(1) You manage Dirt Diggers, the excavating firm which excavates roadside ditches for laying drainpipes. Its output follows the production function:
Q = 10L -.1L2
Where L denotes labor hours and Q length of the ditch in meters. You can hire labor at 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 the offer to excavate 250 meters for lump sum payment of $500. Should you accept offer? Describe with suitable calculations.
(b) Assume that instead of previous offer, you are now offered as much or as little excavation work at a price of $2.00 per meter dug. Must you accept the offer? Why or why not? If you accept offer compute DD's resulting profit. Also, compute the optimal level of output (meter dug) and the level of labor usage.
(2) As the manager of a firm you determine marginal cost of firm to be $10 and the fixed cost $100. For range of prices that you are planning to charge, own price elasticity of demand is believed to be -1.5. Compute the optimal (profit maximizing) price that you muts charge. Illustrtae all calculations.