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# Model 3.2: Specialisation in Trade According to Comparative Advantage in Production

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INTRODUCTION TO LOCATION

63

Ricardo’s principle of comparative advantage asserts that workers

should specialise in producing products in which their productivity, relative to that for alternative goods, is higher than for other people with

whom they can trade. It is a simple application of the principle of opportunity cost. It implies that products should be produced by individuals who

have the lowest opportunity cost for that product in terms of the amount

of other products that they could have produced instead.

Comparative advantage also has a simple mathematical expression.

Recall that worker 1 can produce either b01 units of product 0 or b11 units

of product 1, and worker 2 can produce either b02 units of product 0 or

b12 units of product 1. Worker 1 has comparative advantage in product 0

if b01/b11 > b02/b12, and comparative advantage in product 2 if the inequality is reversed, b01/b11 < b02/b12. If a worker is comparatively advantaged in

one product then they are comparatively disadvantaged in the other.

Comparative advantage is equivalent to relative opportunity cost.

Suppose that worker 1 produces product 1; then their opportunity cost of

product 1 in terms of product 0 is c1 = b01/b11, as noted earlier. Similarly

worker 2’s opportunity cost of product 1 is c2 = b02/b12. It is cheaper for

worker 1 to produce product 1 if c1 < c2, which implies that b01/b11 < b02/b12,

that is, worker 1 has comparative advantage in product 1. Conversely, it

is cheaper for worker 2 to produce product 1 if c1 > c2, which implies that

b01/b11 > b02/b12, that is, worker 2 has comparative advantage in product 1.

A distinction is often drawn between comparative advantage and absolute advantage. If worker 2 is more productive than worker 1 in product 1

then they may be said to have an absolute advantage in product 1, and if

they are more productive in product 2 they may be said to have an absolute advantage in product 2. If they have an absolute advantage in both it

might be said that worker 1 has an absolute advantage over worker 2. As

noted above, absolute advantage alone is not sufficient to determine who

does what, but it does have implications for how much they earn from

what they do. Absolute advantage is a source of ‘economic rent’; in a competitive labour market it provides advantaged workers with higher wages.

Diagrammatic Analysis

The case where both countries can produce both products is illustrated in

Fig. 4.3. The figure uses supply and demand analysis to portray the global

market for product 1. It illustrates the case where country 1 has comparative advantage in product 0 and country 2 has comparative advantage in

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M. CASSON

Price of product 1

relative to product 0

D1

D2

T

D

S1

C1

Equilibrium

price, p

P

E2

E

E1

S2

C2

D 2´

O

S1´

Q2

Consumption

of product 1

In country 2

D1 ´

Q1

S

Quantity of product 1

Consumption

of product 1

in country 1

Supply of product 1

by country 2, which has

product 1

Fig. 4.3  Supply and demand analysis of trade with no international price

discrimination

product 1. The quantity of product 1 is measured along the horizontal

axis and unit costs and prices for product 1 along the vertical axis.

The unit cost of production in country 2 is measured by the height OC2

and the higher cost of production in country 1 by OC1. The global supply

curve is the line C2S2S1S1′T. The vertical section S2S1 represents the jump in

costs when country 2 becomes fully specialised and additional p

­ roduction

is undertaken in country 1. The vertical section S1′T represents the situation when both countries are fully specialised in product 1 and there is no

remaining capacity to be released from production of product 0.

When no country is completely specialised in producing product 1, the

equilibrium lies on the lower horizontal segment of the supply curve C2S2;

INTRODUCTION TO LOCATION

65

under these conditions country 1 is fully specialised in producing product

0. When country 2 is completely specialised in producing product 1 and

country 2 is completely specialised in producing product 0 (as assumed in

Model 3.1), the equilibrium lies on the vertical segment S2S1. When country 2 is completely specialised and country 1 produces both products then

the equilibrium lies on the right-hand segment S1S1′.

When country 2 is incompletely specialised in product 1 the equilibrium price is OC2, and when country 2 is completely specialised and

country 1 produces product 1 as well the equilibrium price is OC1. When

both countries are specialised—country 1 in product 0 and country 2 in

product 1—it is demand that determines the price. The price lies between

the limits OC2 and OC1, but it is the intersection of the global demand

schedule with the global supply schedule that determines the exact price.

Demand for product 1 in country 1 is indicated by the demand curve

D1D1′, and in country 2 by D2D2′. Global demand is derived by horizontal

aggregation, i.e. by adding the quantities demanded in each market at

any given price. The global demand curve D1DD′ has a kink at D where

demand from country 2 begins to supplement demand from country 1.

The intersection E of global supply and global demand determines the

equilibrium price OP.  Consumption of product 1  in countries 1 and 2

are asset at E1, E2 respectively; consumption is OQ1 in country 1 and

OQ2 = Q1S in country 2.

Model 4. Monopoly

Model 4 synthesises the insights from Model 2 (monopoly) and Model 3

(location and trade) to examine the exploitation of monopoly power in a

two-country world. The focus is on a monopolist that serves both domestic market and an export market. This analysis prepares the way for the

study of international production in Model 5.

