PDF International Trade

1

International Trade

Conventional Trade Theory vs.

New Trade Theory

1.

Introduction

Conventional Trade Theory (

before 1980

)



Ricardian: McKenzie (1954), Jones (1961)



Specific Factors: Jones (1971), Samuelson (1971)



Heckscher-Ohlin: McKenzie (1955), Jones (1965,JPE)

2

3

• Comparative advantage by endowment:

Heckscher-Ohlin.

• The empirical plausibility of Heckscher-Ohlin model was once questioned.

• Leontief Paradox: Show a table that US is

actually importing (in net terms) capital intensive goods.

2. Hecksher-Ohlin Model

4

• A critique to Leontief’s test by Leamer (1980):

Leontief did the wrong test. If look at factor

contents and allowing for unbalanced trade, US still export capital intensive goods.

2. Hecksher-Ohlin Model (con’t)

5

• The beliefs that trade patterns are not well explained by Heckscher-Ohline model and the fact that there are a lot of “intra-industry” trade among OECD

countries prompt a so-called “New Trade Theory” by Krugman (1979,1980,1981,1991a,1991b,1993,1995, 1996,1998)¸etc.,

2. Hecksher-Ohlin Model (con’t)

6

• Trefler (1993, 1995), however, provide rescue to the H-O model.

• Allowing for differences in labor productivity, a H-O model can fit in any patterns of trade.

• Well, the model then has no empirical content.

2. Hecksher-Ohlin Model (con’t)

7

• But, can compare the labor productivity backed out by trade flows and then compare them with real wages.

• It turns out highly correlated.

• It is constrained by the Constant Return to Scale (CRS) production function

2. Hecksher-Ohlin Model (con’t)

8

• Trade is really about specialization and

exchange...other models of specialization based on increasing returns include Yang and Borland (1991), Becker and Murphy (1992).

• Now, turn to Dixit-Stiglitz (1977) which is the

Monopolistic Competition Model used in Krugman (1979,1980,1981,1991a,1991b,1993,1995,1996)¸

fixed cost of production. scale economies, one product monopolized by one firm.

The Trade Theory by

Increasing Returns to Scale (IRS)

9

Dixit and Stiglitz, 1977, Monopolistic Competition and Optimum Product Diversity, American

Economic Review 67, 297-308.

3. Dixit-Stiglitz Models

- Monopolistic Competition Model

References:

10

• It is one of the most convenient forms of

monopolistic competition, and hence we

need to be very familiar with it and tie it as

a lemma with your belly.

11 3.1. Assumption:

(1) A separable utility function with convex indifference surfaces.

(2) is a symmetric function, thus all commodities have equal fixed and marginal costs.

(3) Commodities with a pair close together have better mutual substitutes than a pair farther apart.

(4) can be regarded as representing Samuelsonian social indifference curves, or regarded as a multiple of a

representative consumer’s utility.

(5) Product diversity can be interpreted either as different consumers using different varieties, or as diversification on the part of each consumer.

V

u

12

3.2. The Characteristics of Monopolistic Competition

(1) The number of firms is large enough.

(2) The commodities produced by each firm are good substitutes among themselves.

(3) Firms enter the market until the next potential entrant would make a loss.

(4) Each firm has not the dominant power to determine the commodity’s price, it is also not as perfect competition

market to take the price as given variable (i.e., exogenously determined)

13 3.3.Utility Function:

(1) (i) For concavity, we need

(ii) For allowing a situation where several of the are zero, we need

(iii) denotes the substitution index among

commodities, , it also interprets the preference of diversity commodities for the consumers, the

smaller of the , implies the consumers prefer to consume the commodities more diversity.

(iv) is a homothetic function in its arguments.



) 1 , 0

(





u









1 0 1

1

0,[ 1 ] ) ( )

(x x di x x di

u

u ^ ⁿ _i ^{ } ⁿ _i

1



xi

 0



14

) ) (

, (

1 0 1

0,

di 

x x

U

Max ⁿ _i

x

x _i 

I di x p

x0 



1ⁿ _{i i} 

s.t

(2)

(3)

Lagrange function:

] [

)

( ₀

1 1

0 1 x di I p x di x

x

L   ⁿ _i^{ }  ^  ⁿ _{i i} 

: Lagrange parameter, it denotes the marginal contribution of income to utility.



