Midterm #2 (100pts)
Name:
Model comparison and general questions (20pts)
a. Assuming two firms have the same constant marginal cost, and some positive fixed cost, both firms
produce a homogeneous product, and face a linear demand
i. Under what type of market structure is the market price the highest?
Monopoly or cartel
ii. Rank Cournot, Stackelberg, and Bertrand by the total market output (from the highest to the
lowest)
Bertrand, Stackelberg, Cournot
iii. Rank Cournot, Stackelberg, and Bertrand by the total market profit (from the highest to the
lowest)
Cournot, Stackelberg, Bertrand
b. What is the difference between Cournot and Bertrand
Cournot – firms compete on quantity, Bertrand – on price
c. Under what type of competition even with two firms the market price equals the perfectly competitive
price?
Bertrand
d. How can you determine whether firms are in a collusive cartel agreement from the elasticity of demand?
Cartels price at monopoly price which is on the elastic part of the demand
e. If two out of three Cournot firms merge and the two resulting firms compete in Cournot fashion. Will the
profits of the merged firm exceed the total pre-merger profits of the two merged firms? Assume that each
firm still has to incur its own fixed cost, marginal cost is constant, and the demand is linear.
No
f.
Two identical firms A and B compete in Cournot fashion. Which firm’s reaction function is shown below
A
g. What is the highest profit that a Stackelberg leader can make
if it cannot credibly commit to quantity (and neither can the
follower)
QA
Cournot profits
QB
1
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Cournot (#2-20pts, #3-5pts)
2. Setup: the demand is given by Q  18  P .There are two firms: A and B. The cost of each firm is given
by C  Q   8  6Q . The firms compete in Cournot fashion by simultaneously choosing quantity
a. Write firm A’s residual demand
QA=18-QB-P
Some answers had the demand written as a function of both quantities – partial credit.
b. Write firm B’s reaction function
QB=6-0.5QA
Technically reaction function has to be of the form QB=…QA... many answers just wrote the right side of the
equation. I did not take points away for this
c. Find firm A’s quantity
4
d. Find firm B’s quantity
4
3. (+) Continuing with the previous setup. Can firm B increase profits through investment that
would double its (fixed cost) but lower marginal cost by half?
Yes because the profit will increase to 20 from 8.
With the new cost CB  Q   8  6QB the reaction function becomes QB  7.5  0.5QA . The
quantities of B and A are respectively 6 and 3. The price becomes 9.
A common mistake here was to assume that both firms A and B will increase the fixed cost and have lower
marginal cost. If the rest of the solution was correct it resulted in a minimal reduction.
2
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Stackelberg (#4-20pts, #5-pts)
4. Setup: the demand is given by Q  38  2 P There are two firms. The cost of each firm is given by
C  Q   3  Q The firms compete in Stackelberg fashion by sequentially choosing quantity.
a. Find leader’s residual demand after the leader takes into account follower’s quantity
QL=40-4P
b. Present this game in extensive form and show how to find an equilibrium of this game by adding
arrows
QFollower=9
Firm 2
QLeader=
Q=0
_159_, 0
QFollower=9
_87__, _64.5__
QCournot=12
69, 69
Firm 1
QCournot=12
_78__, _37.5__
Firm 2
Wrong profits without calculation were not credited. I did my best to trace the mistakes.
5. (+)Continuing with the previous setup, can the leader prevent entry by producing 20 units? Show
calculations.
No, the follower will make profit of 29.
1
2
Follower’s reaction function is QF  18  QL , the leader demand after follower enters is then QL  40  4 P ,
leader’s MR is then MRL  10 
1
P . Setting it equal to the marginal cost leader will produce 9x2=18, the
2
follower reacts with 9. The price is then P=19-0.5(9+18)=5.5.
Yes, or no without calculations were not credited but even a wrong answer received partial credit if the
calculations were correct and the wrong answer resulted from an arithmetic mistake.
3
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Bertrand (5pts)
6. Setup: the demand is given by Q  6  0.5P . There are two firms. The cost of each firm is given by
C  Q   2Q . The firms compete in Bertrand fashion by simultaneously choosing price
a. Find Bertrand equilibrium price and quantity
P=
2
Q= 5
b. On the graph below, explain why your answer to the previous question is not an equilibrium if
producers are capacity constrained. Assume each firm has capacity that equals half of the
Bertrand quantity. (notice this question is not asking to prove that the equilibrium does not exist)
4
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Game theory (#7-5pts, #8-15pts)
7. Find all Nash equibria of the following game or show that none exist
Player 2
Player 1
A
A
1, 2
B
3,3
B
2,1
10,0
{B,A}
8. The demand is given by Q  18  P .There are two firms: A and B. The cost of each firm is given by
C  Q   8  6Q . Setup the collusion game as a prisoner’s dilemma game. Assume that when both firms
collude they produce monopoly output and split the profits; when both firms compete they revert to
Cournot equilibrium; when one firm colludes and the other competes the colluding firm still produces half
of monopoly output and the competing firm produces its best response quantity.
Firm 2
Collude, Q=3
Compete
Collude, Q=3
_10__, _10__
_7__, _12__
Compete
_12__, __7_
_8__, _8__
Firm 1
a. Which set of strategies represents the best outcome for both firms? Is it also the best choice?
{Collude, collude}, not the best choice
b. Find Nash equilibrium of the game by showing arrows
Solving for monopoly price and quantity we get P=12, Q=6. When each firm produces half QA=QB=3, so that the
profits of each firm are 12x3-6x3-8=10.
In on
A common mistake was to fill in quantities instead of payoffs. This is a big mistake because it shows that the
student thinks that the firms are maximizing quantity, not profits.
Another common mistake was not to subtract the fixed cost for each of the participants in the cartel. The collusive
profits were then 14, not 10. Resulted in a deduction.
5
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Reading and discussion questions (15pts)
9. Orbitz reimburses customers for the difference in price if another customer books the same hotel at a
lower price. How can this behavior lead to collusion?
Orbitz is less likely to reduce price because it is now more costly.
The key to this question was to realize that it is Orbitz committing to high price, not the other firms.
10. Why do firms need to announce price increases if they are in a collusive agreement?
Because the firm that increases price unilaterally would lose revenues. Announcements are necessary to allow
other firms to follow or rescind the increase otherwise.
11. Give 3 reasons for price wars
Deflation,
Differential rates of growth (e-books vs regular)
New entrant
Decrease in the demand
12. What is a “network industry”? Give an example
Consumers’ utility increases in the number of users in a network industry. Examples: Zip drive, Windows
operating system
13. When can a firm gain advantage by increasing everyone’s cost?
When it can produce at a lower marginal cost or when it has incurred the sunk cost
14. What is the difference between predatory pricing and limit pricing?
Predatory pricing: pricing below MC to drive out competition
Limit pricing: producing a quantity that would prevent entry (deteriorate entrant’s profits)
6
Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.