Econ 490International Economics PROBLEM SET #2– ANSWER KEY

PROBLEM SET #2– ANSWER KEYEcon 490International EconomicsUIUC, Fall 2019Mauro Rodrigues

INTERNATIONAL ECONOMICS, UIUC, FALL 2019 - MAURO RODRIGUES 1

QUESTION 1

a) Firms choose how many workers to employ so that value of the marginal product of each input is equal to its price

Food sector (f)Wage of experienced workers:

𝑤𝑤𝑁𝑁𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑀𝑀𝑃𝑃𝑀𝑀𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓

𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝑀𝑀𝑓𝑓

Wage of younger workers:

𝑤𝑤𝐿𝐿𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑀𝑀𝑃𝑃𝐿𝐿𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓

𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝐿𝐿𝑓𝑓


QUESTION 1

Textile sector (t)Wage of experienced workers:

𝑤𝑤𝑁𝑁𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑀𝑀𝑃𝑃𝑀𝑀𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝑀𝑀𝑡𝑡

Wage of younger workers:

𝑤𝑤𝐿𝐿𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑀𝑀𝑃𝑃𝐿𝐿𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝐿𝐿𝑡𝑡


QUESTION 1

Since younger workers are mobile, 𝑤𝑤𝐿𝐿𝑓𝑓 = 𝑤𝑤𝐿𝐿𝑡𝑡 = 𝑤𝑤𝐿𝐿:

𝑤𝑤𝐿𝐿 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝐿𝐿𝑓𝑓

= 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝐿𝐿𝑡𝑡

Equilibrium in factor markets:

𝐿𝐿𝑓𝑓 + 𝐿𝐿𝑡𝑡 = �𝐿𝐿𝑀𝑀𝑓𝑓 = �𝑀𝑀𝑓𝑓𝑀𝑀𝑡𝑡 = �𝑀𝑀𝑡𝑡


QUESTION 1Production functions are homogeneous of degree 1 (they exhibit constant returns to scale)

Therefore their derivatives are homogeneous of degree zero they depend only on the ratio 𝑛𝑛𝑖𝑖 = 𝑀𝑀𝑖𝑖/𝐿𝐿𝑖𝑖, 𝑖𝑖 = 𝑓𝑓, 𝑡𝑡.

𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝐿𝐿𝑓𝑓

increasing with 𝑛𝑛𝑓𝑓𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝑁𝑁𝑓𝑓

decreasing with 𝑛𝑛𝑓𝑓

𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝐿𝐿𝑡𝑡

increasing with 𝑛𝑛𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝑁𝑁𝑡𝑡

decreasing with 𝑛𝑛𝑡𝑡


QUESTION 1

We can then write the model’s equations as:


(�𝑀𝑀𝑓𝑓/𝐿𝐿𝑓𝑓) = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝐿𝐿𝑡𝑡

(�𝑀𝑀𝑡𝑡/𝐿𝐿𝑡𝑡)

𝐿𝐿𝑓𝑓 + 𝐿𝐿𝑡𝑡 = �𝐿𝐿

From the above equations we can derive the diagram in next slide. It allows to determine the wage of younger workers (𝑤𝑤𝐿𝐿) and the allocation of younger workers across sectors (𝐿𝐿𝑓𝑓 and 𝐿𝐿𝑡𝑡).

We can then use these values to find the wages of experienced workers in each sector:

𝑤𝑤𝑁𝑁𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓


(�𝑀𝑀𝑓𝑓/𝐿𝐿𝑓𝑓)

𝑤𝑤𝑁𝑁𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝑀𝑀𝑡𝑡



INTERNATIONAL ECONOMICS, UIUC, FALL 2019 - MAURO RODRIGUES7

𝐿𝐿1


( �𝑀𝑀𝑓𝑓/𝐿𝐿𝑓𝑓)

