Download Answers to ECMC02 First Test, October 15, 2004

Answers to ECMC02 First Test, October 15, 2004
1. There are two distinct markets: United States and Brazil. In the United States, the
demand curve can be turned around: P = 1000 - Q. Therefore, MR = 1000 – 2Q.
Since MC = 100, we have 1000 – 2Q = 100 or Q = 450. Substituting into the
demand curve, we find P = 1000 - 450 = $550. The correct answer is (S).
2. In Brazil, the demand curve is P = 1700 – 4Q. Therefore, MR = 1700 – 8Q.
Since MC = 100, we have 1700 – 8Q = 100, or Q = 200. Substituting into the
demand curve, we find P = 1700 – 800 = $900. The correct answer is (W).
3. If the diamond producer is unable to discriminate between markets, he must serve
the entire market. We can find the joint market by summing across the quantity
dimension. We have:(Q1 = 1000 - P1)+(Q2 = 425 – 0.25P2) = (Q = 1425 – 1.25P).
This can be inverted to find P = 1140 - .8Q. Therefore marginal revenue in the
joint market is MR = 1140 - 1.6Q. MC = 100, so profit maximization is at 1140 –
1.6Q = 100 or Q* = 650. Substituting into the joint demand function, we find P =
1140 – 0.8(650) = $620. Profit before markets are joined together – profit with
price discrimination - is [(550 x 450) + (900 x 200)] – [10,000 + (100 x 650)] =
$352,500. Profit after markets are joined together is [(620 x 650) – (10,000 +
(100 x 650)] = $328,000. Profit falls by $24,500 if the diamond producer is
unable to discriminate between markets. The correct answer is (M).
4. In the United States, consumer surplus under price discrimination is [(1000 – 550)
x 450]/2 = $101,250. Without price discrimination, the price is $620. At this
price, we can calculate using the United States demand curve that 380 units will
be sold to United States consumers. The consumer surplus will therefore be
[(1000 – 620) x 380]/2 = $72,200. The fall in consumer surplus is $29,050. The
correct answer is (A).
5.
In Brazil, consumer surplus under price discrimination is [(1700 – 900) x 200]/2
= $80,000. Without price discrimination, the price is $620, and the quantity sold
is 270. The consumer surplus will, therefore, be [(1700 – 620) x 270]/2 =
$145,800. The rise in consumer surplus by moving to the combined market is,
therefore, $65,800. The correct answer is (T).
6.
With no trade, domestic supply is P = .0025Q and demand is P = 60 - .005Q.
The intersection of these functions gives equilibrium, where 60 - .005Q = .0025Q,
or where Q* = 8000. By substituting into the demand curve, we find P = 60 .005(8000) = $20. The correct answer is (U).
7. If a perfectly elastic supply of running shoes is available at $5, we can find the
amount traded where 60 -.005Q = 5 or where Q* = 11,000. The domestic supply
at a price of $5 is given by 5 = .0025Q, or Qdom = 2,000. Imports are therefore
9,000. The correct answer is (W).
8. A tariff of 100% will drive the price from international sources up to $10. Before
the tariff, the amount of imports was 9,000. After the tariff, the total amount
traded is given by 60 - .005Q = 10 or Q* = 10,000. Domestic production after the
tariff is at .0025Q = 10 or at Q = 4,000. Therefore, after the tariff the amount of
imports is 10,000 – 4,000 = 6,000. The amount of imports fell by 3,000 because
of the tariff. The correct answer is (Q).
9. Consumer surplus before the tariff was [(60 – 5) x 11000]/2 = $302,500.
Consumer surplus after the tariff is [(60 – 10) x 10000]/2 = $250,000. The loss of
consumer surplus is $52,500. The correct answer is (G).
10. The deadweight loss from the tariff is the sum of two triangles: [(4000 – 2000) x
5]/2 + [(11000 – 10000) x 5]/2 = 5000 + 2500 = $7500. The correct answer is
(C).
11. Demand is P = 596 – 4Q, so MR = 596 – 8Q. MC = 20, so the profit maximizing
output is found where 596 – 8Q = 20, or where Q* = 72. Substituting into the
demand curve, we find that P = 596 – 4(72) = $308. This is the joint monopoly
result in this market. The correct answer is (R).
