Intra industry trade, Krugman simplified model

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Intra industry trade, Krugman simplified

model

Jan J. Michalek

Introduction

Measuring intra-industry trade Dixit-Stiglitz demand

Demand effects; income, price elasticity , and price index Increasing returns to scale

Optimal pricing and zero profits Simple Krugman model

Explaining intra-industry trade Conclusions

INTRA - INDUSTRY TRADE

International Trade & the World Economy;  Charles van Marrewijk

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Measuring intra-industry trade (= two-way trade in similar goods)

i i

i Ex

GL Ex

Im 1 Im



  Use the Grubel-Lloyd (GL) index 

to measure intra-industry trade:

Table 10.1 International trade between The Philippines (RP) and Japan; 1998*

SITC Exports

from RP

Imports into RP

GL index

8 Miscellaneous manufactured articles 383,167 576,412 0.80

81 Prefabricated buildings 4,147 2,186 0.69

82 Furniture and parts thereof 42,332 6,155 0.25

83 Travel goods, handbags and similar containers 4,804 67 0.03 84 Articles of apparel and clothing accessories 115,627 3,255 0.05

85 Footwear 13,283 920 0.13

87 Prof. scientific & controlling instruments 24,091 175,018 0.24

88 Photographic apparatus 72,174 123,333 0.74

89 Miscellaneous manufactured articles 106,709 265,477 0.57

Grubel-Lloyd indices of intra-

industry trade, 2006

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Increasing importance of intra-industry trade

Intra-industry trade (2-digits)

0 1

1961 1966 1971 1976 1981 1986 1991 1996

Japan

USA Germany

Measuring intra-industry trade

Table 10.2 Intra-industry trade, GL-index manufacturing sector 1995 (3-digit level, %) Country World OECD 22 NAFTA East Asia Dev. Latin America

Australia 36.6 17.5 16.0 39.2 41.6

Bangladesh 10.0 3.5 1.7 3.4 8.0

Chile 25.7 10.1 11.5 3.6 47.8

France 83.5 86.7 62.7 38.7 22.9

Germany 75.3 80.1 61.2 36.2 22.8

Japan 42.3 47.6 45.7 36.1 7.0

Malaysia 60.4 48.5 57.9 75.0 10.4

Hong Kong 28.4 20.2 25.2 19.9 13.6

UK 85.4 84.0 72.5 46.6 38.6

USA 71.7 74.0 73.5 41.4 66.0

Source: NAPES website, http://napes.anu.edu.au/

Variations in extent of intra-industry trade

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Early explantions: Overlapping- demand hypothesis

Staffan Linder (1961)

I US max I GB max I US

min I GB min

Income p. capita Quality

Intra-industry trade

Q GB min Q GB max Q US min Q US max

 JJ Michalek

Product cycle theory Raymond Vernon, 1966

IV V II III

I

Quantity

time Domestic

consumption

Exports

Domestic production

 JJ Michalek

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Introduction

Optimal pricing and zero profits Krugman model

Explaining intra-industry trade Conclusions

Dixit-Stiglitz demand

If there are N (= ‘large’) different varieties of manufactures

And the utility function is:

; 0 1

/ 1

1



 

 



  





 N 

i

c

i

U

Then, subject to the budget constraint;

the demand for a variety, say j, is:

(discussed below)

I c p

N

i i i





1

 

1 ) 1 /(

1 ,

/

,

1 ,









 ^ ^





P I U

index price P

where I

P p c_j _j

  _

 







 









 



 



 







resourceson claim l

N i

Nc N

c N Nc

c

U    

varietyove of 1 ) / 1 ( /

/ 1 1 /

1



 



Characteristic is the love-of-variety effect, e.g. if c_i = c for all i:

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Increasing returns to scale: linear cost function

q c F TC  

TC: total cost of production F: fixed cost

c: marginal cost (cost of production of additional unit) AC: average cost

 c

q F q

ACTC   q  AC

AC AC1

q1 q2

AC2

c AC

0 Q

Optimal pricing and zero profits

• As a result of IRS each variety is produced by single producer.

• This producer has market power and charges a monopolistically competitive price (determines the optimal price by MR = MC, taking the prices charged by the other firms [the price index P] as given).

• Because the price elasticity of demand is constant (equal to the parameter ) the mark-up over marginal costs charged by the producer is also constant.

• Firms will enter the market (producing new varieties) if profits are positive; they will exit if profits are negative.

• The number of varieties N produced is therefore determined by the zero-profit condition.

• In the Dixit-Stiglitz model the number of varieties N produced is proportional to the size of the economy as measured by the labor force

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Introduction

Optimal pricing and zero profits

Simple Krugman model (chapter 6) of the textbook Explaining intra-industry trade

An alternative interpretation: intermediate goods Conclusions

Krugman’s simplified model of intra-industry trade (1)

Assumptions:

 Linear demand function;

 „Love for variety” (Dixit-Stiglitz) utility function (one product (e.g.

car) produced in many varieties)

 we analyze 1 products in many varieties (one producer produces only one variety)

 Increasing returns to scale (IRS)

 Symmetric firms (same cost functions)

 Chamberlin competition (perfect monopolistic competition)

 JJ Michalek

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Krugman’s simplified model of intra-industry trade (2)

Linear demand function for the product:

P B A

q   (1)

