Answers to ECMC02 test, November 5/ 2004
1. A firm has a dominant strategy when its best move does not depend on the move of the other
firm, in other words, the firm has a best move which does not change when the other firm
changes its strategy. In both Game #3 and Game #5, Firm 1 will choose Strategy B no matter
what strategy is chosen by Firm 2. The correct answer is (N).
2. A Nash equilibrium is a pair of strategies (i.e., one for Firm 1 and one for Firm 2) which is
stable in the sense that neither firm will have an individual incentive to change strategy once
it knows what the move of the other firm is. Game #1 and Game #4 both have two Nash
equilibria. In Game #1, Strategy A and Strategy Y is a Nash equilibrium, but so is Strategy B
and Strategy Z. In Game #4, Strategy A and Strategy Z is a Nash equilibrium, but so is
Strategy A and Strategy Y. The correct answer is (H).
3. A Prisoners’ Dilemma is a game where the Nash equilibrium does not best serve the
collective interests (profits) of the two firms. However, each firm has incentives which lead
it to “cheat” on these collective best interests, resulting in an equilibrium with lower total
returns for the two firms combined. There are no Prisoners’ Dilemma results shown in these
games. The correct answer is (Z).
4. In a sequential game, the first mover knows the payoffs faced by the second mover, and
therefore knows what the second mover will do under different circumstances. The first
mover will figure out the different moves that the second mover would make under every
possible circumstance, and then will choose its own first move, so that the payoff to the first
mover is as high as possible (this is called “looking forward and reasoning back”). In Games
#1, #2 and #4, the Nash equilibrium will be different for a sequential game in which Firm II
moves first than it is for a simultaneous game. The correct answer is (Q).
5. In a sequential game, the first mover knows the payoffs faced by the second mover, and
therefore knows what the second mover will do under different circumstances. The first
mover will figure out the different moves that the second mover would make under every
possible circumstance, and then will choose its own first move, so that the payoff to the first
mover is as high as possible (this is called “looking forward and reasoning back”). In Games
#1, #2 and #4, the Nash equilibrium will be different for a sequential game in which Firm I
moves first than it is for a simultaneous game. The correct answer is (Q).
6. A firm following a “maximin” strategy will be maximizing the minimum return from a
strategy. In other words, for any strategy that Firm I plays, the return is uncertain. If Firm I
is risk-averse, it will want to minimize possible poor returns or losses. Therefore, Firm I will
determine what is the minimum possible return from a strategy and then choose the strategy
which gives the best (max) of these minimum (min) returns. Following this logic, games #3
and #5 will give a different Nash equilibrium when Firm I plays a maximin strategy. The
correct answer is (N).
7. All of these statements are true about the firm in a Chamberlinian monopolistically
competitive model. The correct answer is (O).
8. Only answer II is correct about the Chamberlinian model in the long run. The correct answer
is (B).
9. The information in the question creates a matrix in which Big Pig has a dominant strategy to
press the button. If Big Pig presses the button, Little Pig has the incentive to wait at the
trough. The Nash equilibrium is therefore that Big Pig presses the button while Little Pig
waits at the trough. The payoffs are therefore 4 for Little Pig and 3 for Big Pig. The correct
answer is (F), none of the above.
10. If Durrum enters, UTSC will have incentives to decide not to build, yielding payoffs of 30
each. If Durrum does not enter, UTSC will have a payoff of 60, while Durrum earns 20. The
best decision for the first mover (Durrum) is to enter to gain an equal share of the market.
The correct answer is (B).
11. Now, if Durrum enters, UTSC will have incentives to build, yielding payoffs of 25 to UTSC,
but only 10 to Durrum. If Durrum does not enter, UTSC will have a payoff of 45, while
Durrum earns 20. The best decision for the first mover (Durrum) is to not enter, and get a
payoff of 20, while UTSC gets 45. The correct answer is (M).
12. Demand is P = 15 - .05Q, so MR = 15 - .1Q. MC = 10, so profit maximization occurs when
15 - .1Q = 10 or Q* = 50. The correct answer is (F).
13. The equilibrium price under monopoly is found by substituting the answer from question 12
into the demand curve, so P = 15 - .05(50) = $12.50. The competitive (or quasi-competitive)
solution occurs where MC crosses the demand curve, or where 10 = 15 - .05Q, or where Q =
100. The deadweight loss from monopoly is, therefore, [(12.5 – 10) x (100 – 50)]/2 = $62.50.
The correct answer is (Z) – none of the above.
14. Both the player and the goalie will try to eliminate the advantage the other player might get,
by adjusting their strategic probabilities to make payoffs equal. So, for instance, the payoff
for the goalie for jumping left depends on the probability that the kicker will kick to the left.
If PKL is the probability that the kicker will kick left, then the payoff to the goalie of jumping
left = 1PKL + 0.5(1 - PKL) = 0.5 + 0.5 PKL. The payoff to the goalie of jumping right is 0PKL +
1(1 - PKL) = (1 - PKL). If the kicker wants to make the goalie’s job as difficult as possible,
he/she will choose PKL to make these payoffs equal. In other words to make 0.5 + 0.5 PKL =
(1 - PKL). This is accomplished if PKL = 0.333. By a similar logic, we can find that the goalie
will choose to make the probability of jumping left = 0.66666. The correct answer is (J).
15. If Right, Down is going to be a pair of strategies forming a Nash equilibrium, player #1 must
have an incentive to choose down instead of up when player #2 chooses right. In other
words, “g” must be greater than “c”. Further, player #2 must have an incentive to choose
right instead of left when player #1 chooses down. In other words, “h” must be greater than
“f”. The correct answer is (F).
