Assignment:
1.A study of the costs of electricity generation for a sample of 112 British firms in 1946 - 1947 yielded the following long-run average variable cost and marginal cost functions:
AVC = 2.48 + .0066Q + .0000058Q2 -.000092QZ -.052Z + .00036Z2
MC= 2.48 + .0132Q + .0000174Q2 - .000184QZ -.052Z + .00036Z2
Where:
AVC = average variable cost measured in pence per kilowatt-hour (kWh). (A pence was a British monetary unit equal, at that time to 2 cents U.S.).
MC =marginal cost measured in pence per kilowatt-hour (kWh).
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. (Hint VC = AVC*Q)
b)Holding Z (the plant size) constant at 100,000, determine the AVC and MC functions for electricity. (Hint: substitute 100,000 for Z in both equations.)
c)Holding Z constant at 100,000 kilowatts, determine the output level that minimizes AVC. (Hint: Set AVC = MC and solve for Q or set dAVC/dQ = 0 and solve for Q. Both will generate the same value of Q.)
2.Assuming that all other factors remain unchanged, determine how a firm's breakeven point is affected by each of the following:
a)The firm finds is can raise price due to a decrease in foreign competition. (Hint: See graph on page 319.)
b)The firm's direct labor costs are reduced as a result of a new labor contract.
c)The Occupational Safety and Health Administration (OSHA) requires that the firm to install new ventilating equipment in its plant. (Assume this does not affect worker productivity.)
3.Cool-Aire Corporation manufactures a line of room air conditioners. Its breakeven sales level is 33,000 units. Sales are approximately normally distributed. Expected sales next year are 38,000 with a standard deviation of 3000 units.
a)Determine the probability that Cool-Aire will incur an operating loss (Hint: Find your Z statistic first and then refer to the Z table.)
b)Determine the probability that Cool-Aire will operate above its breakeven point. (Hint: The probability of operating above breakeven is one minus your answer above.)
1.Assume that a firm in a perfectly competitive industry has the following total cost schedule:
|
Output
|
Total Cost
|
Average Cost
|
Marginal Cost
|
|
10
|
110
|
|
na
|
|
15
|
150
|
|
|
|
20
|
180
|
|
|
|
25
|
225
|
|
|
|
30
|
300
|
|
|
|
35
|
385
|
|
|
|
40
|
480
|
|
|
a)Calculate the average and marginal costs for the firm.
b)At a market price of $15 per unit, how many units will be produced and sold? What is the profit per unit? What is total profit?
c)Is the industry in long run equilibrium at this price? Why or why not?
2.The Poster Bed Company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function (P), inverse demand function (Q), total revenue function (TR), and marginal revenue function (MR):
P = 910 - 6Q è Q = 151.67 - .167P
TR = 910Q -6Q2
MR = 910 - 12Q
The cost analysis department has estimated the total cost function (TC) and the marginal cost function (MC) for the poster bed as:
TC = 30Q2 + 10Q + 2000
MC = 60Q + 10
a)Calculate the level of output that should be produced to maximize short run profits.
(Hint: Set MR = MC and solve for Q)
b)What price should be charged?
c)Compute total profit at this price - output combination
d)Compute the point price elasticity of demand at the profit-maximizing level of output.