Download Answers to PS 3

Econ 322, Spring 2016
Answers to Problem Set 3
Chapter 6,Problem 1:
In the presence of increasing returns to scale, countries benefit from trade by moving down
their average cost curve (reduce their average costs) via expansion of output. This happens because they get access to a larger
market. Consumers gain from the lower prices and greater product variety.
Chapter 6,Problem 3:
Starting from the long-run equilibrium without trade in the monopolistic competition
model, as illustrated in Figure 6-5, consider what happens when the home country begins trading with two identical
countries. Because the countries are identical, the number of consumers in the world is three times larger than in a single
country, and the number of firms in the world is three times larger than in a single country.
Figure 1
Long-run equilibrium
without trade
P
Short-run Equilibrium
without trade
Po
PA
AC
MC
A
mr1
D/N
d1
d0
Q
Q1
Q0
Figure 1: Short-run and Long-run Monopolistic Competition Equilibrium without Trade
Figure 2
Long-run equilibrium
without trade
P
Short-run equilibrium
with trade (3 countries)
Po
PA
P2
d2
AC
MC
A
mr2
D/N
Q
Q1
Q’2
Q0
Q2
Figure2 : Short-run and Long-run Monopolistic Competition Equilibrium after Trade
a) Compared with the no-trade equilibrium, how much does industry demand D increase? How much does the
number of firms (or product varieties) increase? Therefore, does the demand curve D/NA still apply after the
opening of trade? Explain why or why not?
Industry demand is 3 times larger compared to that without trade. The number of firms also triples. The demand
curve D/NA still applies (3D/3NA = D/NA ).
b) Does the d1 curve shift or pivot due to the opening of trade? Explain why or why not?
d1 curve becomes flatter (see d2 in Figure 2) due to an increase in the number of varieties available to consumers
after trade (which makes them more price sensitive).
c) Compare your answer to (b) with the case in which Home trades with only one other identical country.
Specifically, compare the elasticity of the demand curve d1 in two cases
In this case (with three countries), since the consumers choose from a greater variety of products, the demand
curve facing each firm is flatter (more elastic) than in the case where only two countries trade (see Figure 3)
Figure 3
A Long-run equilibrium
without trade
P
Short-run equilibrium with
trade (2 countries)
PA
dt
Pt
Ac
MC
mrt
A
D/N
Q
Q1
Q’t
Qt
Figure3 : Short-run and Long-run Monopolistic Competition Equilibrium after Trade
d) Illustrate the long –run equilibrium with trade and compare it with the long-run equilibrium when Home trades
with only one other identical country.
Comparison Home country trading with two more countries versus one more countries (see Fgiure 4 and 5):
Q3 (trade three countries) > Q’3 (trade with two countries)
Pw (trade three countries) < Pw” (trade with two countries)
Figure 4
A Long-run equilibrium
without trade
P
Long-run equilibrium
with trade (3 countries)
T
D/N
PA
Pw
AC
d3
MC
mr3
D0
Q
Q1
Q3
Figure4 : Short-run and Long-run Monopolistic Competition Equilibrium after Trade
Figure 5
A Long-run equilibrium
without trade
P
Long-run equilibrium
with trade (2 countries)
((two(countries)
T
D/N
PA
Pw”
Pw
Ac
d’3
MC
m’r3
Q
Q1
Q’3
Q3
Figure 5 : Short-run and Long-run Monopolistic Competition Equilibrium after Trade
Chapter 6, 4-Starting from the long-run trade equilibrium
in the monopolistic competition model, as illustrated in
Figure 6-7, consider what happens when industry demand D increases. For instance, suppose that this is the market for
cars, and lower gasoline prices generate higher demand for D
a) Redraw Figure 6-7 for the Home market and show the shift in D/NT curve and the new short-run equilibrium.
See Figure below.
Short run equilibrium takes place at D where the equilibrium price and quantity has increased. The increase in demand
shifts the D/NA curve to the right, dragging along the curves d3 and mr3. Each firm produces Q4 at a price of P4 attempting
to earn monopoly profits at point D, and when all firms do so they move along the new D/NT curve to point E.
b) From the new short-run equilibrium, is there exist or entry of firms, and why?
Since, in the short-run firms are making monopoly profits (Pw” > AC), new firms will enter.
c) Describe where the new long-run equilibrium occurs, and explain what has happened to the number of firms and
the prices they charge.
In the long run, the number of firms will increase because some firms will enter the market as a result of short-run profit
opportunities in this industry. Firm entry shifts D/NT and d4 to the left and makes d4 more elastic until it is tangent to
the average cost curve. At that point, monopoly profits are zero and firms no longer enter the industry. Relative to the
short-run equilibrium in (b), the number of firms increases and price decreases.This is because each firm moves down its
average cost curve (due to economies of scale)
Chapter 8 Problem 2: Consider a small country applying a tariff, t, to imports of a good like that represented in
Figure 8.5
a) Suppose that the country decides to reduce its tariff to t’. Redraw the graphs for the Home and import markets and
illustrate this change. What happens to the quantity and price of goods produced at Home? What happens to the
quantity of imports?
As can be seen from Figure 8 the price of goods produced at Home decreases from Pw +t to Pw +t’ and quantity of goods
produces at home decreases from S2 to S3, quantity of imports increases from M2 to M3 . Home consumers buy more at the
lower price and home producers produce less, hence imports increase.
