Question

Suppose that the output Q (in units) of a certain company is Q = 75K1/3L2/3, where...

Suppose that the output Q (in units) of a certain company is

Q = 75K1/3L2/3,

where K is the capital expenditures in thousands of dollars and L is the number of labor hours.

Find ?Q/?K when capital expenditures are $343,000 and the labor hours total 8000. (Round your answer to the nearest whole number.)
?Q/?K =   thousand units per thousand dollars

Interpret ?Q/?K.

If labor hours remain at 8000 and K increases by $1000, Q will increase about ____ thousand units.


Find ?Q/?L when capital expenditures are $343,000 and the labor hours total 8000. (Round your answer to the nearest whole number.)
?Q/?L =  thousand units per labor hour

Interpret ?Q/?L.

If capital expenditures remain at $343,000 and L increases by one hour, Q will increase about ____ thousand units.

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Homework Answers

Answer #1

Equation be = Q = 75K^1/3L^2/3.....................(1)

K = $ 343000

L = 8000 hours

Putting values in equation,

Q = 75 * (343000)^1/3 * (8000)^2/3

Q = 75 * 70 * 400

Q = 2100000 units

1 Q/K = 2100000 / 343000

Q/K = 6.12 units per thousand dollars

2 L = 8000 hours

K = $ 344000

Putting the values in equation (1)

Q = 75 * (344000)^1/3 * (8000)^2/3

Q = 75 * 70.068 * 400

Q = 2102040 units

Increase in units = 2102040 - 2100000

Increase in units = 2040 units

3 Q/L = 2100000 / 8000

Q/L = 262.5 thousand units per labor hour

4 K = $ 343000

L= 8001 hours

Putting the values in equation (1)

Q = 75 * (343000)^1/3 * (8001)^2/3

Q = 75 * 70 * 400.033

Q = 2100173.25 units

Q/L = 2100173.25 / 8001

Q/L = 262.49 thousand units per labor hour

Increase in units = 2100173.25 - 2100000

Increase in units = 173.25 units

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