Download Answers to PS 4

Econ 322, Spring 2016
Answers to Problem Set 4
Chapter 9, Problem 1: a. Refer to Figure 9-1: Consumer surplus is the area under the demand curve D and above the
market price, and producer surplus is the area above the marginal cost curve MC and below the market price. Under perfect
competition, consumer surplus is PCBPD, where PD is the intersection of the demand curve with the vertical axis. Producer
surplus is PCBPMC, where PMC is the intersection of the marginal cost curve with the vertical axis. Total surplus is thus
represented by the triangle PMCBPD.
b. Refer to the following figure: Consumer surplus is the triangle PMAPD.
c. Refer to the following figure: Producer surplus is represented by the trapezoid PMAB’P .
MC
d. Refer to the figure from part (c): Total surplus is represented by the trapezoid PDAB’PMC.
e. Refer to the figure from part (c): This is called the deadweight loss due to monopoly, and is represented by the triangle ABB’.
It is called a deadweight loss because it is a loss that is not gained by any other party.
Chapter 9, Problem 6:
Quantity
Price=
(P=10-Q)
0
1
2
3
4
5
6
7
8
9
10
Total Revenue (P.Q)
10
9
8
7
6
5
4
3
2
1
0
0
9
16
21
24
25
24
21
16
9
0
Marginal Revenue
(Change in Revenue)
9
7
5
3
1
-1
-3
-5
-7
-9
a) Draw a graph containing both the demand curve and marginal revenue curve.
Figure 7
P
MR=10-2Q
10
Slope=-2
P=10-q
Slope=-1
10
5
Q
b) Is the marginal revenue curve a straight line as well? What is the slope of the marginal revenue curve? How does
that slope compare with that of the demand curve?
As shown in the figure above, the slope of the MR curve is twice that of demand curve. This is a special property of linear
demand curves.
c) Does the marginal revenue curve contain negative values over the specified range of quantities? Explain why or
why not?
Marginal revenue does not include negative values. The fall in price on every extra unit sold is large enough so that after
the fifth unit sold, the marginal revenue turns negative.
(Note: For a monopoly the only relevant part of its demand curve is the elastic portion of the demand because if a
monopoly firm produces in the inelastic range, its profit decreases in response to a decrease in price. In the elastic part, the
marginal revenue is always positive.)
Chapter 9, Problem 7: Consider the case of a foreign monopoly with no Home production shown in Figure 9-7.
Starting from free trade at point A, consider a $10 tariff applied by the Home government.
Increase in P is
less than $10, the
increase in MC
P
d
P2
P1
P3 = P2-$10
e
MC*+$10
MC*
MR
X2
X1
D
Foreign
Exports
a) Assuming that the demand curve is linear, as in Problem 10 of Chapter 6, and then what is the shape of the
marginal revenue curve.
The marginal Revenue curve will be linear with a slope twice that of the demand curve.
b) Therefore, how much does the tariff-inclusive Home price increase because of the tariff, and how much does the
net-of-tariff price received by the foreign firm fall?
Since the slope of demand curve is half of the MR, the tariff inclusive home price will increase by $5. The net of
tariff price received by the foreign firm will fall by $5.
c) Discuss the welfare effects of implementing the tariff. Use a graph to illustrate under what conditions, if any,
there is an increase in Home welfare.
In this case, the amount of deadweight cost is the area of the triangle d and there is also a terms of trade gain equal
to the triangle e. So, the total amount of welfare change depends on the size of deadweight cost relative to terms
of trade gain. The latter, in turn, depends on the elasticity of demand (which is related to the slope of the demand
curve) and the size of the tariff.
If the tariff rate is not very high the welfare of the Home country could increase because the terms of the trade
gain (e) will be larger than the deadweight loss (d). You can see this in the graph. The tariff t can be made small
enough so that the deadweight loss triangle almost disappears. This is not true for area e. Similarly, we can make
the demand curve steep enough so that “d” becomes really small. This is not true for the area “e.”
Chapter 9, problem 8:
Suppose the Home firm is considering whether to enter the Foreign market. Assume that
the Home firm has the following costs and demand:
Fixed cost =$140
Marginal Cost =$10 per unit
Local price = $25
Local Quantity = 20
Export Price=$15
Export Quantity= 10
a) Calculate the firm’s total costs from selling only in local market.
TC= Variable Cost +Fixed Cost
= 10Q+140
=10*20+140
=$340
b) What is the firm’s average cost from selling only in the local market?
AC= TC/Q
= 340/20
=$17
c) Calculate the firm’s profit from selling only in the local market
Profit= Total Revenue-Total Cost
=P.Q-TC
=25*20-340
=$160
d) Should the Home firm enter the foreign market? Briefly explain why?