𝐿𝐿2

A

B

𝑧𝑧𝑓𝑓′ > 𝑧𝑧𝑓𝑓

�𝐿𝐿

𝑤𝑤𝐿𝐿𝑤𝑤𝐿𝐿

𝑤𝑤𝐿𝐿 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓′𝜕𝜕𝐹𝐹𝑓𝑓𝜕𝜕𝐿𝐿𝑓𝑓


𝑤𝑤𝐿𝐿 = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝐿𝐿𝑡𝑡


QUESTION 1

Increase in 𝑧𝑧𝑓𝑓 sector f firms expand demand more of both type of workers

As a result, sector f’s curve shifts up in the diagram wages of younger workers increase

Food sector attracts younger workers from textile sector food sector expands, textile sector shrinks


QUESTION 1

Wages of experienced workers in the food industry:

𝑤𝑤𝑁𝑁𝑓𝑓 = 𝑃𝑃𝑓𝑓𝑧𝑧𝑓𝑓



𝑤𝑤𝑁𝑁𝑓𝑓 increases because of higher demand for these workers, which happens for two reasons shown

in the equation above: (i) higher 𝑧𝑧𝑓𝑓 , (ii) lower �𝑀𝑀𝑓𝑓/𝐿𝐿𝑓𝑓 , which leads to an increase in the marginal product of this input.

Wages of experienced workers in the textile industry:

𝑤𝑤𝑁𝑁𝑡𝑡 = 𝑃𝑃𝑡𝑡𝑧𝑧𝑡𝑡𝜕𝜕𝐹𝐹𝑡𝑡𝜕𝜕𝑀𝑀𝑡𝑡


𝑤𝑤𝑁𝑁𝑓𝑓 decreases because of lower demand for these workers (textile sector is shrinking). In the

equation, this corresponds to an increase �𝑀𝑀𝑡𝑡/𝐿𝐿𝑡𝑡 , which leads to lower marginal product of this input.


QUESTION 1

b) The new technology benefits younger workers and experienced workers of the food industry. It hurts experienced workers of the textile industry.

Experienced workers of the textile industry would then support the law, while the others would oppose it. Therefore, the law will be aproved if it has at least 50% of support, that is:

�𝑀𝑀𝑡𝑡�𝐿𝐿 + �𝑀𝑀𝑓𝑓 + �𝑀𝑀𝑡𝑡

≥ 0.5


QUESTION 2

See presentations “Economies of Scale and Imperfect Competition – Part I” (slides 11-37) and “Economies of Scale and Imperfect Competition – Part II” (slides 1-11)


QUESTION 3

a) Monopolist chooses quantity so that marginal revenue (MR) = marginal cost (MC)

Domestic Revenue: 𝑅𝑅(𝑄𝑄) = 𝑃𝑃 × 𝑄𝑄 = 10−𝑄𝑄2

𝑄𝑄 = 5𝑄𝑄 − 𝑄𝑄2

2

Domestic Marginal Revenue: 𝑀𝑀𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑅𝑅′ 𝑄𝑄 = 5 − 𝑄𝑄

𝑀𝑀𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑀𝑀𝑀𝑀5 − 𝑄𝑄𝑐𝑐 = 2𝑄𝑄𝑐𝑐𝑄𝑄𝑐𝑐 = 1.67

𝑃𝑃𝑐𝑐 =10 − 𝑄𝑄𝑐𝑐

2= 4.17


MC

A

Copyright © 2003 Pearson Education, Inc.

Slide 6-13

Cost, C andPrice, P

Quantities producedand demanded, Q

MRDOM

DDOM

Pc = 4.17

Qc = 1.67

QUESTION 3

b) If the monopolist can sell in both markets, then it chooses quantity so that:

𝑀𝑀𝑅𝑅𝑡𝑡𝑑𝑑𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑀𝑀𝑀𝑀

Since the MC curve crosses the Total MR curve in its flat segment (check), then:

𝑀𝑀𝑅𝑅𝑡𝑡𝑑𝑑𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑃𝑃𝑊𝑊 = 4 = 𝑀𝑀𝑀𝑀 = 2𝑄𝑄𝑑𝑑