 MRPqB (mathematical proof is in the annex to chap.6) qB

MR

P  (2)

q c F

TC   Linear cost function (3)

 c

q F q

ACTC   q  AC (i.e. IRS) (4)

Specific form of the linear demand function:

 _^

  

 bP P

S n

q 1

(5)

S: total (constant) sales of the industry, n: number of firms, P : average price of product (car)

 JJ Michalek

Krugman’s simplified model of intra-industry trade (3)

Relationship between number of firms (n) and AC:

Symmetric firms  PP  qSn  S c

F c n Sn c F Fq

AC       (CC curve) (6)

i.e. ⁿ^ ^ ^AC^ (more firms  higher AC)

Relationship between number of firms (n) and market prices:

Now: q is f P

(5) qSnSbP SbPABP (from equation 1) (7)

(2)  MRPqSb (8)

Market equilibrium: MR=MC=c  b c

qS P

MR     we can derive price equation:

b qS c

P   (9)

If firms are symmetric  practice the same average price  ^{q }^Sⁿ 

(9)    _

 

c S n S b P

n c b P 1 

(PP curve) (10)

 JJ Michalek

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Krugman’s simplified model of intra-industry trade (4)

 equilibrium in autarky: intersection of CC and PP curves

A

0 PA

nA

C

C P

P A C , P

n

Introducing trade: single market  the size of the common market grows 

 JJ Michalek

Krugman’s simplified model of intra-industry trade (5)

Introducing trade: single market  the size of the common market grows 

 S

 The curve CC shifts down:

S c F

ACn  because S^ ^ AC^

equilibrium under free trade : intersection of C’C’ and PP curves

B A

C ’

C ’ 0 PA

PT

nA nT

C

C P

P A C , P

n

 JJ Michalek

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Krugman: example of equilibrium in autarky

P. Krugman: chap. 6, car market

c=F+(c*q) F= 750000000

AC=F/q+c c= 5000

P=c+(1/1(b*n)) b=1/30000

Domestic market, S= 900 000

n q=S/n AC P

1 900 000 5 833 35 000

2 450 000 6 667 20 000

3 300 000 7 500 15 000

4 225 000 8 333 12 500

5 180 000 9 167 11 000

6 150 000 10 000 10 000

7 128 571 10 833 9 286

8 112 500 11 667 8 750

9 100 000 12 500 8 333

10 90 000 13 333 8 000

11 81 818 14 167 7 727

12 75 000 15 000 7 500

13 69 231 15 833 7 308

14 64 286 16 667 7 143

15 60 000 17 500 7 000

 JJ Michalek

Krugman: example of equilibrium in autarky

Domestic market equilibrium

0 10000 20000 30000 40000

0 5 10 15 20

number of firms

costs, prices

costs prices

 JJ Michalek

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Krugman: example of

equilibrium under free trade

 JJ Michalek

Domestic market, S= 900 000 Foreign market, S= 1 600 000 Intgrated market, S= 2 500 000

n q=S/n AC P n q=S/n AC P n q=S/n AC P

1 900 000 5 833 35 000 1 1 600 000 5 469 35 000 1 2 500 000 5 300 35 000

2 450 000 6 667 20 000 2 800 000 5 938 20 000 2 1 250 000 5 600 20 000

3 300 000 7 500 15 000 3 533 333 6 406 15 000 3 833 333 5 900 15 000

4 225 000 8 333 12 500 4 400 000 6 875 12 500 4 625 000 6 200 12 500

5 180 000 9 167 11 000 5 320 000 7 344 11 000 5 500 000 6 500 11 000

6 150 000 10 000 10 000 6 266 667 7 813 10 000 6 416 667 6 800 10 000

7 128 571 10 833 9 286 7 228 571 8 281 9 286 7 357 143 7 100 9 286

8 112 500 11 667 8 750 8 200 000 8 750 8 750 8 312 500 7 400 8 750

9 100 000 12 500 8 333 9 177 778 9 219 8 333 9 277 778 7 700 8 333

10 90 000 13 333 8 000 10 160 000 9 688 8 000 10 250 000 8 000 8 000

11 81 818 14 167 7 727 11 145 455 10 156 7 727 11 227 273 8 300 7 727

12 75 000 15 000 7 500 12 133 333 10 625 7 500 12 208 333 8 600 7 500

13 69 231 15 833 7 308 13 123 077 11 094 7 308 13 192 308 8 900 7 308

14 64 286 16 667 7 143 14 114 286 11 563 7 143 14 178 571 9 200 7 143

15 60 000 17 500 7 000 15 106 667 12 031 7 000 15 166 667 9 500 7 000

Krugman’s simplified model of intra-industry trade (6)

Benefits from trade (under Krugman’s model):

- lower prices: P _T P_A;

- larger variety if goods: n T nA

-  intra industry trade

- trade possible between similar countries but some firms must disappear (10<6+8) and wy do not know which firms

 JJ Michalek

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Belgium 5 million laborers

10,000 varieties produced, 10,000

consumed

Netherlands 7 million laborers

consumed

Belgium 5 million laborers

consumed

Netherlands 7 million laborers

consumed a. Autarky

b. International trade

10,000 varieties;

7/12 ^th of production

14,000 varieties;

5/12 ^th of production

Explaining intra-industry trade

Conclusions

•

Intra industry trade, Krugman simplified model