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Econ10A_PSET5

# Econ10A_PSET5 - Problem Set 5 THEORY OF PRODUCTION 1 a If a...

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Problem Set 5 THEORY OF PRODUCTION 1. a. If a firm’s production function is given by F(L,K) = 3 9 18 K L , which is larger AP L (8, 8) or AP K (8, 8)? 2. a. What is the MRTS of the function F(L,K)= L 2 + K? b. Does this function exhibit diminishing MRTS? c. Does this function exhibit increasing returns to scale? 3. Suppose MP L (9, 20) =3 and AP L (9,20) = 6. a. Is AP L (9,20) smaller than, larger than, or equal to AP L (10, 20)? b. Is AP L (9, 20) smaller than, larger than, or equal to AP K (10, 20)? 4. Suppose AP L (L, K) is always 17K. a. What is F(L,K)? b. What is MP L (L,K)? c. Does F(L,K) exhibit diminishing MRTS? 5. If MRTS(L,K) is always 3/2, draw the isoquants of F(L,K). 6. Let F(L,K) = 5LK. When K rises does MP L rise or fall? Can you think of a reason why this might be a good description of a real firm’s production? 7. My firm digs ditches. Its production inputs are workers and shovels and its output, measured in cubic feet per day, is ditches. Each worker needs a shovel (the ground is too hard to dig with bare hands) and each worker is then able to dig 50 cubic feet in a

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