrange multiplier
Let Λ(K,L,λ)=KaL1-a-λ(pK+qL-B)
∂Λ/∂K=aKa-1L1-a-λp=0
∂Λ/∂L=(1-a)KaL-a-λq=0
∂Λ/∂λ=pK+qL-B=0
Solving, pK/a=B, K=(1-a)B/q
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由 訪客 於 星期三 一月 27, 2010 3:35 pm
[大學]Partial Derivative
由 數學白痴一號 於 星期三 一月 27, 2010 11:41 am
這題我真的是搞不清楚狀況
不知道要做什麼
我算了三個ｄｅｒｉｖａｔｉｖｅ但是不知道接下來要怎麼辦
Suppose you have a production function P=f(K,L)=K^(a)L^(1-a), where 0小於等於a小於等於1, and K is the capital available and L is the labour available. Suppose that you have a budget constraint pK+qL=B, where p, q, and B are given positive constants. Show that the production P is maximized when K=aB/p and L=(1-a)B/q.
我算出df/dk df/dL 和 df/d入
就不知道要怎麼做了
不知道要做什麼
我算了三個ｄｅｒｉｖａｔｉｖｅ但是不知道接下來要怎麼辦
Suppose you have a production function P=f(K,L)=K^(a)L^(1-a), where 0小於等於a小於等於1, and K is the capital available and L is the labour available. Suppose that you have a budget constraint pK+qL=B, where p, q, and B are given positive constants. Show that the production P is maximized when K=aB/p and L=(1-a)B/q.
我算出df/dk df/dL 和 df/d入
就不知道要怎麼做了