4 (ii) You manage Dirt Diggers, an excavating firm that excavates

Question

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.

(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’s resulting profit. Also, calculate the optimal level
of output (meter dug) and the level of labor usage.

(iii) As a manager of a firm you find the marginal cost of the firm to be $10 and
the fixed cost $100. For the range of prices that you are planning to charge,
own price elasticity of demand is believed to be –1.5. Calculate the optimal
(profit maximizing) price that you should charge. Show all calculations.