16. Alpha moves first and may choose either no expansion, small expansion or large expansion.
In the first case, Beta will choose small expansion (giving Alpha a payoff of 15). In the
second case, Beta will choose a small expansion (giving Alpha a payoff of 16). In the third
case, Beta will choose no expansion (giving Alpha a payoff of 18). Logically, Alpha will
choose a large expansion, and Beta will therefore not expand. The correct answer is (G).
17. Now the logic is opposite. Beta decides on a large expansion and Alpha does not expand.
The correct answer is (C).
Short Answer and Graphical Questions
18. (a) Consumers buy from the firm that has the lowest “delivered” price, taking into account
both the price at the factory gate plus the cost of transportation. The representative firm has a
factory-gate price of PR , and a delivery cost of $1 per unit of distance. Since the
neighbouring firms charge a price of P = $100, the dividing point X’ between the two firms
will come where PR + 1X’ = 100 + (L – 1X’). Therefore 2X’ = 100 + L - PR, or X’ = (100 +
L - PR)/2. Since there are 1000 customers evenly spread around the circle and 10 evenly
spaced firms, L = 1000/10 = 100, so X’ = (200 - PR)/2. Since this situation is true on both
sides of the representative firm, the entire market is 2X’ = 200 - PR. Replacing 2X’ with Y to
represent the quantity demanded, we have Y = 200 - PR or PR = 200 – Y. This is the demand
curve for the output of the representative firm.
(b) When all firms are in short-run equilibrium, they will charge the same prices, so PR = P.
The demand curve for the representative firm’s output will be PR = P + L – Y, so MR = P + L
– 2Y. MC = dTC/dY = 30, so the representative firm will profit maximize by setting P + L –
2Y = 30 or (since L = 1000/10 = 100), 2Y = 70 + P, or Y* = 35 + P/2. Substituting this
profit-maximizing equilibrium output into the demand curve, the representative firm will
charge PR* = P + L – Y = P + 100 – 35 – P/2 = 65 + P/2. However, in SR equilibrium,
because all firms face the same costs and (because they are equally spaced and have the same
transport costs), they face the same demand situation, PR = P. Therefore, PR = 65 + P/2, can
be written as PR = 65 + PR/2, or PR* = $130. Output of the representative firm is therefore,
Y* = 35 + 130/2 = 100. The profit of this representative firm is TR – TC = (130 x 100) –
(4000 + [30 x 100]) = $6,000.
(c) The entrant faces a situation which is the same as other firms in costs but where the
market is half the size = L/2. Therefore, the entrant’s demand curve is PE = P + L/2 – Y, so
MRE = P + L/2 – 2Y. MC = dTC/dY = 30, so the potential entrant will profit maximize by
setting P + L/2 – 2Y = 30 or (since L = 1000/10 = 100), 2Y = 20 + P, or Y* = 10 + P/2. Since
the incumbent firms are charging P = $130, the market for the entrant’s output is = 10 +
130/2 = 75 units. Substituting this profit-maximizing equilibrium output into the demand
curve, the potential entrant will charge PE* = P + L/2 – Y = 130 + 50 – 75 = $105.
(d) The profit of the new entrant would be TR – TC = (105 x 75) – (4000 + [30 x 75]) =
$1625. This is less profit than earned by the incumbent firms, but enough to justify entry.
19. The monopolist sells in two distinct markets. Q1 = 140 - 2P1 , so P1 = 70 - .5Q1. This means
that MR1 = 70 - Q1. Since MC = dTC/dQ = 15, profit maximization implies 70 - Q1 = 15 or Q1 =
55. Substituting into the demand function, we have P1 = 70 - .5(55) = $42.50.
In the second market, we have Q2 = 120 - 2P2 , so P2 = 60 - .5Q2. This means that MR2 = 60 –
Q2. Since MC = dTC/dQ = 15, profit maximization implies 60 – Q2 = 15 or Q2 = 45.
Substituting into the demand function, we have P2 = 60 - .5(45) = $37.50.
The profit of this price-discriminating monopolist is TR – TC = (42.50 x 55) + (37.50 x 45) –
(100 + [15 x 100]) = $2,425.
20. (a) With a Cournot duopoly, P = 36 – 3Q2 - 3Q1. For firm #1, MR = 36 – 3Q2 – 6Q1. Since
MC = 18, we have 36 – 3Q2 – 6Q1 = 18 or 18 – 3Q2 = 6Q1. This gives us the reaction
function of Firm #1, which is Q1 = 3 – .5Q2. The reaction function of Firm #2 is similar: Q2 =
3 – .5Q1. Substituting, we find that these two reaction functions can be satisfied at only one
point. Q1 = 3 – .5 (3 – .5Q1) or .75Q1 = 1.5. So Q1* = 2 and Q2* = 2. Total output in the
industry is 4, so P = 36 – 3(4) = $24. Profits for each producer are (24 x 2) – (18 x 2) = $12.
(b) Each Cournot duopolist believes that the other firm will keep its output constant (at the
current level), so each firm believes it can profit maximize with the “residual” demand. In
the Stackelberg equilibrium (assuming that the first firm is the Stackelberg leader), the first
firm understands that the second firm will react to firm 1’s output. The Stackelberg leader
incorporates the expected reactions of the second firm into its profit-maximizing decision and
firm #2’s output is no longer a constant from Firm #1’s point of view. Instead, firm #2’s
reaction function is expected to remain constant (i.e. predictable).
(c) Acting as a joint monopoly, we have P = 36 – 3Q, so MR = 36 – 6Q. Since MC = 18, we
have 36 – 6Q = 18, or 6Q = 18 or Q* = 3. Substituting into the demand function, we have P
= 36 – 3(3) = $27. In other words, each firm produces 1.5 units of output and prices this
output at $27 per unit. The profit of each producer is TR – TC = (27 x 1.5) – (18 x 1.5) =
$13.50.