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# Homework 5 Answers - ECO 301 Intermediate Microeconomics...

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ECO 301: Intermediate Microeconomics Marco A Castaneda Homework 5: Answers 1. ANSWER For this production function, we have 2 / 1 L L 1 MP = and 2 / 1 K K 1 MP = a) The problem can be stated as max 50q – (10K + 5L) K,L q = 2(K) 1/2 + 2(L) 1/2 Therefore, the necessary conditions for the optimal quantities (K*, L*) of the inputs are L L w pMP = 5 L 1 50 2 / 1 = (1) K K w pMP = 10 K 1 50 2 / 1 = (2) q = F ( K , L ) q = 2(K) 1/2 + 2(L) 1/2 (3) Equations (1) and (2) imply L* = 100 and K* = 25 Therefore, the optimal quantity of output is q* = 2(K*) 1/2 + 2(L*) 1/2 = 2(25) 1/2 + 2(100) 1/2 = 30 Finally, we have C = w K K* + w L L* = 750 R = pq* =1500 Π * = pq* - [w K K* + w L L*] = 100(15) – [10(25) + 5(100)] = 7 5 0

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b) The problem can be stated as min 10K + 5L K,L 30 = 2(K) 1/2 + 2(L) 1/2 Therefore, the optimal quantities (K*, L*) of the inputs are determined by the equations ) L , K ( F q w w MP MP K L K L = = 2
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Homework 5 Answers - ECO 301 Intermediate Microeconomics...

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