Figure 8
Import Market
Home Country
S
Price
Price
X* +t
Pw +t
Pw +t`
X* +t`
D
X*
S3
S2
D2
D3
Quantity
M2
M3
M1
Quantity
b) Are there gains or losses to domestic consumer surplus due to reduction in tariff? Are there gains or losses to
domestic producer surplus due to reduction in tariff? How is government revenue affected by the policy change?
Illustrate these on your graphs
Figure 9
Import Market
Home Country
Price
Price
Pw +t
X* +t
Pw +t`
k
m
o
D
n
X* +t`
Pw
X*
S3
S2
D2
D3
Consumer surplus at Home country increases by k+m+n+o
Quantity
M2
M3 M1
Quantit
y
Producer surplus decreases by k
The effect on government revenue is ambiguous. The size of the tariff is lower but now the country imports more.
c) What is the overall gain or loss welfare due to the policy change?
The overall gain arises from smaller dead-weight loses. Notice that the deadweight loss triangles are now much smaller
than before.
Chapter 8 Problem 3- Consider a large country applying a tariff t, to imports of a good like that represented in Figure 8.7
a) How does the export supply curve in panel (b) compare with that in the small-country case? Explain why these
are different?
Figure 10
Home Country
World Market
Price
Price
X* +t
Pw +t
X*
a
c
b
Pw
d
f
e
S1
S2
D
D2
D1
Quantity
e
M2
M1
Quantit
y
The export supply curve is not horizontal anymore which means that home country is not a price taker. This is because
Home is now large enough so that if it buys more from abroad, the international price rises.
In other words, since the home country is large, a change in its demand for a good affects world prices.
b) Explain how the tariff affects the price paid by consumers in the importing country and the price received by
producers in the exporting country. Use graphs to illustrate how the prices are affected if (i) the export supply
curve is very elastic (flat) or (ii) the export supply curve is inelastic (steep)
The price paid by consumers in the importing country increases from Pw to Pw +t The price received by producers in the
exporting country decreases from Pw to P* (see Figure 10). The latter decline is due to the fact that Home consumers are
now demanding less of the imported good, creating a glut of it in the world market.
Figure 11
World Market
Home Country
Price
Price
X* +t
Pw +t
D
X*
Pw
P*
S1
S2
D1
D2
Quantity
M2
M1
Quantit
y
Figure 12 compares the effect of a tariff when i) foreign country is inelastic (curve X * ) and ii )when the foreign export
supply is relatively inelastic (curve X* Steep )
As can be seen in Figure12, the more inelastic the export supply curve is, the lower the price received by the producers of
the exporting country. In the elastic case the price received by producers of export country drops to P* whereas the price
drops to (P*)s in the inelastic case. On the other hand, the price paid by home country increases less in the inelastic case
(from Pw to (Pw +t)s )
The intuition is simple. When foreign exporters cannot change the quantity of their exports in response to price changes
(the inelastic case), they need to lower their price more in order to ensure that they can sell the desired amount. If , on the
other hand, exporters need to reduce their price just by a little in order to export more (the elastic case), they will lower
their price only by a little bit.
Figure 12
World Market
Home Country
Price
Price
X*steep+t
X* +t
Pw +t
X* Steep
(Pw +t)s
D
X*
Pw
P*
(P*)s
S1
S2
D2
D1
Quantity
M2
M1
Quantit
y
Chapter 8, problem 4: Consider a large country applying a tariff, t, to imports of good like the represented
in
Figure 8-7. How does the size of the terms-of trade gain compare with the size of dead-weight loss when i) the tariff is
very small and ii)the tariff is very large? Use graphs to illustrate your answer.
Figure 13
World Market
Home Country
Price
Price
X* +t
Pw +t
X*
a
c
b
d
D
f
Pw
e
e
S1
S2
D1
D2
Quantity
M2
M1
Quantit
y
In the graph above, the net gain of home from implementing tariff is e(terms of trade gain) – (b+d) dead weight loss. We can
similarly calculate the net gain of home from implementing very small amount of tariff. In this case, the net deadweight loss
approaches zero while the terms of trade gain is positive. Hence, in the latter case (i.e., small tariff), the net gain from
implementing tariff appears to be positive . See the discussion on pp 295-296 of the text book for more details)
Figure 14
World Market
Home Country
Price
Price
d-loss
b-loss
X* +t
X*
Pw +t
D
f
Pw
e
e=terms of
trade gain
S1
S2
D1
D2
Quantity
M2
M1
Quantit
y
Chapter 8-Problem 6: Comparing (a) and (b), the deadweight losses are offset to a lesser or greater degree by the
terms of trade gain. Since the quantity of imports is the same in both cases, the overall efficiency (or ``welfare’’) loss is
smaller for the large country. A large country applying an optimal tariff actually gains since the terms of trade gain
dominates the deadweight losses. In case (c), the tariff applied is lower than that applied in cases (a) and (b). We know
this because M’>M. If we assume that the optimal tariff was applied in case (b), then the terms of trade gain will now be
smaller, so that national welfare too will be lower.
Thus, assuming that the optimal tariff is applied in case (b), we can rank the outcomes in ascending order of Home
Welfare as follows: (a) < (c) < (b). If the tariff applied in part (b) was not at the optimal level then the ranking between
(b) and (c) will be unclear.