(4)

15

Budget Constraint:

I (5)

di x p

x0 



1ⁿ _{i i} 

0 1

0





 

 

x L

 1



16

0 )

1 ( ^{1 1} ₁

1   

 

 ^ _

^{n i i i}

i

p x

di x x

L  

 ^{  }

i i

n

i di x p

x^{  }  

 (



1 )^{11 1}

i i

n

i di x p

x ^{ } 



 

 ^



1 )¹ ¹

(

i i

n

i di x p

x^{   }  

 [(1 ) ¹ ]^{1 1} (6)

i i

n

i di x p

x 

 [(1 ^ )^1 ]^{1 1} (7)

17

V p p

x

i i

i

1 1 1

1

1 ^{ }

 



 ^



p V p

i i

1 1

1

1 ^

 





i i

p x 1 1

 



(10) V

p

x_{i i} ¹

1

)

( ^

 ^

Therefore, we have:

Where: ^{ }

1

1 )

( x di V ^ ⁿ _i

i pi

x

V)^{1 1} 

( ^{ }

In turn:

(8)

(9)

18

i i i i

i i i

i

x p p x p

p x

x



 

 





 

i i i i

x p p x 1 1

 

 

) , 1 (

where 1 ,

1  

  



(11)

the higher , the larger , it implies the close substitution among commodities, that is , the difference between a pair of commodities

become smaller.

 ^

19

 If we assume there are symmetric across the commodities , that is, the consumers buy each commodity with the same amount, then the utility function can be simplified as:

xi



 1

1 )

( x di V ^



ⁿ _i



 1

)

 (nx

x n^

1

 V_e V 1 lnn lnx

ln  



 

x n Ve e e

V ^

1

 ln



(12)

(13)

20

n ln ) (

V e

V e_{Ve l lnn x}







 

 

 



2

1 1









1 ¹ 0

2   



 n^ x lnn



(i)

(14)

1 0

1 ^{1 1}   ¹  

 

 ^{ }

x n

x n n

V _{ }^





(ii) (15)

 Given , the smaller implies consumers prefer to consume

commodities more diversity, and thus the smaller among commodities, the higher utility level for the consumers enjoying.

 Given the large number of , the higher the utility level can achieved.

n



 n 

21

Firm’s Profit function:

F cx

x p

x_i)  _{i i}  _i 

 (

) (

max _i

x

x

i



x c x p x p

x

i i i i

i

i 



 

 

 ( )

c p

x x p

i i i

i 



 

 1

c p

x x p

i i i

i 







1 1

1



0 )

1

(   



 p_i  p_i c c

p_i 



c p_i



*  1

(16)

(17)

22

S.O.C

2 2 2

2

i i i

i i i

i

i x

x p x

p x

p

x 

 



 



 



 

2 2

2

i i i

i i

x x p

x p



 



 

2

1 2

2

i i i

i

i x

x p

p

x 

 



 

2 2

1 1 2 1

i i

i

i x

x p

p

x 

 







] 1[

) 1 2(

i i i

i i

i i

i

x p x

p x x

x p



 

 

 

  

23

) 2 (

) 1 ) (

1

2(    

   

i i i

i

x p x

p

] 2 2

[ ) 1

(   

  

i i

x p

, 0 )

1

(  



i i

x

 p



] ) 1 (

)[

1 ) (

1 2(

i i i

i i

i

x p x

p x

p     

    

(18)

i i i

i

x p x

p  ( 1)



 

i i i

i i i

i

x p x

x p x

p



 







 

 1

) 1 (

) 1

( ₂

2 2





where

(19)

(20)

24

p_i  i

max  0



 



 

 



i i i

i i i

i i

p c x p

p x p x



0 ) )(

( 



 





i i

i p

c x p x

) )(

(

i i

i p

c x p

x 

 





1 ) )( 1

(

i i

p c x

p  

 

i i

p c x

p )

1 )( 1

(   

 ₍₂₁₎

25

i i

p c p 

  ) 1

( 1

1 

i i

p c p 



 ) 1

( 

c p

p_i  _i 

 ) 1

( 

pi

c [1 (1 )]

pi

c  

c p_i



*  1 ⁽²²⁾

26

F x c p

x)  (  ) 

 (

F x c

c  

 1 )

(

F cx 

 



 1

 From the firm’s profit function, we know that the smaller , then the lower

substitution among commodities, and the difference between each pair of commodities is larger, thus the firm can get the higher profit.