Since Marginal Cost of Home Country (10) <Marginal Revenue of Export (15), home firm should enter foreign
market which will increase its total profit.
e) Calculate the firm’s profit from selling to both markets.
Total Profit= Total Revenue-Total Cost
=Revenue from selling at Home + Revenue from exporting- (Marginal Cost*Q+Fixed Cost)
=25*20+15*10-(30*10+140)
=650-440 = $210
f) Is the Home firm dumping? Briefly explain
Dumping takes place if a firm sells a product in foreign markets at a price that is either less than the price it charges
in domestic market, or less than its average cost to produce the product. In our case, since, the export price (15) of the
good is lower than both the domestic price of the good (25) and the average cost of the product (17), the Home firm is
dumping.
Chapter 10, problem 2:
Consider a large country with export subsidies in place for agriculture. Suppose the country
changes its policy and decides to cut its subsidies in half.
a. Are there gains or losses to the large country, or is it ambiguous? What is the impact on domestic prices for agriculture and
on the world price?
Answer: There are unambiguous gains to the large exporting country. Not only do deadweight losses decrease but terms-oftrade losses due to the subsidy are also diminished.
b. Suppose a small food-importing country abroad responds to the lowered subsidies by lowering its tariffs on agriculture by the
same amount. Are there gains or losses to the small country, or is it ambiguous? Explain.
Answer: From our discussion of small-country tariffs, the optimal tariff level is zero. Hence, the small food importer gains
from reducing its tariff as deadweight losses decrease.
c. Suppose a large food-importing country abroad reciprocates by lowering its tariffs on agricultural goods by the same amount.
Are there gains or losses to this large country, or is it ambiguous? Explain.
Answer: From our discussion of large-country tariffs, the optimal tariff level is positive because (for small tariffs) terms-oftrade gains exceed deadweight losses. If we assume that the (tariff-reducing) country was previously at its optimal tariff, then
welfare is reduced by cutting its tariff, but there is still an overall gain from the bilateral reduction in subsidies and tariffs.
Because terms-of-trade gains for one party are terms-of-trade losses for the other, we can measure the net overall benefits of
bilateral trade barrier removal as the reduction in both countries’ deadweight losses..
Chapter 10, problem 3:
What is the quantity exported under free trade and with the export subsidy?
Answer: Under the export subsidy, exports increase to 40 tons, whereas the amount exported under free trade is 20 tons.
b. Calculate the effect of the export subsidy on consumer surplus, producer surplus, and government revenue.
Answer: Refer to the following figure:
Consumer surplus decreases by the area a + b:
∆CS = (40∙10) – 0.5(40∙10) = -600
Producer surplus increases by the area a +b + c: ∆PS = (40∙40)- 1⁄2(40∙10) = 1,800
Government revenue decreases by the area b + c +d: ∆G = - (40 ∙ 40) = -1,600
c. Calculate the overall net effect of the export subsidy on Home welfare.
Answer: The net effect on Home welfare is the sum of changes in consumer surplus, producer surplus, and government
revenue: 400. This is the total deadweight loss of the subsidy, equal to the area b + d.
Chapter 10, problem 4:
Refer to problem 3. Rather than a small exporter of wheat, suppose that Home is a large
country. Continue to assume that the free-trade world price is $100 per ton and that the Home government provides the
domestic producer with an export subsidy in the amount of $40 per ton. Because of the export subsidy, the local price increases
to $120 while the foreign market price declines to $80 per ton. Use the following figure to answer these questions.
a. Relative to the small-country case, why does the new domestic price increase by less than the amount of the subsidy?
Answer: The new domestic price increases by less in the large-country case because part of the subsidy is offset by decreasing
world prices. This reflects a downward-sloping import demand curve in the rest of the world.
b. Calculate the effect of the export subsidy on consumer surplus, producer surplus, and government revenue.
Answer: Refer to the following figure:
Consumer surplus decreases by the area a + b:
∆CS = - (20 ∙ 12) + 0.5 (20 ∙ 8) = -320
Producer surplus increases by the area a + b +c :
∆PS = (20 ∙40) + 0.5 (20 ∙8) = 880
Government revenue decreases by the area b + c +d + e:
∆G=- (40 ∙ 36) = - 1,440
c. Calculate the overall net effect of the export subsidy on Home welfare. Is the large country better or worse off compared with
the small country with the export subsidy? Explain.
Answer: The net decrease in welfare due to the subsidy is -880. This is a larger loss than in the small country because of
Home’s terms-of-trade loss.