Total quantity produced:

𝑄𝑄𝑑𝑑 = 2


QUESTION 3

b) Monopolist sells prodcut domestically up to point C (𝑀𝑀𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 ≥ 𝑃𝑃𝑊𝑊)

At point C:

𝑀𝑀𝑅𝑅𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑃𝑃𝑊𝑊 = 45 − 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 = 4

Domestic sales: 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 = 1


QUESTION 3

Therefore, exports are:

𝑄𝑄𝑑𝑑 − 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 = 1

Domestic price:

𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑 =10 − 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑

2= 4.5


MC


Slide 6-17

Cost, C andPrice, P


MRDOM

DDOM

DEXT = MREXTPEXT = 4

MRTOTAL

C

Qo = 2

B

Qdom = 1

ExportsDomestic sales

Total output

PDOM = 4.5

QUESTION 3

c) See diagram in the next slide:

Closed economy:

Consumer surplus = D + E + FProducer surplus = G + H + K + J

Open economy:

Consumer surplus = DProducer surplus = (E + G + J) + (K + L + M)


MC


Slide 6-19

Cost, C andPrice, P


MRDOM

DDOM


MRTOTAL

Qo = 2Qdom = 1

PDOM = 4.5D

EF

G H I

JK L

M

QUESTION 3

Change in consumer surplus = – E – FChange in producer surplus = E + L + M – H

Change in welfare = (L + M) – (F + H)


MC


Slide 6-21

Cost, C andPrice, P


MRDOM

DDOM


MRTOTAL

Qo = 2Qdom = 1

PDOM = 4.5 F

H

L

M

PX = 2

QUESTION 3

L + M =(𝑃𝑃𝑊𝑊 − 𝑃𝑃𝑋𝑋) × (𝑄𝑄𝑑𝑑 − 𝑄𝑄𝑐𝑐)

2= 0.11

F + H =[ 𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑 − 𝑃𝑃𝑊𝑊 + 𝑃𝑃𝑐𝑐 − 𝑃𝑃𝑊𝑊 ] × (𝑄𝑄𝑐𝑐 − 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑)

2= 0.22

Change in welfare:

L + M − F + H = −0.11


QUESTION 3

d) You just need to recalculate prices and quantities with the new demand function.

Results:

Closed economy:Quantity: 𝑄𝑄𝑐𝑐 = 1.5Price: 𝑃𝑃𝑐𝑐 = 3.75

Open economy:Total quantity: 𝑄𝑄𝑑𝑑 = 2Domestic sales: 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 = 0.5Exports: 𝑄𝑄𝑑𝑑 − 𝑄𝑄𝑑𝑑𝑑𝑑𝑑𝑑 = 1.5Domestic price: 𝑃𝑃𝑐𝑐 = 4.25

Now the international price is higher than that of a closed economy.


MC


Slide 6-24

Cost, C andPrice, P


MRDOM

DDOM


MRTOTAL

C

Qo = 2

B

Qdom = 0.5

ExportsDomestic sales

Total output

PDOM = 4.25

MC


Slide 6-25

Cost, C andPrice, P


MRDOM

DDOM


MRTOTAL

Qo = 2Qdom = 0.5

PDOM = 4.25D

E FG

H

I

L

J K

3

3.6

1.8

QUESTION 3

Closed economy:

Consumer surplus = D + E + F + G + HProducer surplus = I + J

Open economy:

Consumer surplus = DProducer surplus = (E + G + I) + (H + J + K + L)

Change in consumer surplus = – E – F – G – HChange in producer surplus = E + G + H + K + L

Change in welfare = K + L – F


QUESTION 3

K =12

× 0.75 × 0.3 = 0.1125

L =12

× 1 × 0.4 = 0.2

F =12

× 0.25 × 0.5 = 0.0625

Change in welfare = K + L − F = 0.25


QUESTION 4a) Import Demand (Brazil):