Under the assumption of free entry, then the profit would be zero for the last entrant, thus,



(23)

27

1 0 )

(x   cx  F 



 

F cx 

 ) (1





c F

x 



  1

* 1

c F





 

1 ⁽²⁴⁾

28

1 0 1

* 

 





c F

x





0 (26)

1 ² 

 

 



c F c

x^*





(25)

c F x

2

*

) 1

(

) 1 ( )

1 (







 _





 





) 0 1

( 1

2 

 

c F

 ⁽²⁷⁾

29

c

p 

*  1

1 0

2

*   



p c

 

(28)

(29)

(i) the quantity produced by each firm is increasing in and F, but decreasing in c,

(ii) the price charged by each firm is decreasing in .

 

30

Under the symmetric assumption:

, for all Then

(30)

x

x_i  p_i  p ⁱ

I npx

x₀   x0

I npx  

c

p 

*  1

c x F





  1

* (31)

31

x0

I npx  



1 I x0

c F

n c   

 

 





) )(

1 1 (

* 0

x F I

n    

0

* 



 F n

0

* 



 I n

0

* 





 n

(32)

(33)

(34)

(35)

32

• Use this partial equilibrium version.

max V = ( di)

=

• = ( / , and ,

and .

4.The Modify Model

x(.)

x

0

I 

33

• First-order condition:

= ( .

4. The Modify Model (con’t)

34

4. The Modify Model (con’t)

• Think of V as real GDP.

• Use P = ( di) ^/ to define P.

• Get P = ( di) ^/

• Note that this price index is not a weighted average of prices.

35

• Suppose = p for some p that is independent of n. We see that P strictly decreases in n.

P = p

So, when there are more varieties, the whole

composite commodity becomes “cheaper” even when the price of each good remains the same (love for

variety).

4. The Modify Model (con’t)

36

• Now, turn to the producers’ side.

• Infinite pool of entrants.

• To enter, pay a fixed cost F. Constant marginal cost c.

• For each variety i, Bertrand competition. Let n(i) be the number of entrants.

• When n(i) ≥ 2, all firms lose money. So, n(i) = 1 in equilibrium.

4.1. Entry

37

4.1 Entry (con’t)

• p = c, and hence = c .

= (p c) F

=

F

38

4.2. Zero-profit condition

• Free entry

= F

•

^∗

= F . The larger the elasticity of

substitution, the smaller the markup, the

less attractive an entry is.

39

4.3 Social planner's problem

• Imagine the following social planner’s problem to find optimal variety

max V = ( di)

F =

n

40

4.3 Social planner's problem (con’t)

• That is, the total resource in the society is I - , and unit cost of production is c. Then, symmetry and the convexity of the preference implies that

= ,

Therefore,

max V =

41

4.3 Social planner's problem (con’t)

• Know that n . Note that the objective

increases in n when n and decreases when n > .

• So, = . Optimal number of variety equals equilibrium one!!!

42

4.3 Social planner's problem (con’t)

• Hence, the smaller the elasticity of substitution (the more the preference is convex), the more the optimal variety. So, σ is often called a love for variety parameter.

• The optimal x = . This is again the equilibrium quantity.

43

5. Krugman 1980, AER

44

• To set up, need β units of labor, and to produce a unit, need α units of labor.

• To produce x units for a product i, the production cost is α + β.

45

5.1 Autarky

• First consider autarky equilibrium. The two countries have L, ^∗.

• Now, F = β and c = α , I - = L.

• Equilibrium number of variety, however, is easy:

∗= = .

46

5.1 Autarky (con’t)

• Equilibrium price is then p = = α and the

quantity x consistent with zero-profit condition:

= F = F = β = 0,

entailing x = .

47

5.1 Autarky (con’t)

• Equilibrium quantity x depends on the price ( ) as well as P, V. Given resources L, n is pinned by zero-profit condition and hereforce P,V and

therefore x. (note that does not matter, can set it to be 1 for the autarky general equilibrium, but

later there will be differences in , ^∗....so still keep it.)