Chapter 10, problem 7:
Boeing and Airbus are the world’s only major producers of large, wide-bodied aircrafts. But
with the cost of fuel increasing and changing demand in the airline industry, the need for smaller regional jets has increased.
Suppose that both firms must decide whether they will produce a smaller plane. We will assume that Boeing has a slight cost
advantage over Airbus in both large and small planes, as shown in the following payoff matrix (in millions of U. S. dollars).
Assume that each producer chooses to either produce only large, only small, or no planes at all.
a. What is the Nash equilibrium of this game?
Answer: Recall that the idea of Nash equilibrium is that each firm must make its own best decision, taking as a given each
possible outcome from the other firm. In this case, if Boeing produces large planes, Airbus’ optimal reaction is to choose to
produce small planes: Its payoff is 125 million (vs. 0 million and _5 million for the other alternatives). Similarly, if Airbus
produces small planes, Boeing’s optimal reaction is to produce large planes: Its payoff is 115 million. In this case, considering
both firms’ optimal reaction to each choice of its rival yields two Nash equilibria: where one firm produces large planes and the
other firm produces small planes.
b. Are there multiple equilibria? If so, explain why. Hint: Guess at an equilibrium and then check whether either firm would
want to change its action, given the action of the other firm. Remember that Boeing can change only its own action, which
means moving up or down a column, and likewise, Airbus can change only its own action, which means moving back or forth
on a row.
Answer: Starting from either of the equilibria illustrated in the payoff matrix below, it is possible to verify that no action on the
part of any player can improve its payoff. It also makes intuitive sense why these two equilibria are the best possible outcomes
for the firms because they make both firms a monopolist in different aircraft markets.
Chapter 10, problem 8:
Refer to problem 7. Now suppose the European government wants Airbus to be the sole
producer in the lucrative small-aircraft market. Then answer the following:
a. What is the minimum amount of subsidy that Airbus must receive when it produces small aircraft to ensure that outcome as
the unique Nash equilibrium?
Answer: Assume that the firms start out in the Nash equilibrium wherein Boeing produces small planes and Airbus produces
large planes. To get Airbus to change production to small planes, the European Union needs the small-plane payoff to exceed
large-plane payoff; that is, small-plane payoff must increase by at least 101 million. Given a subsidy of 101 million, Airbus
switches production to small planes; then, Boeing switches production to large planes because it is no longer Boeing’s optimal
response to produce small planes at the same time as Airbus. The new unique Nash equilibrium (with subsidy) is for Airbus to
produce small planes and Boeing to produce large planes.
b. Is it worthwhile for the European government to undertake this subsidy?
Answer: When judging whether a policy is worth it, we consider its implication for welfare (i. e. , its effect on the sum of
producer surplus, consumer surplus, and government revenue). In this case, changing from the production of large planes to the
production of small planes increases Airbus producer surplus by 25 as profits increase from 100 to 125. Producers also collect
101 from the government in the form of a subsidy. Government expenditure increases (revenue decreases) by 101 to finance the
subsidy. Adding up, overall welfare increases by 25. It is worth it.
3.
a. Chipland is a small country. You can tell because it is a price-taker in world markets (i.e., the world supply curve
is perfectly horizontal in figure 1). Any increase in Chipland’s supply of computers does not affect the world price of
computers.
b. Increasing domestic production by 20 thousand computers would require a price increase of $20 (to increase domestic
supply from 80 to 100 requires an increase in the price from $50 to $70). The ad valorem tariff rate necessary to
achieve this price increase is t = (7050)/50 = 0.40 = 40%.
To calculate gains and losses, we need to calculate the areas a, b, c, and d, using the formulas for areas of rectangles
and triangles:
Area of a = (20 x 80) + (0.5 x 20 x 20) = 1600 + 200 = $1,800
Area of b = (0.5 x 20 x 20) = $200
Area of c = 50 x 20 = $1,000
Area of d = (0.5 x 20 x 30) = $300
Change in consumer surplus = -(a + b + c + d) = - (1,800 + 200 + 1,000 + 300) = - $3,300
Change in producer surplus = a = $1,800
Government gain (from tariff revenues) = c = $1,000
Net national loss = b + d = $500 (sometimes called “deadweight loss). The two sources of this loss are:
b = Loss of production efficiency (due to selling more at a higher price); and
d = Loss of consumption efficiency (due to consuming less at a higher price)
Also, you can calculate this as follows:
Net national loss = total consumers’ loss  gains to domestic producers and the government;
Therefore, net national loss = 3,300  1,800  1,000 = $500.
c. The government will have to subsidize in the amount of $20 (= $70  $50) per unit to stimulate the domestic
production of an additional 20 thousand chips (i.e., to increase production from 80 to 100 thousand in Figure 1). In
this case:
Change in producer surplus = a = $1,800
Consumer loss (in the form of taxes to pay for the subsidy) = a + b = 1,800 + 200 = $2,000 (note that this is different
from loss in consumer surplus or consumption efficiency, which equals zero in this case).