𝑀𝑀𝐷𝐷𝑏𝑏 = 𝐷𝐷𝑏𝑏 − 𝑆𝑆𝑏𝑏 = 40 − 4𝑃𝑃𝑏𝑏

Export Supply (Argentina):

𝑋𝑋𝑆𝑆𝑡𝑡 = 𝑆𝑆𝑡𝑡 − 𝐷𝐷𝑡𝑡 = −20 + 4𝑃𝑃𝑡𝑡

If there are no barriers to trade, then 𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑏𝑏 = 𝑃𝑃𝑊𝑊. Equilibrium in world market:

𝑀𝑀𝐷𝐷𝑏𝑏 = 𝑋𝑋𝑆𝑆𝑡𝑡

40 − 4𝑃𝑃𝑊𝑊 = −20 + 4𝑃𝑃𝑊𝑊


QUESTION 4

𝑃𝑃𝑊𝑊 = 7.5

Consumption in Brazil: 𝐷𝐷𝑏𝑏 = 100 − 2𝑃𝑃𝑊𝑊 = 85

Production in Brazil: 𝑆𝑆𝑏𝑏 = 60 + 2𝑃𝑃𝑊𝑊 = 75

Imports = 85 − 75 = 10


Copyright © 2003 Pearson Education, Inc. Slide 8-30

Pb = 7.5 + 0.5t

PW = 7.5b c d

e

D

a

= consumer loss (a + b + c + d)= producer gain (a)= government revenue gain (c + e)

S

75 85

Price, P

Quantity, Q

Pa = 7.5 – 0.5t

75 + t 85 – t

QUESTION 4b) With the introduction of the tariff:

𝑃𝑃𝑏𝑏 = 𝑃𝑃𝑡𝑡 + 𝑡𝑡Equilibrium in world market:

𝑀𝑀𝐷𝐷𝑏𝑏 = 𝑋𝑋𝑆𝑆𝑡𝑡

40 − 4𝑃𝑃𝑏𝑏 = −20 + 4𝑃𝑃𝑡𝑡

40 − 4(𝑃𝑃𝑡𝑡 + 𝑡𝑡) = −20 + 4𝑃𝑃𝑡𝑡


QUESTION 4

𝑃𝑃𝑡𝑡 = 7.5 − 0.5𝑡𝑡

𝑃𝑃𝑏𝑏 = 7.5 + 0.5𝑡𝑡

Consumption in Brazil: 𝐷𝐷𝑏𝑏 = 100 − 2𝑃𝑃𝑏𝑏 = 85 − 𝑡𝑡

Production in Brazil: 𝑆𝑆𝑏𝑏 = 60 + 2𝑃𝑃𝑏𝑏 = 75 + 𝑡𝑡

Imports = 10 − 2𝑡𝑡


QUESTION 4

c) Terms of trade gain = Area “e” in diagram

Area “e” = 85 − 𝑡𝑡 − 75 + 𝑡𝑡 × 7.5 − 7.5 − 0.5𝑡𝑡 = 5𝑡𝑡 − 𝑡𝑡2

Efficiency loss = Area “b” + Area “d”

=12

7.5 + 0.5𝑡𝑡 − 7.5 × 75 + 𝑡𝑡 − 75 +12

7.5 + 0.5𝑡𝑡 − 7.5 × [85 − 85 − 𝑡𝑡 ]

= 0.25𝑡𝑡2 + 0.25𝑡𝑡2 = 0.5𝑡𝑡2

Change in welfare = Terms of trade gain – Efficiency Loss

∆𝑊𝑊𝑏𝑏 = 5𝑡𝑡 − 𝑡𝑡2 − 0.5𝑡𝑡2 = 5𝑡𝑡 − 1.5𝑡𝑡2


QUESTION 4

Optimum tariff:

max∆𝑊𝑊𝑏𝑏 = 5𝑡𝑡 − 1.5𝑡𝑡2

�𝑑𝑑∆𝑊𝑊𝑏𝑏

𝑑𝑑𝑡𝑡 𝑡𝑡𝑜𝑜

= 0 → 5 − 3𝑡𝑡𝑑𝑑 = 0

𝑡𝑡𝑑𝑑 =53


QUESTION 4

d) Welfare variation in Brazil:

