Download Exam 2 Fall 2006 Answer Key

Econ 4333 Economics of Organizations
Exam 2 Fall 2006
Name __________
You have one hour and twenty minutes to complete this exam. The exam consists of 15
multiple choice / explanation questions worth 4 points each. There are three written
problems worth 20 points each. You can select two of the written problems to count
towards your grade. If you do not clearly denote two, we will grade the first two.
Therefore the total number of points is 100. Please turn off all cell phones and pagers as
they can be a distraction to your classmates. When leaving the exam please try to be
courteous to those who are still taking the test.
Q1. Define the term dominant strategy.
A dominant strategy is a strategy that a player wants to select regardless of what actions
other players select.
Q2. Circle each of the following that would lead to monopoly power
*a. sole ownership of an input
*b. a production function that exhibits diminishing ATC over the relevant range
*c. a patent or copyright
Q3. & Q4. The following table gives the values for goods A and B for 5 potential
customers. You are a monopolist in both markets and you TC = qa + qb. (That is you
MC is 1 for each item)
Customer
Value of A
Value of B
Elmo
6
3
Bert
3
6
Ernie
8
2
Oscar
2
8
Grover
5
5
Q3. If you sell the item separately, the most profit you can make is?
*a.
24
b.
30
c.
35
d.
45
Q4. If you sell the goods in a bundle, the most profit you can make is?
a.
24
b.
30
*c.
35
d.
45
Q5. Explain why there is a dead weight loss from monopoly.
A profit maximizing firms operates where MR=MC. Since the monopolist faces a
downward sloping demand curve P>MR. So the firm will operate where P>MR=MC.
But the efficient quantity is where P=MC so the monopolist is inefficient. That is, the
monopoly produces where the value of the good (Price) is above the cost of the good
(MC) so that quantity is too low relative to the social optimum.
Q6. From the DeBeer’s case we discussed in class, how did DeBeers deal with defection
on the cartel by mines in Zaire?
a. branded their own diamonds
b. bought out the Zaire mines
c. filed suit in US district court
*d. flooded the market with diamonds
Q7. The CSO through which the diamond cartel functioned was located in
a. Belgium
*b. England
c. South Africa
d. Zaire
Q8. The experiment on the first day of class in which you had to decide if you should
allocate your time in the forest collecting food for yourself or in the communal field is an
example of
*a. a prisoner’s dilemma
b. a game of chicken
c. a battle of the sexes game
d. a rock, paper scissors game
Q9. Based on the Hotteling model, we would expect to see the two political candidates in
an election
a. at the extremes of the distribution of voters
b. in the center of their own party’s base
*c. in the center of the entire distribution of voters.
Q10. Give an example of third degree price discrimination in practice.
Senior citizen discounts, discounts fro locals
Q11. Give an example of second degree price discrimination in practice.
Super sized fries, weekend only delivery of the paper.
Q12. You run the only still in the county. Zeke’s value for jugs of moonshine is P=30Q. It costs $2 to produce a jug of moonshine in addition to the $25 fixed costs. If you
were going to use a two-part tariff, what per unit price should you charge Zeke?
*a. $2
b. $14
c. $16
d. $392
Q13. Explain what it means for a strategy to be rationalizable. It is sufficient to explain
your answer by referring to the Princess Bride clip we watched in class.
It means that an action can be justified as the best reaction to an infinitely long pattern of
previous choices, which in turn we best responses.
Q14. Consider the following game. For what interest rates would a player be willing to
defect on the cooperative outcome?
Cooperate
Defect
Cooperate
5,5
20,0
Defect
0,20
0,0
a. i > 2/3
b. i < 2/3
*c. i > 1/3
d. i < 1/3
Q15. If a firm engages in perfect price discrimination, then
a. CS>0 but DWL=0
b. CS>0 and DWL>0
*c. CS=0 and DWL=0
d. CS=0 but DWL>0
Written Problem 1 (20 points) [Grade this problem? YES
NO ]
Three firms operate in a market where demand is given by P=120-Q. Each firm has
TC=10 so there is no marginal cost.
If the three firms compete according to the Cournot model, what profit will each firm
earn?
1=(120-q1-q2-q3)*q1-10. Taking the derivative and setting it equal to 0 we find 120-2q1q2-q3=0. Since the firs are symmetric we have that q1=q2=q3 so that 120-4q1=0 or q1=30.
Therefore, Q=90 and P=30 so 1=30*30-10=890.
Now suppose that firm 1 is a first mover and sets its quantity before either of the other
firms. If the second and third firms select their output level simultaneously after
observing the first firm’s choice, what quantity should each firm choose?
