Homework 4
1. Production and Costs
Assume that we are in the short-run and complete the following table containing various measures of costs.
|
Quantity
|
Labor
|
FC
|
VC
|
TC
|
AFC
|
AVC
|
ATC
|
MC
|
MPL
|
|
0
|
0
|
|
|
|
--
|
--
|
--
|
--
|
--
|
|
5
|
1
|
|
|
|
120
|
|
|
24
|
|
|
20
|
2
|
|
|
|
|
|
42
|
|
|
|
40
|
3
|
|
|
960
|
|
|
|
|
|
|
60
|
4
|
|
|
|
|
|
|
6
|
|
|
75
|
5
|
|
600
|
|
|
|
|
|
|
|
80
|
6
|
|
|
|
|
9
|
|
|
|
Use the information you calculated in the table above to answer the following questions.
a. Between which two quantities of output does the average total cost curve attain its minimum?
b. Define what it means for a production technology to exhibit diminishing returns to labor. Does the technology reflected above exhibit decreasing returns to labor? Why or why not?
2. Perfect Competition
The market for gasoline in the City of Madison is characterized by perfect competition. Firms and consumers are price takers and there is free entry and exit. Assume this industry is a constant cost industry.
The total cost and marginal cost functions for an individual firm are given by the following equations (assume all firms are identical in terms of their technologies, and therefore their cost functions):
TC = (Qs)2 + 2*(Qs) + 9
MC = 2*Qs + 2
(Hint: You do not need the demand equation to solve parts a. and b.)
a. What is the equilibrium price that will prevail in the market?
b. What will be the output of each firm in the long-run equilibrium?
Suppose that the aggregate demand is given by the following equation:
Demand: Pd = 500 - 2*Qd
c. How many firms will exist in the long-run equilibrium?
Suppose that the City Council votes for an increase in the price of public transportation such that the new aggregate demand curve for gasoline shifts out and is given by the following equation:
Pd = 900 - 2*Qd
(Hint: Before diving into calculations think about the questions and about what you know about perfect competition.)
d. Will the new short-run profits be negative, positive, or zero?
e. Will the new long-run profits be negative, positive, or zero?
f. What will be the new long-run equilibrium price?
g. What will be the output of each firm in the new long-run equilibrium?
3. Perfect Competition with a Tax
Now suppose that the City Council of Madison notices that due to its increase in the price of public transportation, more people are driving to work and air pollution is increasing. They therefore decide that in order to discourage people from driving, they will issue a $4 excise tax on consumers on the consumption of gasoline. Assume the market demand curve is Pd = 900 - 2Qd.
a. What is the new long-run equilibrium price with the tax from a consumer's perspective and from the firms' prospective? (Think about this one for a minute before diving into the calculations.)
b. Will the number of firms in the long-run equilibrium be higher or lower than without the tax?
c. What will happen to firm profits in the short-run due to the tax?
d. What will happen to firm profits in the long-run due to the tax?
e. What is the value of the deadweight loss due to the tax? (Compare the long-run equilibrium at the end of question number 2 to the long-run equilibrium in this question.)