## (Solved) Problem 1 : Transfers and trade with non-traded goods. Suppose we

Suppose we have two countries and three goods.

• Good zero is non-traded, and produced by both countries with labor cost
• Good 1 is tradable, and can be produced only by country H.  Country H has labor cost  for good 1.
• Good 2 is tradable, and can be produced only by country F.  Country F has labor cost   for good 2.

Marginal labor costs are constant (effectively,

) and Labor supply in country

is

Preferences are given by

Suppose Country  pays a flat transfer to country  equal to   ().

Questions

1.i) Write down and solve the consumer?s problem (follow the notation in the slides, so you can do it for country  where  can be either  or ; so you don?t have to write everything twice)

1.ii) Write down the firm?s problem.  What does the firm?s problem imply about wages and prices?

1.iii) Write down the market clearing constraints.  What does a balanced current account mean?

i.iv) What do preferences imply about the utility of consumers if they cannot consume one of the goods?  What do we know about what the pattern of specialization will be in the free trade equilibrium?

i.v) Define an equilibrium for this economy.  (You do not need to re-type the equations).

i.vi) Solve for the equilibrium of this economy.  Don?t forget to normalize one of the prices or wages.

i.vii) What happens to relative wages () and relative prices ) as the transfer changes.  How does this compare to the economy in worksheet 1 where there was no non-traded good?

Does what happens to the Terms of Trade affect how much the transfer hurts the Foreign country?  In what way?

ECO 445/545: Problem Set 1

Professor Jack Rossbach

Due Date: Sunday, March 6 at 11:59PM EST

Spring 2016

Problem Set 1

Complete the questions for each problem. Answers must be typed and uploaded to blackboard as either

a word document or PDF to blackboard. You are encouraged to discuss the problems with each other,

however, everybody needs to submit their own assignment and type up their own answers.

Suppose we have two countries and three goods.

H

a0 =a F =1

0

Good zero is non-traded, and produced by both countries with labor cost

Good 1 is tradable, and can be produced only by country H. Country H has labor cost

H

a1

for

good 1.

Good 2 is tradable, and can be produced only by country F. Country F has labor cost

F

a2

for good

2.

Marginal labor costs are constant (effectively,

F

H

a1 =a2 =? ) and Labor supply in country i is Li

Preferences are given by

U i ( c i0 , ci1 , c i2 )=? logc i0 +

Suppose Country

( 1?? ) ( logc +log c )

2

i

1

i

2

F pays a flat transfer to country

H

equal to

T

( T ? 0 ).

Questions

1.i) Write down and solve the consumer?s problem (follow the notation in the slides, so you can do it for

country

i where i can be either

H

or

F ; so you don?t have to write everything twice)

1.ii) Write down the firm?s problem. What does the firm?s problem imply about wages and prices?

1.iii) Write down the market clearing constraints. What does a balanced current account mean?

i.iv) What do preferences imply about the utility of consumers if they cannot consume one of the goods?

What do we know about what the pattern of specialization will be in the free trade equilibrium?

i.v) Define an equilibrium for this economy. (You do not need to re-type the equations).

i.vi) Solve for the equilibrium of this economy. Don?t forget to normalize one of the prices or wages.

F

i.vii) What happens to relative wages ( w / w

H

p2 / p1

) as the transfer

¿

) and relative prices

changes. How does this compare to the economy in worksheet 1 where there was no non-traded good?

Does what happens to the Terms of Trade affect how much the transfer hurts the Foreign country? In

what way?

Problem 2

For this problem we are going to combine Comparative Advantage with another reason to trade: Taste

for Variety.

There are two countries,

i, j=H , F , and two types of goods, m=1,2 . For each good, each

country produces their own variety of that good. Preferences in country

?

?

?

U i ( c i1 H , c i2 H ,c i1 F , ci2 F ) =?1 log ( ( c i1 H ) + ( c i1 F ) ) +?2 log (( c i2 H ) + ( ci2 H )

i

c1 H

Where

is the consumption of H?s variety of good 1 in country

i

c mj is the amount of

?

i are given by

)

i . Similarly for the other goods,

j ?s variety of good 1 consumed in country i . We require ? ? ( 0,1 ) ;

?1 ,? 2&gt; 0 .

These preferences imply that consumers want to consume some of each variety of each good. They are

referred to as CES (Constant Elasticity of Substitution) preferences, since the elasticity of substitution

between varieties for each good is constant and equal to

The budget constraint for consumers in country

2

1

1?? .

i is standard:

2

? ? pimj c imj=w i Li

m=1 j=1

Where

i

pmj is the price of variety

j of good m consumed in country i . Prices may differ

across countries, as there are iceberg trade costs to ship goods. This means that to export 1 unit of a

good, it is necessary to ship

? ? 1 units ( ? =1 is frictionless trade).

Firms are perfectly competitive and internalize trade costs into their production. Firms located in

j for good m can produce output for country i according to the production function:

country

1 i

l mj

? a mj

i

y mj=

i

j

? jj=1 (no trade costs to serve own market) and ? ij=?

Where

cost for firms to produce one unit of good

m in country

if

i? j .

amj is the unit labor

j for the domestic market.

