Homework 9&10
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1. Assume that this is a simultaneous move one shot game, i.e., each player moves simultaneously, and the game is played once. Two firms compete by advertising, and you are given the profit matrix for the advertising game. The numbers in the table show the profit for each firm from each outcome1
3
2
4
Firm 2
Do Not Advertise
Advertise
Firm 1
Do Not Advertise
0
Advertise
1
2
0
(a) What is each firm’s best response to its rival’s possible actions?
(i) If Firm 1 does not advertise what is Firm 2’s best action?
(ii) If Firm 1 advertises what is Firm2’s best action?
(iii) If Firm 2 does not advertise what is Firm 1’s best action?
(iv) If Firm 2 advertises what is Firm 1’s best action?
(b) What is Firm 1’s dominant strategy (if they have one)?
(c) What is Firm 2’s dominant strategy (if they have one)?
2. Assume that this is a simultaneous move, one shot game, i.e., each player moves simultaneously, and the game is played once. The two firms face the following profit matrix. The number in the table show the profit for each firm from each outcome
6
6
0
7
Firm 2
Low Price
High Price
Firm 1
Low Price
High Price
0
2
1
2
(a) What is the Nash equili
ium for this game?
(b) If these two firms were able to collude (negotiate) what outcome would they settle on?
(c) What is Firm 1’s secure strategy?
(d) What is Firm 2’s secure strategy
3. Refer to the following game.
Player 2
t1
t2
t3
Player 1
S1
4, 10
3, 0
1, 3
S2
0, 0
2, 10
10, 3
(a) What is Player 1’s dominant strategy (if they have one)?
(b) What is Player 2’s dominant strategy (if they have one)?
(c) For each of the following options please point out which options constitute a Nash
equili
ium?
A. S1, t1
B. S2, t2
C. S2, t3
D. S1, t2
4. Refer to the normal-form game of price competition in the payoff matrix below.
Firm B
Low Price
High Price
Firm A
Low Price
0, 0
50, −10
High Price
−10, 50
20, 20
Suppose the game is infinitely repeated, and the interest rate is 10 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid and each firm may make independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.
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1. In most cities all lumber yards advertise that they have the lowest price in town. In addition, they often claim that they will match the prices of any other lumber yards. Will this form of competition
ing about constantly lowering prices and zero economic profits for firms? Please explain.
2. The American Baker's Association reports that annual sales of bakery goods last year rose 15 percent, driven by a 50 percent increase in the demand for
an muffins. Most of the increase was attributed to a report that diets rich in
an help prevent certain types of cancer. You are the manager of a bakery that produces and packages gourmet
an muffins, and you cu
ently sell
an muffins in packages of three. However, as a result of this new report, a typical consumer's inverse demand for your
an muffins is now P = 8 - 1.5Q. If your cost of producing
an muffins is C(Q) = 0.5Q (MC = 0.5), determine the optimal number of
an muffins to sell in a single package and the optimal package price. Please show all calculations and give any necessary explanation.
3. A computer hardware firm sells both laptop computers and printers. It has a large inventory of laptops and printers that it wants to sell, so it has not variable production cost. The firm has determined that there are three type of consumers for its products
Laptop
Printe
Bundle (Laptop + printer)
Customer type A
$800
$100
$900
Customer type B
$1,000
$50
$1,050
Customer type C
$600
$150
$750
To simplify the analysis, you may assume that there is one customer of each type.
(a) If the firm were to charge only individual prices and not the bundle price, what price should it charge for its laptops and what price should it charge for its printers in order to maximize revenue? Assume that the firm has one customer of each type. Please explain.
(b) If the laptop and printer are bundled together, what price will the firm charge for the bundle in order to maximize revenue? Assume that only the bundle is sold and the laptop and printer are not available separately. Please explain.
(c) Assume that the laptop and the printer are bundled together, and the laptop is available separately for $600 and the printer is available separately for $100. What will the bundle price now be in order to maximize revenue? Please explain.
4. Refer to the figure below
MC
Q
P
MRHigh
MRLow
DLow
DHigh
Q3
Q2
Q1
P1
P2
P3
P4
(a) What is the capacity of this firm?
(b) What price and quantity will the firm charge during low demand (off-peak) times?
(c) What price and quantity will the firm charge during high demand (peak) times?