Download Solutions to Test #1, Oct 10, 2003

ECMC02
Term Test - October 10, 2003
Professor Gordon Cleveland
Time: 100 minutes
ANSWERS TO TERM TEST #1, FALL 2003
The correct answers to the multiple choice questions are
1) _T__________
2) _E__________
3) _U__________
4) _I__________
5) _K__________
6) _U__________
7) _Q__________
8) _Q__________
9) _W__________
10) _L_________
11) _M_________
12) _E________
13) _W________
14) ___R________
15) ___M________
16) ___B________
17) ___O________
18) ___U________
19) ___R________
20) ___K________
21) ___F________
22) ___C________
23) ___G________
24) ___E________
25) ___I________
1. TC = 0.5q2 + 10q + 5, so dTC/dq = q + 10. There are 100 identical firms,
so 100q = Q or q = 0.01Q. We can substitute in, to get industry supply,
since the “horizontal” sum of the MC curves makes up industry supply.
So, P = 10 + .01Q is industry supply. Demand is Q = 1100 – 50P or P =
22 - .02Q. Equilibrium quantity can be found in a competitive market
where quantity demanded and quantity supplied are equal or where 22 .02Q = 10 + .01Q. This is true when Q* = 400. The correct answer is
(T).
2. Each firm sells 400/100 = 4 units per month. The equilibrium price is P
= 22 - .02(400) = $14. Profit = TR – TC = (14 x 4) – (0.5 x 16 + 10 x 4 +
5) = $3. The correct answer is (E).
3. Consumer surplus = (22 – 14) x 400/2 = $1600. Producer surplus = (14 –
10) x 400/2 = $800. Total surplus = $2400. The correct answer is (U).
4. Short run producer surplusis the excess of total producer revenues over
variable costs, and is therefore greater than profit by the amount of fixed
costs. Other statements are incorrect. Statements II and IV are correct.
The correct answer is (I).
5. A tax of $3 per unit will change the price demands of suppliers as
reflected by the S + T function: S + T: P = 13 + .01Q. The new
equilibrium quantity will meet the condition that 22 - .02Q = 13 + .01Q,
or Q1* = 300. Therefore, P1* = 22 - .02(300) = $16. The new producer
surplus is (16 – 13) x 300/2 = $450. Since the former producer surplus
was $800, producer surplus has fallen by $350. The correct answer is
(K).
6. There are 1000 identical firms so 1000q = Q or q = .001Q. TC = 100 +
5q + 0.5q2, so dTC/dq = 5 + q. Substituting in to find industry supply, we
have P = 5 + .001Q. Demand is Q = -2000P + 70,000 or P = 35 .0005Q. Equilibrium will come where 5 + .001Q = 35 - .0005Q or where
Q0* = 20,000. P0* = 35 - .0005(20,000) = $25. Therefore, Consumer
Surplus is (35 – 25) x 20,000/2 = 100,000. The correct answer is (U).
7. We need to find the demand curve faced by the dominant firm (which
nets out the supply provided by the competitive fringe of firms). At a
price of $25, we have just calculated that the supply by the competitive
fringe and the market demand will intersect, so at this point there will be
zero quantity demanded from the dominant firm (price leader). On the
other hand, from the supply curve/function of the competitive fringe, we
can see that at a price of $5 or below, there will be zero quantity supplied
by the competitive fringe, so the entire demand will be left to the
dominant firm. At P = $5, market demand is 5 = 35 - .0005Q or Q =
60,000. Therefore the slope of the dominant firm’s demand function is
(25 – 5)/60,000 = .0003333 and the equation of this demand function is P
= 25 - .0003333Q. The marginal revenue of the dominant firm is given
by 25 - .0006666Q and the marginal cost is constant at $15. Therefore 25
- .0006666Q = 15 or Q = 15,000. This is the profit-maximizing output of
the dominant firm. The correct answer is (Q).
8. The price charged can be found by substituting this quantity into the
dominant firm’s demand function or P = 25 - .0003333(15,000) = $20.
The correct answer is (Q).
9. The competitive fringe will take the price given by the price leader and
will supply output accordingly. 20 = 5 + .001Q or QCF = 15,000.
Therefore, total quantity traded in this industry is 30,000 units.
Consumer Surplus is (35 – 20) x 30,000/2 = $225,000. The correct
answer is (W).
10. This is a price discrimination problem. In market #1, Q1 = 60 – P1 or P1
= 60 - Q1. Therefore, MR = 60 - 2 Q1. Since MC = 10, the profitmaximizing output if this market can be served completely separately is
60 - 2 Q1 = 10 or Q1 * = 25 and P1* = 60 – 25 = $35. The correct answer
is (L).
11. In market #2, Q2 = 70 – P2 or P2 = 70 – Q2. Therefore, MR = 70 - 2 Q2.
Since MC = 10, the profit-maximizing output if this market can be served
completely separately is 70 - 2 Q2 = 10 or Q2 * = 30 and P2* = 70 – 30 =
$40. The correct answer is (M).
12. The demand across the two markets needs to be added together such that
Q1+
Q2 = QT. So, QT = (60 – P1) + (70 – P2) = 130 – 2P. Therefore, P = 65 –
0.5QT. MR = 65 – Q and MC = 10, so 65 – Q = 10 or Q = 55.
