Economics 301 – Intermediate Microeconomics
Final Exam
Exam A
John Moran
Fall 2005
INSTRUCTIONS – PLEASE READ BEFORE BEGINNING THE EXAM.
Please write your name on your examination book.
The exam consists of 3 pages. Please make sure that you have all of the pages.
There are 4 questions worth a total of 100 points. The point values associated with each
question are listed on the exam.
With the exception of the True-False questions, you must show your work (explanations,
diagrams, calculations, etc.) to receive full credit. Simply having stated the correct
conclusion is not sufficient, and will not earn you many points.
Please write neatly (particularly in constructing and labeling any diagrams). If I can’t
read it, it’s wrong!
Partial credit is available, so you should attempt to answer all of the questions, even if
you think that you do not know the answer.
Cheating is forbidden. If caught, you will be penalized severely.
You have the entire class period to complete the exam. Good luck!
1.
Some True-False Questions (25 points)
Please indicate whether each statement is “true” or “false.” You do not need to
explain your answer. Be sure to write out the words “true” and “false.”
a) (5 points) True or False? “Total variable cost is equal to zero when output is
zero.”
True. When output is zero, the optimal quantity of the variable input is zero.
b) (5 points) True or False? “In a perfectly competitive market, it is possible to
calculate the long-run market equilibrium without information on the market
demand curve.”
True. See your class notes for a discussion. In a nutshell, because firms
produce at the minimum of their long-run AC curves in any long-run
competitive equilibrium, each firm’s optimal quantity, the total quantity
produced by all firms, and the equilibrium price in the market can all be
determined from the long-run average and marginal cost curves.
c) (5 points) True or False? “When a perfectly competitive firm is maximizing
profits in the short-run, the profit-maximizing quantity occurs at the minimum of
average total cost.”
False. This occurs in the long run, but not (generally) in the short run. Draw
a standard diagram with price above the minimum of average cost to see this.
d) (5 points) True or False? “The difference between average total cost and average
variable cost falls as output rises.”
True. This is one of the two properties of short-run cost curves discussed in
class. The difference between ATC and AVC is AFC. AFC declines with
output because output “Q” is in the denominator and the numerator is a
constant (TFC).
e) (5 points) True or False? “Economic profits are zero in a short-run competitive
equilibrium.”
False. For the same reason (c) is false.
2.
Short-Run Profit Maximization (25 points)
Suppose the short-run marginal and average variable cost curves for a perfectly
competitive firm are given by
MC  20  40Q
AVC  20  20Q
a) (20 points) How many units of output will the firm produce at a price of $100 per
unit? Explain how you arrived at your answer and be sure to show all of your
calculations.
There are two steps required to compute the profit-maximizing level of output.
Many of your neglected the first step.
Step 1: Is P > AVC for some Q > 0, i.e. should the firm remain open and produce
a positive level of output? Plugging P = 100 and the equation for AVC into this
inequality leads to the expression: 4 > Q. Clearly there are many positive values
of Q that satisfy this inequality. Thus, the firm should remain open (i.e. produce
Q > 0).
Step 2: Set P = MC in the region where MC is increasing. Here, MC is increasing
for all Q > 0, so simply set P = MC and solve for Q. Doing so yields Q = 2.
b) (5 points) At what level of total fixed costs will this firm earn zero economic
profit?
Plug P = 100 and Q = 2 into the following expression and solve for TFC:
Profit = PQ – TVC(Q) – TFC = 0
Doing so yields TFC = 80.
Note: TVC is obtained by multiplying AVC by Q.
3. Two-Part Pricing (25 points)
You own a large amusement park located in rural central Pennsylvania. Your
customers all have the daily demand curve for rides displayed below. If you are
currently charging a unit price of $2.00 per ride, what is the optimal daily entrance fee
for the park?
Q  16  2 P
The optimal entrance fee for the park owner is equal to the consumer surplus
earned when customers purchase all the rides they want at a price of $2.00 per ride
(Q = 12 rides for the demand curve given above). Consumer surplus is calculated as
the area below the demand curve, above the unit price, and out to the quantity
purchased (consult your class notes for the graph). Mathematically, the area is given
by:
CS = 0.5*(Pint – P*)*Q*
where Pint = 8 is the vertical intercept of the demand curve, P* = 2 is the unit price,
and Q* = 12 is the quantity purchased. Here CS = $36.
4.
Optimal Choice of a Variable Input (25 points)
Standard Enterprises produces a product that it sells in a highly competitive market at
a price of $100 per unit. Its inputs include four machines (which cost the firm $50
each) and workers, who can be hired on an as-needed basis in the labor market at a
cost of $2800 per worker. Using the information contained in the following table,
answer the questions listed below.
Machines
Workers
Output
4
4
4
4
4
4
4
0
1
2
3
4
5
6
0
100
180
240
270
290
300
a) (5 points) How much are your fixed costs?
Fixed costs = r*K = $50*4 = $200.
b) (5 points) What is the variable cost of producing 100 units of output?
To produce 100 units of output the firm must hire 1 worker at a wage of
$2800, so VC(100) = $2800.
c) (15 points) How many units of the variable input should be used to maximize
profits? Thoroughly explain the reasoning behind your answer and be sure to
show all of your calculations.
The variable input should be hired up to the point where VMP = w, in the
region where MP is declining. When it’s not possible to set VMP exactly
equal to w, the firm should continue hiring workers as long as VMP exceeds
w (in the region where MP is declining). Remembering that VMP = P*MP,
the table can be expanded as follows:
Machines
Workers
Output
Marginal
Product of
Labor
VMP
4
4
4
4
4
4
4
0
1
2
3
4
5
6
0
100
180
240
270
290
300
-100
80
60
30
20
10
-10,000
8,000
6,000
3,000
2,000
1,000
Given a wage of $2800 per worker, the firm should hire 4 workers.