Firms two and three select quantities simultaneously after observing q1.Hence their
problems look like firm 1’s problem from part 1. That is 120-q1-2q2-q3=0. By symmetry
q2=q3, so q2 = 40-q1/3. Plugging these values into Firm1’s profit function we have
1=(120-q1-40+ q1/3-40 + q1/3)*q1-10 = (40-q1/3)*q1-10. Taking the derivative and
setting it equal to zero gives q1=60. So Firm 1 produces 60 and Firms 2 and 3 each
produce 40-60-3=20.
Now suppose the second and third firms merged to form a single firm. Assuming this
firm sets its quantity after the first firm, what would be the change in HHI?
If Firms 2 and 3 merge we would have the merged firm’s best response as 120-q1-2q2=0
and taking this into account Firm 1 would maximize 1=(120-q1-60+ q1/2)*q1-10= (60q1/2)*q1-10. Taking the derivative and setting it equal to 0 yields the solution that q1=60.
In response the merged firm will produce 30. The original HHI was 602+202+202=4400.
(Since the quantities sum to 100, a firm’s quantity and market share are the same.) The
new HHI is (60/90*100)2+(30/90*100)2=5578. So the change in the HHI is 1178
(something the FTC would likely consider anticompetitive).
Written Problem 2 (20 points) [Grade this problem? YES
NO ]
You are a monopolist with a total cost of $5Q. Currently you are working with two
customers. Alan has demand given by P = 25-Q and Sharon has demand given by P =
41-3Q. If you were able to set prices for each customer, who can then decide how many
units to buy, what is the maximum profit you could make?
For Alan, the optimal price is 15 and the optimal quantity is 10.
For Sharon, the optimal price is 23 and the optimal quantity is 6.
The profit to the firm would be 15*10+23*6-5*(10+6)=208.
If you were able to engage in first degree price discrimination, what profits could you
make?
You would sell Alan 20 units for a total payment equal to the area under demand, which
is 300. You would sell Sharon 12 units for a total payment of 276. Your total costs
would be 5*(20+12) so your profits would be 416.
Now suppose you could not treat the two people differently, but could offer a quantity
discount to engage in price discrimination. One possible quantity discount you could
offer is P=20 if Q< 10 and P=15 if Q >10. Define incentive compatible and individually
rational and determine if this scheme satisfies these properties for Sharon, the person for
whom the high price was designed.
Individually ration means that person prefer trading to doing nothing. Incentive
Compatible means that each type prefers the package designed for their type. CS
If Sharon were to pay 20 per unit, she would buy 7 units and here surplus would be
(1/2)*(41-20)*7 = 73.5. This is positive so it beats not buying; it is IR. If Sharon bought
10 units at a price of 15, the value to her of what she bought would be 260 and she would
pay 150. This would leave her a surplus of 110, which is greater than 73.5 so it is not IC.
Written Problem 3 (2 parts totaling 20 points) [Grade this problem? YES NO ]
Part A (worth 10 points)
The market demand curve is given by P=100-Q. Suppose that there are two firms that
each have TCi= 20qi. If the two firms compete according to the Bertrand model where
they simultaneously pick prices and the lowest priced firm serves the entire market, what
is the equilibrium price?
P=20.
Draw the best response curves for the two firms and clearly label the Nash equilibrium.
The key to this figure is realizing that the firm wants to be just below the competitor,
unless the competitor is at or below 20 or charging more than the monopoly price. Firm
1’s best response is 20 as long as
The black line is Firm 1’s best response curve and the Blue dashed line is Firm 2’s best
response.
q2
PM=60
MC=20
MC=20
PM=60
q1
Written Problem #3
Part B (worth 10 points)
Consider the following two player game of predatory pricing.
New Firm Enters
New Firm Does Not Enter
Incumbent Competes
2,2
0,10
Incumbent Predatory Prices
-1,-1
0,10
Draw the best response curve for each firm and identify all pure and mixed strategy Nash
equilbria.
Competes
Incumbent
Predatory Prices
Enters
Not Enters
New Firm
The solid blue line is the best response for the incumbent and the dotted red line is the
best response for the new firm. The Nash equilbria are circled. To determine where the
new firm is indifferent between entering and not entering, we set the expected payoffs
from the two actions equal. Let p = probability that the incumbent competes. The
expected payoff from entering is 2p-1(1-p)=3p-1. The expected payoff from not entering
is 0p+0(1-p)=0. setting the two expected values equal and solving gives p=1/3 as the
new firm’s switching point.
Draw the extensive form game in which the New Firm is the first mover. Explain the
concept of backwards induction and identify the subgame perfect Nash equilibrium.
N
0
10
I
-1
-1
2
2
Backwards induction means that you consider what will
happen in the last stage of the game, use this information
to determine what will happen at the next to last stage,
which one uses at the preceding step, and so on back to
the beginning of the game to determine what will occur.
The subgame perfect Nash equilibrium in which the new
firm enters and the incumbent competes is highlighted in
red.