international trade

ECO 364: International Trade

Problem Set 5

Due date: 5:00 PM, 29 November 2018

Trade Policy under Perfect Competition

There are two countries, Home and Foreign, and a single good, Icecubes. Households in

both countries consume Icecubes, and have linear inverse demand functions given by:

Home demand: PH = a D H − bDHQDH

Foreign demand: PF = a D F − bDFQDF

Icecubes are also are supplied by �rms from both countries under perfect competition, with

linear supply functions given by:

Home supply: PH = a S H + b

S HQ

S H

Foreign supply: PF = a S F + b

S FQ

S F

In what follows, assume that the demand-side parameter values are:

aDH = 6, b D H = 2

aDF = 4, b D F = 2

and that supply-side parameter values are:

aSH = 4, b S H = 2

aSF = 2, b S F = 2

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Autarky

First, suppose that both countries are in autarky and hence cannot trade with each other.

(a) What are the prices {PH , PF} and quantities {QH , QF} of icecubes produced and consumed in each country?

(b) What are the values of consumer surplus {CSH , CSF} and producer surplus {PSH , PSF} in each country?

Free trade

Next, suppose that both countries can trade icecubes freely with each other, so that there

is a common world price of icecubes with PH = PF = PW . In order for the world icecube

market to clear, exports by Home must equal imports from Foreign:

QSH −QDH = − ( QSF −QDF

) (c) What must the world price of icecubes PW be for the world icecube market to clear?

(d) What are the quantities of icecubes produced { QSH , Q

S F

} and consumed

{ QDH , Q

D F

} in

each country?

(e) What are the values of consumer surplus {CSH , CSF} and producer surplus {PSH , PSF} in each country?

(f) What is the total change in welfare (CS+PS) in each country under free trade relative

to autarky? Which country bene�ts from trade?

Trade under a Home tari�

Now, suppose that the Home government decides to impose a tari� of t on imports from

Foreign, so that prices in the two countries are related by PH = PF + t.

(g) What must the price of icecubes {PH , PF} be in each country to clear the world icecube market?

(h) What are the quantities of icecubes produced { QSH , Q

S F

} and consumed

{ QDH , Q

D F

} in

each country?

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(i) Show that consumer surplus {CSH , CSF}, producer surplus {PSH , PSF}, and tari� revenue TRH (for Home) are given by:

CSH =

( 1− 1

4 t

)2 , PSH =

1

16 t2, TRH = t

( 1− 1

2 t

) CSF =

1

16 t2, PSF =

( 1− 1

4 t

)2 (j) What is the optimal value of the tari� t∗ for the Home government (i.e. the value of t

that maximizes CSH + PSH + TRH)?

(k) What is the value of welfare (CS+PS) in Foreign under the tari� t∗? Is Foreign better

or worse o� with the tari� compared to free trade?

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