Due to trade costs, we require markets clear individually for each market. That means there are 8 goods

market clearing conditions:

i

i

c mj= y mj , m=1,2; i , j=1,2

Labor market clearing for country is given by

2

2

? ? limj=L j , j=1,2

m=1 i=1

Use this model to answer the questions on the following page.

Questions

2.i) What are the exogenous parameters for the model? What are the endogenous parameters for the

model? (You can leave out subscripts and superscripts for this question)

2.ii) The solution to the consumer problem is

(

i

mj

c =

?m

i i

w L

? 1+ ? 2

)

1

i 1? ?

mj

(p )

?

(1? ? )

?

(P )

, m=1,2 ; i, j=1,2

i

Pm is an aggregated price index for good m for consumers in country i

Where

i

i

m

(

i

?

(1? ? )

?

Pm ? ( pmH )

i

1? ?

?

( 1?? ) ?( ? )

?

+ ( p mF )

)

,m=1,2 ; i=1,2

Firms are perfectly competitive, so the solution to the firms problem is given by

i

i

j

pmj=? j amj w ,m=1,2 ; i , j=1,2

List all the equilibrium equations for this economy. How many equations are there? Hint: The number

of equilibrium equations should equal the number of endogenous parameters.

2.iii) On my website you will find notes showing how to solve the model algebraically in the case where

countries are symmetric.

?1=? 2=1 ; ? =1 ; LH =L F =10 ; a1 H =a2 H =a1 F=a2 F =1 ; ?=0.5 . Plug

Assume

these values into the algebraic solutions to find equilibrium prices and allocations.

2.iv) Solve the model on the computer for the same parameter values as above. Make sure that it is easy

to update the parameter values in your code, since we will be changing them. Normalize

H

w =1 and

make sure to remember Walras? law. Verify that your model gives the same solution as you got above.

[Note: it can be useful to plug in market clearing conditions by hand to reduce the number of equilibrium

variables and equations you need to solve for on the computer].

? =1.1 . Report the new equilibrium.

Now suppose that there are iceberg costs of 10%, so that

2.v) Suppose that Home is a large country so that

H

L =100 .

Compute the real income per capita index as

[(

i

i

i

i

)] (( ) ( ) ) (( ) ( ) )

?

i

i

c1H c2H c1 F c2F

c1 H

c1 F

exp U

, i , i , i =

+ i

i

i

L L

L L

L

L

i

? ?1

i

c2H

L

i

?

i

+

c2 H

L

? ?2

i

Report the value of the index for each country when we move from a world with iceberg costs

( ? =1.1 ) to a world with frictionless trade ( ? =1 ) . What do our results say about whether large or

small countries tend to benefit more from free trade?

2.vi) Let

H

L =10 again (and ? =1 ). Suppose Home excels at producing good 1 , so that

a1 H =1 / 2 .

What happens to labor allocations for each country for each good compared to 2.iv? Why?

Consider the following index from Balassa (1965)

RC A i ( z )=

Where

(

Xi (z )

X world ( z )

/

X i ( total )

X world ( total )

)(

)

X i ( z ) is country i ?s exports of good

X world ( z ) is the World?s exports of good

z ,

X i ( total ) is country i ?s total exports,

z , and X world ( total ) is the World?s total exports.

If

RC A i ( z ) &gt;1 , we say that country i has a revealed comparative advantage in good

z .

Questions

3.i) Register an account on http://wits.worldbank.org/

Download data on Mexican Exports and ?All Countries? Exports to the World in 1990 and 2005 at the 4digit 1988/1992 Harmonized System (HS) aggregation level.

Using the Balassa formula, compute the RCA Index for each product that Mexico exports in 1990. Report

the 5 highest RCA Index values and what products they belong to.

3.ii) Report the fraction of Mexico?s exports in 2009 that were in products that were not exported by

Mexico in 1990.

For the remaining exercises, exclude products that were not exported by Mexico in 1990.

3.iii) Compute the percentage change in Mexico?s exports between 1990 and 2005 for each product,

deflated by the percent change of Mexico?s GDP between 1990 and 2009 according to the following

formula:

Change ( z )=100 ×

(

X Mex , 2005 ( z ) / GD PMex ,2005

?1

X Mex , 1990 ( z ) / GD PMex ,1990

)

Use data from the World Development Indicators for Mexico?s GDP in 1990 and 2005. The series you

should use is ?GDP at market prices (current US\$)?.

What is the total value of all exports in 1990 and 2005 for Mexico, as a fraction of GDP? What is the

correlation between the RCA Index and the Percentage Change in Exports?

3.iv) Report the median growth (percent change) of exports with a RCA Index less than 1, and the

median growth of exports with a RCA Index greater than 1.

What was the total growth for the exports of all exports of products with an RCA Index less than 1? The

total growth for all exports of products with an RCA Index greater than 1? Which set of products

experienced greater growth?

3.v) Do the results in 3.iv) surprise you or make sense in the context of the Ricardian model? Why?

Skim this paper: http://www.nber.org/papers/w17969.pdf

Can you think of any reasons why the Balassa RCA Index may not be a good measure of a country?s true

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