Dirt Diggers (DD) is an excavating firm that excavates roadside ditches for laying drainpipe. Its output follows the following production function:
Q = 10L - .1L2
where L denotes labor hours and Q the length of the ditch in meters. DD hires labor at the going wage rate of $16 per hours.
(a) DD has received an offer to excavate 250 meters for a lump sum price of $700. Should it accept the offer? Explain with appropriate calculations.
(b) Suppose instead of the previous offer DD is offered as much or as little excavation work at a price of $2.00 per meter dug. Should it accept the offer? If it does, calculate its profit and the optimal (profit maximizing) output (meters dug) and labor usage.