• Put a on every endogenous variables for the foreign country.

48

5.2 Open to trade

q(.)

• Without loss of generality let j [0, n] be the

goods produced at home and j [n, n + ^∗] be the goods produced at the foreign country. In fact, can have a world representative consumer.

max ( ^{∗ /} dj)

∗ = L + ^{∗ ∗}

49

5.2 Open to trade (con’t)

• No iceberg cost → one price index P.

• From this, we get demand function facing each

firm: .

• Two different labor markets.

50

5.2 Open to trade (con’t)

• If

^∗

, then

∗

= (

^{∗ ∗}

)

^∗

= ( )

^{∗ ∗}

,

( ) =

51

5.2 Open to trade (con’t)

• So, if ^∗, ^∗under ^∗ is such that firm earn zero profit in the foreign country, then firms in the

home country earn positive profit. This is going to draw more entry to the home country, and the

competition for the home labor will push up the home wage until = ^∗.

52

5.2 Open to trade (con’t)

• Now that = ^∗, p = ^∗, x = ^∗ = .

• In each country, we have the accounting identity L = npx, ^{∗ ∗} = ^{∗ ∗ ∗}

• So, L/ ^∗ = n/ ^∗ .

• In fact, n = , ^∗ = ^∗ , which are the same as the autarky entries.

53

5.3 Gains from trade

• Gains from trade is easy to calculate before trade: =

after trade: _∗ = _∗^∗ = ^∗

• The number of variety produced in each country does not change. Neither do price, quantity, wages.

But, due to the more varieties available, there are gains from trade.

54

• Introduce trade cost. This creates a difference, from firms’ point of view, home market and foreign market.

• Like DFS, when shipping 1 unit, only x < 1 units arrives.

• To connect with some models latter, let τ = 1/x. So, in order to sell 1 unit at another country, needs to ship τ units

.

5.4 Trade Cost and Home Market

55

• Let price p(j) the one j′s producer charges the local consumers.

• Price index for home country consumers:

P = ( dj+ τ ) ^/

• ^∗= ( τ dj) ^/

.

5.4 Trade Cost and Home Market (con’t)

56

• Wages are not going to be the same.

p = ,

^∗

=

^∗

.

home: = ^{∗ ∗} ,

foreign: ^∗ = ^{∗ ∗} .

• If τ = 1, then P = ^∗.

• Let the “source” be i and “destination” be n. τ = 1 if n = i, and τ = τ if n = i.

5.4 Trade Cost and Home Market (con’t)

57

• Let total sales (hence total income) in home country be X.

^∗

for the foreign.

• The total expenditure for a commodity j

home: τ ,

foreign:

_∗ ^∗

τ

5.4 Trade Cost and Home Market (con’t)

58

• Let η be the ratio of the foreign demand of any particular home good to the home

demand of that good. η

^∗

similarly defined.

Let the home consumers’ demand for home good be x and the foreign consumers’

demand for a foreign good be

^∗

.

5.4 Trade Cost and Home Market (con’t)

59

• The zero-profit conditions are

home firm:

= (p c)x + τ (p c) ηx = 0 foreign firm:

∗ ∗ = ( ^{∗ ∗}) ^∗ + τ ( ^{∗ ∗}) η^{∗ ∗} = 0

• Then, pricing rule still the same, and x(1+ τη) = ^∗(1+τη^∗) = .

• So, n = and ^{∗ ∗} .

5.4 Trade Cost and Home Market (con’t)

60

• Use balanced trade condition and the

definition of price index, you can verify that if defining =ω/

^∗, get

∗ = τ

τ .

• Show that ω is a strictly increasing function on

τ τ .

• Thus, the larger the ^∗, the larger the equilibrium ω, and when ^∗ =1, =1.

5.4 Trade Cost and Home Market (con’t)

61

• Things are not proportional any more. The labor in the larger country are rewarded more (because the goods they produced are desired more).

• In DFS, with or without transportation cost, the more the labor force, the lower the wag

e.

5.4 Trade Cost and Home Market (con’t)

62

•

Krugman (1991): Almost the same model, but add an agricultural sector and labor mobility across the

“countries” or two “regions”