Eco 550 Week 5 Problems Chapter 9 and 10
3. A study of the costs of electricity generation for a sample of 56 British firms in 1946–1947 yielded the following long-run cost function:16 AVC = 1.24 + .0033Q + .0000029Q2 − .000046QZ − .026Z + .00018Z2 where AVC = average variable cost (i.e., working costs of generation), measured in pence per kilowatt-hour (kWh). (A pence was a British monetary unit equal, at that time, to 2 cents U.S.) Q = output; measured in millions of kWh per year Z = plant size; measured in thousands of kilowatts
a. Determine the long-run variable cost function for electricity generation.
b. Determine the long-run marginal cost function for electricity generation.
c. Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost functions for electricity generation.
d. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs.
e. Determine the short-run average variable cost and marginal cost at the out- put level obtained in Part (d).
4. Assuming that all other factors remain unchanged, determine how a firm’s break- even point is affected by each of the following:
a. The firm finds it necessary to reduce the price per unit because of increased foreign competition.
b. The firm’s direct labor costs are increased as the result of a new labor contract.
c. The Occupational Safety and Health Administration (OSHA) requires the firm to install new ventilating equipment in its plant. (Assume that this action has no effect on worker productivity.)
5. Cool-Aire Corporation manufactures a line of room air conditioners. Its break- even sales level is 33,000 units. Sales are approximately normally distributed. Expected sales next year are 40,000 units with a standard deviation of 4,000 units.
a. Determine the probability that Cool-Aire will incur an operating loss.
b. Determine the probability that