∆𝑊𝑊𝑏𝑏 = 5𝑡𝑡𝑑𝑑 − 1.5𝑡𝑡𝑑𝑑2 = 4.17

For Argentina (see next slide):


Change in consumer surplus A + B

Change in producer surplus – (A + B + C)

Change in welfare – C


PW = 7.5B

Da

A

Sa

75 85

Price, P

Quantity, Q

Pa = 7.5 – 0.5t

75 + t 85 – t

C

QUESTION 4

Production and consumption in Argentina:

𝐷𝐷𝑡𝑡 = 90 − 2𝑃𝑃𝑡𝑡 = 75 + 𝑡𝑡𝑆𝑆𝑡𝑡 = 70 + 2𝑃𝑃𝑡𝑡 = 85 − 𝑡𝑡

Change in Welfare in Argentina = – Area “C”

∆𝑊𝑊𝑡𝑡 = −12 10 + 10 − 2𝑡𝑡 × 0.5𝑡𝑡

For 𝑡𝑡 = 𝑡𝑡𝑑𝑑 = 5/3:

∆𝑊𝑊𝑡𝑡 = −6.94


QUESTION 5a) Import Demand (Argentina):

𝑀𝑀𝐷𝐷𝑡𝑡 = 𝐷𝐷𝑡𝑡 − 𝑆𝑆𝑡𝑡 = 30 − 5𝑃𝑃𝑡𝑡

Export Supply (Brazil):

𝑋𝑋𝑆𝑆𝑏𝑏 = 𝑆𝑆𝑏𝑏 − 𝐷𝐷𝑏𝑏 = −10 + 5𝑃𝑃𝑏𝑏

If there are no barriers to trade, then 𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑏𝑏 = 𝑃𝑃𝑊𝑊. Equilibrium in world market:

𝑀𝑀𝐷𝐷𝑡𝑡 = 𝑋𝑋𝑆𝑆𝑏𝑏

30 − 5𝑃𝑃𝑊𝑊 = −10 + 5𝑃𝑃𝑊𝑊


QUESTION 5

𝑃𝑃𝑊𝑊 = 4

Consumption in Argentina: 𝐷𝐷𝑡𝑡 = 50 − 4𝑃𝑃𝑊𝑊 = 34

Production in Brazil: 𝑆𝑆𝑡𝑡 = 20 + 𝑃𝑃𝑊𝑊 = 24

Imports = 34 − 24 = 10



Pb = 7.5 + 0.5t

PW = 4b c d

e

D

a

= consumer loss (a + b + c + d)= producer gain (a)= government revenue gain (c + e)

S

24 34

Price, P

Quantity, Q

Pa = 7.5 – 0.5t

24 +0.5t 34 – 2t

QUESTION 5With the introduction of the tariff:

𝑃𝑃𝑡𝑡 = 𝑃𝑃𝑏𝑏 + 𝑡𝑡Equilibrium in world market:

𝑀𝑀𝐷𝐷𝑡𝑡 = 𝑋𝑋𝑆𝑆𝑏𝑏

30 − 5𝑃𝑃𝑡𝑡 = −10 + 5𝑃𝑃𝑏𝑏

30 − 5(𝑃𝑃𝑏𝑏 + 𝑡𝑡) = −10 + 5𝑃𝑃𝑏𝑏


QUESTION 5

𝑃𝑃𝑏𝑏 = 4 − 0.5𝑡𝑡

𝑃𝑃𝑡𝑡 = 4 + 0.5𝑡𝑡

Consumption in Argentina: 𝐷𝐷𝑡𝑡 = 50 − 4𝑃𝑃𝑡𝑡 = 34 − 2𝑡𝑡

Production in Argentina: 𝑆𝑆𝑡𝑡 = 20 + 𝑃𝑃𝑡𝑡 = 24 + 0.5𝑡𝑡

Imports = 10 − 2.5𝑡𝑡


QUESTION 5

Terms of trade gain = Area “e” in diagram

Area “e” = (10 − 2.5𝑡𝑡) × 0.5𝑡𝑡 = 5𝑡𝑡 − 1.25𝑡𝑡2

Efficiency loss = Area “b” + Area “d”

