# Does the short-run production function from (b) exhibit diminishing marginal returns to labor?

Suppose that the local moving company has: q = 6L^0.25 K^0.5 where q: is the number of boxes moved p Show more Suppose that the local moving company has: q = 6L^0.25 K^0.5 where q: is the number of boxes moved per day L is labor (measured in worker hours) and Kis the number of moving trucks. a).Does DrexelHauls production function exhibibit increasing or decreasing constant or increasing returns of scale! explain your answe using math. b. Suppose that the number of trucks is fixed in the short run at 16. Wat is theshort-run production function? c. Using the short-run production f unction from (b) calculate the marginal product of labor. d. Does the short-run production function from (b) exhibit diminishing marginal returns to labor? Show why it does or does not using math and explain in words what diminishing marginal returns to an input means. e. Using the short-run production function from (b) graph the relationship between output q and labor L (putting output on the y-axis and quantity of labor on the x-axis). In a separate figure graph the relationship between the marginal product of labor and labor (putting the marginal product of labor on the y-axis and quantity of labor on the x-axis). Note: these graphs do not need to be to scale. f. Now suppose that we are in the long run such that both capital and labor are adjustable (i.e. K is no longer fixed at 16). What is the marginal rate of technical substitution (MRTS) for DrexelHauls production function? g. Suppose that that the company develops a new truck routing system that changes its production function to q = 8L^0.25 K^0.5 Does this new technology constitute neutral technical progress non-neutral technical progress or neither? Explain your answer. h. Calculate the MRTS given the company new production function. How does it compare to that which you calculated for the old production function in part (f)? i. Now suppose that DrexelHaul adopts new driverless technology for its trucks that changes its production function from that in part (g) to q = 8L^0.25 K^ Does this new technology constitute neutral technical progress non-neutral technical progress or neither? Explain your answer. j. Calculate the MRTS given new production function. How does it compare to that which you calculated for the old pr oduction functions in parts (f) and (h)? Show less

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