Suppose that the local moving company has q 6L025 K05 where

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 DrexelHaul’s 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 DrexelHaul’s 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)?

Solution

Does DrexelHaul’s 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?

q = 6L^0.25 K^0.5

c.

Using the short-run production f

unction from (b), calculate the marginal product of labor.

q = 5

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.