Net national loss = b = $200
Thus the net national loss is smaller in this case, because there is only the loss of productive efficiency
(consumers can still buy the chips at the world price of $50). Thus, the subsidy policy is relatively more
advantageous (or, rather, less costly) than tariffs. Moreover, domestic producers would be indifferent between a
subsidy and a tariff. However, domestic consumers may prefer a subsidy since they continue to pay the same price as
before (however, this has to be qualified by the fact that domestic consumers are likely to have to pay higher taxes to
finance the subsidies – see below). Some factors that could nevertheless inhibit governments from using subsidies
are:

Free trade agreements or WTO rules may prohibit certain types of subsidies, and allow other countries to
retaliate with “countervailing duties” (if the subsidies encourage exports that injure other countries’ producers).

Taxes required to pay for subsidies might be unpopular (or, if the government doesn’t raise taxes to pay for
them, the resulting budget deficits could also be unpopular). As a rule, taxes are more “visible” to consumers than the
higher costs of protected goods, even if in theory the former are actually smaller (a+b rather than a+b+c+d).

It is often politically more convenient to use protectionism because one can blame foreign countries for an
industry’s problems, rather than admitting that the industry has internal difficulties.
d. In the presence of the tariff, Chipland’s production increases by 20,000 computers, so that domestic demand exceeds
supply by 50,000. This excess demand has to be satisfied through imports (see Figure 1 above). The same effect
could be achieved by imposing an import quota that restricts imports to 50,000 computers. The welfare effects of the
import quota are similar to those of a tariff, except for the fact that the rents (area ‘c’ = 1,000) are not necessarily
captured by the government, and could be distributed instead in several different ways:
(1) The government could auction quota licenses to domestic retailers, who buy abroad at the international price and
sell at home at the higher (due to quotas) domestic price. In this case, the retailers would be glad to pay for the license
as long as the price differential is not less than the cost of getting the license. The government captures the difference
between the domestic price without quotas and the international price (the quota rents).
(2) If the foreign producers operate in an oligopolistic environment (that is, they have some market power), they could
raise the price of the good to the level of the domestic price of the good under the quota. In this case, the rent goes to
the foreign producers.
(3) The foreign government could auction quota licenses to their producers. The producers would be glad to export
at the higher price, and the rents go to the foreign government.
Notice that in case (1), the overall welfare effects are the same as in the case of an import tariff since the quota rents
stay within the country. However, in cases (2) and (3), the country is worse off than with a tariff since the quota rents
flow to either the foreign producers or the foreign government. In other words, since no domestic group captures
these rents, the net national loss is larger: Net national loss with quota in cases (2) and (3) = b + c + d = 1,500. The
other effects are the same as in parts b and c: Consumers lose 3,300; domestic producers gain 1,800.
e. If the foreign country agrees to replace the tariff with a “voluntary” export restriction (VER) it will have to reduce its
exports of computers by 50 thousand.
The welfare effects are similar to those of cases (2) or (3) under an import quota. Net national loss with VRA = b + c
+ d = 1,500. The other effects are the same as in parts b and c: Consumers lose 3,300; domestic producers gain 1,800.
Obviously the foreign producers (exporters) will prefer this arrangement to the tariff or subsidy because they gain the
rents in this case, although they would probably rather have no trade restriction at all.
f. The Stolper-Samuelson theorem predicts that an import tariff raises the real returns to the factor that is scarce in a
country (and is therefore used relatively intensively in the production of the import good), and lowers the real return
to the other factor. In our example, computers are being imported. Since we assume that the production of computers
is K-intensive, an import tariff on computers will benefit the owners of capital while lowering real wages. This is
consistent with the implications of our answer to part (a). A tariff (or subsidy) increases the production of computers
while (by extension) reducing the production of the export good. Since computers are relatively K-intensive, this
raises the relative demand for capital while lowering the relative demand for labor. With full employment of all
resources, this lowers real wages and raises real returns to capital. In other words, the import tariff must benefit the
producers of computers while harming the other factor (workers). However, note that since owners of capital produce
both the export and import goods, there is no one-to-one correspondence between “producer gains” (which equaled
$1,800 in part (a)) and the real returns to capital. Similarly, there is no one-to-one correspondence between consumer
losses” and real wages.