12. With a Cournot duopoly, P = 596 – 4Q2 - 4Q1. For firm #1, MR = 596 – 4Q2 –
8Q1. Since MC = 20, we have 596 – 4Q2 – 8Q1 = 20 or 576 – 4Q2 = 8Q1. This
gives us the reaction function of Firm #1, which is Q1 = 72 – .5Q2 . The reaction
function of Firm #2 is similar: Q2 = 72 – .5Q1. Substituting, we find that these
two reaction functions can be satisfied at only one point. Q1 = 72 – .5 (72 – .5Q1)
or .75Q1 = 36. So Q1* = 48 and Q2* = 48. Total output in the industry is 96, so P
= 596 – 4(96) = $212. The correct answer is (N).
13. 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 = 596 – 4(72 – .5Q1) - 4Q1, which can
be simplified to P = 308 - 2Q1 . Therefore, MR1 = 308 - 4Q1 = 20 or Q1* = 72.
From Firm #2’s reaction function, we can calculate that Q2* = 36. Therefore,
total output in the Stackelberg industry is 108 and P = 596 – 4(108) = $164. The
correct answer is (J).
14. In a perfectly competitive equilibrium (or quasi-competitive equilibrium), P =
$20 and Q = 144. Compared to this, a Stackelberg equilibrium has a consumer
surplus loss of (164 – 20) x (144 – 108)/2 = $2592. 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 (212 – 20) x (144 – 96)/2 = $4608. Again,
there is no producer surplus, so this is the total efficiency loss. The Cournot
equilibrium has a larger deadweight loss by $2016, so the correct answer is $2016. The correct answer is (W).
15. We know that MR = P(1 + 1/ED), where elasticity of demand is measured as a
negative number. Also the profit-maximizing monopolist will have MR = MC.
In this case, we know that 48 = (P x 12) – (3 x 12), so P = $7. So, we have 3 =
7(1 + 1/ED) or (1 + 1/ED) = 3/7 or 1/ED = 3/7 – 7/7 = -4/7. We can calculate that
ED = -7/4 = -1.75. The correct answer is (R).
Short Answer Questions
16. We cannot reproduce the diagram here, but note that the MC function before the
tax is MC = 3Q. The tax increases the marginal costs of production, so the new
MC + T = 50 + 3Q. The new P* = $90 and the new Q* = 10.
(a) The original equilibrium price was P = $80; the new equilibrium price is
$90. Therefore the buyers’ share of the $50 tax is $10. Therefore, the
sellers’ share must be $40.
(b) The competitive (or quasi-competitive) result is where P = MC or where
100 – Q = 3Q. The competitive equilibrium is therefore at Q = 25 and P =
$75. Compare the original monopoly solution to this to find the DWL
from monopoly = [(80 – 60) x 5]/2 = $50.
(c) Calculate the deadweight loss from the after-tax equilibrium compared to
the competitive equilibrium. DWL with tax = [(90 – 30) x 15]/2 = $450.
Since the DWL from monopoly was $50, it is clear that the additional
DWL from the tax = 450 – 50 = $400.
17. (a)
Draw the diagram and show the efficiency loss as a triangle. Charging a
minimum price of $8.00 reduces the quantity demanded to 2000 bushels of wheat.
The triangle should shade the area between 2000 and 6000 bushels, with the
demand curve forming the upper boundary and the supply curve the lower
boundary. The efficiency loss = [(8 – 2) x (6000 – 2000)]/2 = $12,000. The
amount of consumer surplus before this minimum-price policy was implemented
= [(10 – 4) x 6000]/2 = $18,000. After the policy, the amount of consumer
surplus = [(10 – 8) x 2000]/2 = $2,000. The loss of consumer surplus due to the
policy is therefore $16,000.
(b)
Now the Canadian government purchases sufficient wheat to bring the
price up to $8.00 per bushel. In other words, the new demand curve must intersect
the existing supply curve at $8.00 per bushel. The equation of the supply curve is P =
1 + .0005Q, so this occurs at Q = 14,000. In other words, the government has to buy
14,000 – 2,000 = 12,000 bushels of wheat. The cost of this wheat at a price of $8 is
$96,000. However, producers gain additional producers’ surplus, over and above the
amount transferred from consumers. The additional producers’ surplus = [(8 – 4) x
(14,000 – 2,000)]/2 = $24,000. The net efficiency loss is therefore $96,000 - $24,000
= $72,000. Consumers’ surplus before the policy was [(10 – 4) x 6000]/2 = $18,000.
