Due at the start of class on January 28. You may work with your teammates. but you must turn in your own version. All solutions should be neatly and clearly written. Be sure to label any graphs and clearly indicate your reasoning.
1. Suppose that the local moving company DrexelHaul has the following production function:
q Wises
where q is the number of boxes moved per day, L is labor (measured in worker hours), and K is the number of moving trucks.
a. Does DrexelHaul's production function exhibit decreasing, constant, or increasing returns to scale? Explain your answer using math, and describe in words what it means to have the type of returns to scale you find.
b. Suppose that the number of trucks is fixed in the short run at 16. What is the short-run production function?
c. Using the short-run production function 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 DrexelHaul's production function?
g. Suppose that DrexelHaul develops a new truck routing system that changes its production function to
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Does this new technology constitute neutral technical progress, non-neutral technical progress, or neither? Explain your answer.
h. Calculate the MRTS given DrexelHaul's new production function. How does it compare to that which you calculated for the old production function in part (t)?
i. Now suppose that DrexelHaul adopts new "driverless" technology for its trucks that changes its production function from that in part (g) to
q Sets!:
Does this new technology constitute neutral technical progress, non-neutral technical progress, or neither? Explain your answer.
j. Calculate the MRTS given DrexelHaul's new production function. How does it compare to that which you calculated for the old production functions in parts (1) and (h)?