) You manage Dirt Diggers, an excavating firm that excavates roadside ditches fo
ID: 1177729 • Letter: #
Question
) You manage Dirt Diggers, an excavating firm that excavates roadside ditches for laying drainpipes. Its output follows the production function:
Q = 10L -.1L2
where L denotes labor hours and Q the length of the ditch in meters. You can hire labor at the going wage rate of $12 per hour. As the manager of DD you want to earn as high a profit as possible.
(a) You have received an offer to excavate 250 meters for a lump sum payment of $500. Should you accept the offer ? Explain with appropriate calculations.
(12 points) (b) Suppose that instead of the previous offer, you are now offered as
much or as little excavation work at a price of $2.00 per meter dug. Should you accept the offer ? Why or why not ? If you accept the offer calculate DD%u2019s resulting profit. Also, calculate the optimal level of output (meter dug) and the level of labor usage.
Explanation / Answer
Q = 10L -.1L2
250 = 10L - 0.1L^2
L = 50
Total Cost = 50*$12 = $600
Offer = $500
Profit = 500-600 = -$100
should not take the offer
Offer = $2/meter
Shall accept the offer, as
Total Cost = 12L
Total Revenue = 2Q = 20L - .2L^2
Profit = 20L - .2L^2 - 12L > 0
for optimum profit level,
dP/dL = 8 - .4L = 0
L = 20
Profit = 8L - .2L2 = 80
Q = 10L -.1L2 = 160
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