After the policy, it is [(10 – 8) x 2000]/2 = $2,000. Therefore, the loss of consumers’
surplus is $16,000.
18. (a) The demand curve for Type A consumers is P = 20 –10Q. The demand curve
for Type B consumers is P = 40 - 5Q. The maximum amount that Type A
consumers will consume is 2 units; for Type B consumers, this maximum is 8
units. To encourage Type A consumers to just be willing to consume 2 units, the
monopolist can charge them their maximum willingness-to-pay which is the entire
area under the demand curve (20 x 2)/2 = $20. However, Type B consumers
could decide to consume this “Type A” package once it is offered on the market.
If they did they would gain consumer surplus of [40 x 8]/2 – (30 x 6)/2 - 20 =
$50. Because of this, any other package offered to Type B consumers has to offer
them at least this same amount of consumer surplus, or else they will not select it.
Therefore, if the monopolist wishes to get Type B consumers to purchase 8 units
of output, the maximum it can charge is (40 x 8)/2 – 50 = $110 (i.e., the total
willingness to pay under the Type B demand curve, minus the consumer surplus
they need to be given). The two packages are, therefore, 2 units at $20 and 8 units
at $110. Type B consumers will get $50 of consumer surplus.
(b) If Q = 1 for Type A consumers, the maximum that can be charged is the area
under this demand curve out to Q =1, which is [(20 – 10) x 1]/2 + (10 x 1) = $15.
At Q = 1, the marginal valuation along the demand curve is $35. The consumer
surplus given to Type B consumers by purchasing the Type A package would be
(40 x 8)/2 – (35 x 7)/2 – 15 = $22.50. Therefore, the Type B package can be
priced so as to give Type B consumers this same amount of consumer surplus. In
other words, the price can be (40 x 8)/2 – 22.50 = $137.50. The old arrangement
gave the monopolist profit of 20 + 110 = $130. Under the new arrangement, the
profit is 15 + 137.50 = $152.50. The increase in profits is $22.50.
19. In the long run, the amount of producer surplus is determined by the demand for
the good (along with the upward slope of the supply curve which reflects the
scarcity (or differential productivity) of some input to production). Higher
demand, all else equal, will increase producer surplus; lower demand will lower
it. The poem presents two alternative ways of looking at high prices. First, the
conventional wisdom suggests that pigs cost more because their inputs have risen
in price (corn and land are higher priced). In the second half of the poem, the
conventional wisdom is turned on its head. If you would like to know why the
price of farmland is high, you are asked to consider that the price of farmland is
high because suppliers of pigs are willing to pay high prices for farmland because
the price of pigs is high enough to justify it. In other words, the high demand for
pigs creates a high demand for farmland and so the price of these inputs rises. It
is the rising price of inputs that makes up long run producer surplus.
20. There are 5 identical firms so 5q = Q or q = .2Q. The industry supply curve is,
therefore, P = .05 x .2Q = .01Q. Demand is P = 60 - .005Q. The intersection
will come where .01Q = 60 - .005Q or where Q = 4,000 and P = 40. 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 $40, 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 $0 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 = $0, market demand is 0 = 60 - .005Q or Q = 12,000.
Therefore the slope of the dominant firm’s demand function is (40 – 0)/12,000 =
.003333 and the equation of this demand function is P = 40 - .003333Q. The
marginal revenue of the dominant firm is given by 40 - .006666Q and the
marginal cost is constant at $20. Therefore 40 - .006666Q = 20 or Q = 3,000.
This is the profit-maximizing output of the dominant firm. The price charged can
be found by substituting this quantity into the dominant firm’s demand function or
P = 40 - .003333(3,000) = $30. At this price, the competitive fringe of firms will
want to supply 30 = .01Q = 3,000 units of output.
The dominant firm sells 3,000 units at a price of $30 and has average costs of $20
per unit. Profit = (30 x 3000) – (20 x 3000) = $30,000. The dominant firm in this
problem has a cost advantage over other firms, perhaps because of technological
superiority or control of a scarce productive input. The long run profit advantage
of the dominant firm can be viewed as a return to this scarce input or technology
and therefore as an economic rent.