Econ10A_PSET6

Econ10A_PSET6 - machines. a. Write down a production...

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Problem Set 6 Long Run Cost 1. Let F(L,K)=L 1/3 K 2/3 . What are the firm’s output-constrained factor demand functions, L*(Q, w, r) and K*(Q,w, r)? What is the firm’s long run cost minimizing input bundle when w=4, r=1, and Q=4? 2. A firm is producing an output level of Q 0 in a long run cost minimizing manner using input levels L 0 , K 0 , where all we know is that MP L (L o ,K 0 ) = 12 MP K (L o ,K 0 ) = 16 w=3 r=4 . a. If the firm were to spend $1 less on labor , how much production would it lose? b. If the firm were to spend $1 more on capital , how much production would it gain? 3. Let L*(Q, w, r) and K*(Q,w,r) denote a firm’s output-constrained factor demand functions. a. K*(100, 3, 5) =7. Explain in words what this means. b. LTC(100, 3, 5) = 51. Explain in words what this means. c. Given a) and b), what is the numerical value of L*(100, 3, 5) 4. A firm produces cars using automated assembly lines. Each assembly line has 14 machines and produces 20 cars a day. Exactly 2 workers are needed to oversee the 14
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Unformatted text preview: machines. a. Write down a production function for the firm. b. What is the long-run total cost function, LTC(Q, w,r), for this firm? 5. Using 2 isocost lines and at least 1 isoquant, draw a situation in which an increase in the wage rate alters the long run total cost of producing a fixed quantity of output, Q . Does LTC rise or fall? 6. Using 2 isocost lines and at least 1 isoquant, draw a situation in which an increase in the wage rate does not alter long run total cost of producing a fixed quantity of output, Q . 7. If a firms production function takes the form F(L, K) = L + 2K, and it faces wage rate, w=3, and rental rate on capital, r=4, what is LTC(220, 3, 4)? 8. Suppose at Q=100, w=2, r=3, and K =11, we have STC(100,2, 3, 11)=60 Suppose it is also true that LTC(100, 2, 3)=51. What is the most we can say about K*(100, 2, 3)?...
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