=12

0.25𝑡𝑡2 +12𝑡𝑡2 = 0.625𝑡𝑡2

Change in welfare = Terms of trade gain – Efficiency Loss

∆𝑊𝑊𝑡𝑡 = 5𝑡𝑡 − 1.25𝑡𝑡2 − 0.625𝑡𝑡2 = 5𝑡𝑡 − 1.875𝑡𝑡2


QUESTION 5

Optimum tariff:

max∆𝑊𝑊𝑡𝑡 = 5𝑡𝑡 − 1.875𝑡𝑡2

�𝑑𝑑∆𝑊𝑊𝑡𝑡

𝑑𝑑𝑡𝑡 𝑡𝑡𝑜𝑜

= 0 → 5 − 2 × 1.875𝑡𝑡𝑑𝑑 = 0

𝑡𝑡𝑑𝑑 = 1.33


QUESTION 5

b) Welfare variation in Argentina:

∆𝑊𝑊𝑡𝑡 = 5𝑡𝑡𝑑𝑑 − 1.875𝑡𝑡𝑑𝑑2 = 3.33

For Brazil (see next slide):


Change in consumer surplus A + B

Change in producer surplus – (A + B + C)

Change in welfare – C


PW = 4B

Db

A

Sb

26 36

Price, P

Quantity, Q

Pb = 4 – 0.5t

26 + 0.5t 36 – 2t

C

QUESTION 5

Production and consumption in Brazil:

𝐷𝐷𝑏𝑏 = 30 − 𝑃𝑃𝑏𝑏 = 26 + 0.5𝑡𝑡𝑆𝑆𝑏𝑏 = 20 + 4𝑃𝑃𝑏𝑏 = 36 − 2𝑡𝑡

Change in Welfare in Brazil = – Area “C”

∆𝑊𝑊𝑏𝑏 = −12 10 + 10 − 2.5𝑡𝑡 × 0.5𝑡𝑡

For 𝑡𝑡 = 𝑡𝑡𝑑𝑑 = 1.33:

∆𝑊𝑊𝑏𝑏 = −5.56


QUESTION 5

c) From Problem #4, if Brazil imposes its optimum tariff on the importation of wheat (and Argentina plays free trade), payoffs are:

∆𝑊𝑊𝑏𝑏 = 4.17∆𝑊𝑊𝑡𝑡 = −6.94

From Problem #5, if Argentina imposes its optimum tariff on the importation of soybeans (and Brazil plays free trade), payoffs are:

∆𝑊𝑊𝑏𝑏 = −5.56∆𝑊𝑊𝑡𝑡 = 3.33

If both countries implement their optimum tariffs simultaneously, payoffs are:∆𝑊𝑊𝑏𝑏 = 4.17 − 5.56 = −1.39∆𝑊𝑊𝑡𝑡 = −6.94 + 3.33 = −3.61

Welfare variation is relative to free trade. Therefore, if both countries play free trade, their payoffs are zero



ARGENTINA

BRAZIL

0

0

-3.61

-1.39

3.33

-5.56

4.17

-6.94

Free trade

Free trade

Optimum tariff

Optimum tariff

QUESTION 5

(Optimum Tariff, Optimum Tariff) is the only Nash equilibrium of this game.

In the Nash equilibrium, no player has incentive to deviate from it. In this case, a country’s payoff would decline if it unilaterally decides to play free trade.


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Econ 490International Economics PROBLEM SET #2– ANSWER KEY