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3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with b
(6) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part
(c) Setup and solve the profit maximization problem over inputs. Solve for the profit maximizing amounts of capital (p,w,r),
(d) Prove that your answers in part B and part C give you the identical levels of profit maximizing output and profit. (6 poi
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Answer #1

3.a) The firms problem in to minimize qoc= WLtrk . sit ;= k/3,73 K, L> o The required Lagrange function.in: 2 wl+rk ++ [9 -.. TC = WL+rk :.TC = 293/2 Jow (b) The firms problem is to : maximize t = pq - TC = pq - 29 wr The foc ini yao... :. -. Vwriv13 e wlo *** - wzo al ~, K () 2. K : 0) (18 kº? **3= ($) * wers . 7 Yu3 bos 01 alo 27 wra w3a 23 wb 27wr *: (05) 14=1144 weg

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