Substituting into the combined demand function, we get P = 65 – 0.5(55)
= $37.50. The profit level in the joined markets is $37.50 x 55 – 10 x 55
= $1512.50. The profit level in two separable markets was 35 x 25 + 40
x 30 – 10 x 55 = $1525.00. We can conclude that the profit level falls by
$12.50 if markets cannot be separated. The correct answer is (E).
13. This set of questions asks about cartels, Cournot duopoly, Stackelberg
leaders and Bertrand competition. In the case of collusion/a cartel, the
two producers act like a joint monopolist, so that P = 156 – 4Q and MR =
156 – 8Q. MC = 12, so 156 – 8Q = 12 or Q* = 18 and P* = $84. The
correct answer is (W).
14. With a Cournot duopoly, P = 4Q2 – 4Q1. For firm #1, MR = 156 – 4Q2 –
8Q1. Since MC = 12, we have 156 – 4Q2 – 8Q1 = 12 or 144 – Q2 = 8Q1.
This gives us the reaction function of Firm #1, which is Q1 = 18 – .5Q2 .
The reaction function of Firm #2 is similar: Q2 = 18 – .5Q1. Substituting,
we find that these two reaction functions can be satisfied at only one
point. Q1 = 18 – .5 (18 – .5Q1) or .75Q1 = 9. So Q1* = 12 and Q2* = 12.
Total output in the industry is 24, so P = 156 – 4(24) = $60. The correct
answer is (R).
15. In the Stackelberg equilibrium, the first firm incorporates the 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. P = 156 –
4(18 – .5Q1) - 4Q1, which can be simplified to P = 84 - 2Q1 . Therefore,
MR1 = 84 - 4Q1 = 12 or Q1* = 18. From Firm #2’s reaction function, we
can calculate that Q2* = 9. Therefore, total output in the Stackelberg
industry is 27 and P = 156 – 4(27) = $48. The correct answer is (M).
16. In a Bertrand industry, equilibrium comes where P = MC, so P = $12.
The correct answer is (B).
17. In a perfectly competitive equilibrium (or quasi-competitive equilibrium
as described in your text), P = $12 and Q = 36. Compared to this, a
Stackelberg equilibrium has a consumer surplus loss of (48 – 12) x (36 –
27)/2 = $162. Since there is no producer surplus, this is the total
efficiency loss (deadweight loss) from Stackelberg. Comparing the
Cournot equilibrium to the perfectly competitive equilibrium, we find a
loss of consumer surplus of (60 – 12) x (36 – 24)/2 = $288. Again, there
is no producer surplus, so this is the total efficiency loss. The Cournot
equilibrium has a larger deadweight loss by $126, so the correct answer
is -$126. The correct answer is (O).
18. The first firm still has a reaction function given by: Q1 = 18 – .5Q2 . For
Firm #2, MR2 = 156 – 4Q1 – 8Q2 = 60 or Q2 = 12 – 0.5Q1. Setting these
two reaction functions equal to one another, we find Q1 = 18 – .5(12 –
0.5Q1) = 6 + 0.25Q1. Therefore 0.75Q1 = 12 or Q1* = 16. From Firm
#2’s reaction function, we find that Q2* = 4. Total output is 20 units, so P
= 156 – 4(20) = $76. The correct answer is (U).
19. We know that MR = P(1 + (1/ED), and that a profit-maximizing
monopolist has MR = MC. So we know that 9 = 12(1 + (1/ED). We can
readily calculate that ED = -4. The correct answer is (R).
20. A Nash equilibrium is a set of strategies such that neither player can
improve their position by changing his/her strategy. In other words,
individual action cannot make things better for either party. The Cournot
model, perfectly competitive model and Bertrand model all result in Nash
equilibria. However, a Nash equilibrium will not necessarily be efficient.
I and II and III are correct. Therefore, answer (K) is correct.
21. In the Chamberlinian model, firms can make positive profits in the short
run. The entry of firms will drive down the price but not to minimum
average cost. New entrants will compete equally with all existing brands,
rather than locally with only some group of brands/firms. Entry of new
firms will shift the demand curve of the representative firm to the left, but
not the market demand curve. Statements I and III are correct. The
correct answer is (F).
22. Since there is already a restaurant at the end of the beach, setting up at
the 1/3rd mile mark will minimize the distances that people on the beach
will have to travel to get food. The farthest that anyone will have to
travel will be 1/3rd of a mile. The correct answer is (C).
23. In order to maximize its revenue, the restaurant would open at the onemile mark, just beside the existing restaurant (and just closer to all the
people on the beach). The correct answer is (G).
24. In the Hotelling circle model discussed in class, the demand for the
output of each firm depends upon the prices charged by neighbouring
firms, on the distance between firms and on its own price. However, in
equilibrium each firm charges a price above marginal cost (but affected
by marginal cost). Therefore, statements I and II are correct. The correct
answer is (E).
25. Discount stores may offer a different level of service than department
stores, so this is not price discrimination. Insurance companies may offer
a different price to persons in different risk classifications, but this is not
price discrimination. However, discounts to the elderly and to those who
travel on weekends are likely to represent an attempt to separate market
groups having different price elasticities and this is price discrimination.
Statements II and IV are correct. The the correct answer is (I).