Question Details

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


Problem 1: Transfers and trade with non-traded goods.

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.

 

Problem 1: Transfers and trade with non-traded goods.

 

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> 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?

 

Problem 3. Revealed Comparative Advantage

 

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 ) >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

 

Comparative Advantage?

 


 

 


Solution details:

Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .
SiteLock

About this Question

STATUS

Answered

QUALITY

Approved

DATE ANSWERED

Oct 15, 2019

EXPERT

Tutor

ANSWER RATING

YES, THIS IS LEGAL

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

  • As a reference for in-depth understanding of the subject.
  • As a source of ideas / reasoning for your own research (if properly referenced)
  • For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).
This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.

NEW ASSIGNMENT HELP?

Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.

Order Now