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.
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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