A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit. a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)
A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit. a. Is this technology decreasing return to scale? Show your argument. b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example) c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.1P
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- A firm’s production function is given by q = min{M, L1/2}, where M is the number of machines and L is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit.
a. Is this technology decreasing return to scale? Show your argument.
b. Is it true the statement that if average production cost is increasing, a firm’s technology exhibits the decreasing return to scale. (If yes, show the proof. If not, show a counter example)
c. Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)
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