Model 4.1. Uniform Price: No Price Discrimination

Between Countries

Consider, as before, two countries, 1 and 2, each with N identical workers.

There is a monopolistic intermediator who controls production and trade

in product 1.

Let c11 be the opportunity cost of production of product 1 in country

1 and c12 its opportunity cost in country 2. In the absence of barriers to

trade, production of product 2 is specialised in whichever country affords

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M. CASSON

the lowest opportunity cost. This strategy is fully aligned with the principle of comparative advantage. It is assumed that demand for product 1

is sufficiently small that it is unnecessary for any country to specialise fully

in its production. It can be assumed without loss of generality that production of product 1 is specialised in country 2 (i.e. the countries can be

labelled in order to make this true).

The monopolist’s profit is the sum of the profits generated in the two

markets. Country 1 is served by exports from country 2. Unit cost of production for both markets is therefore c12. Let p be the global monopoly price.

Demand for product 1 in each country is

x11 = ( a11 – p ) / 2 a21

x12 = ( a12 – p ) / 2 a22

(4.6a)

(4.6b)

whence total demand is

x1 = x11 + x12 = éë a11 a21 + a12 a21 – ( a21 + a22 ) p ùû / 2 a21 a22

(4.7)

Maximising profit per worker

p = ( p – c12 ) x1

(4.8)

with respect to p determines the optimal monopoly price

p = éë( ( a11 a22 + a12 a21 ) / ( a21 + a22 ) ) + c12 ùû / 2

(4.9)

whence consumption of product 1 is

x1 = éë( a11 a22 + a12 a21 ) – c12 ( a21 + a22 ) ùû / 4 a21 a22

(4.10)

whence profit per worker is

p = éë( a11 a22 + a12 a21 ) – c12 ( a21 + a22 ) ùû / 8a21 a22 ( a21 + a22 ) (4.11)

2

INTRODUCTION TO LOCATION

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Table 4.2  Comparative statics for Model 4.1

Parameter

p

x1

π

Consumer surplus country 1

Consumer surplus country 2

a11

a12

a21

a22

c12

+

+

+

+

+

+

+

+

0

0

0

+

0

Comparative Statics

The comparative statics are very simple, as indicated in Table 4.2.

Model 4.2. International Price Discrimination:

Different Prices in Different Countries

The monopolist can only charge different prices in different markets if

there is some obstacle to trade in product 1. This obstacle mans that

while the intermediator can export product 1 from country 2 to country 1, independent arbitragers cannot ship the product in either direction

between the two countries. This issue is re-visited when local marketing is

formally introduced in Model 5. Note that prices remain uniform within

each country; two-part tariffs are not involved.

Let p1 be the monopoly price in country 1 and p2 the price in country 2.

Demand for product 1 in each country is

x11 = ( a11 – p1 ) / 2 a21

x12 = ( a21 – p2 ) / 2 a22

(4.12a)

(4.12b)

Profit per worker is

p = ( p1 – c12 ) x1 + ( p2 – c12 ) x2

(4.13)

Maximising (4.13) with respect to p1, p2 determines the optimal prices

p1 = ( a11 + c12 ) / 2 a21

(4.14a)

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M. CASSON

p2 = ( a12 + c12 ) / 2 a22

(4.14b)

whence consumption of product 1 in each country is

x11 = ( a11 – c12 ) / 4 a21

x12 = ( a12 – c12 ) / 4 a22

(4.15a)

(4.15b)

and so profit per worker is

(

) (

p = ( a11 – c12 ) / 4 a21 + ( a12 – c12 ) / 4 a22

2

2

)

(4.16)

Comparative Statics

Once again, the comparative statics are straightforward, as indicated in

Table 4.3.

Diagrammatic Representation

Equilibrium with price discrimination is illustrated in Fig. 4.4. The focus is

on the market for product 1; for simplicity, the quantities of product 0 that

are produced and consumed are now suppressed. The quantity of product

1 consumed in country 1 is measured from the left-hand origin O1 and the

quantity consumed in country 2 from the right-hand origin O2. Demands

are represented by the demand curves D1D1′ and D2D2′ respectively. Country

1 is served by exports from country 2, which specialises in the production

Table 4.3  Comparative statics for Model 4.2

Parameter p1 p2 x11 x12 π

a11

a12

a21

a22

c12

+

0

0

+

0

+

0

+

+

0

0

+

0

+

+

Consumer surplus country 1

Consumer surplus country 2

+

0

0

0

+

0

INTRODUCTION TO LOCATION

D1

Consumers’ surplus accruing to workers from

intra-marginal consumption of product 1

Price/unit cost

of product 1

H1

P1

Profit appropriated by intermediator

consumption of product 1

E1

Unit cost of

product 1 in

country2, c2

D2

H2

P2

E2

S

R1

O1

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D2´

D1´

F1

R2

F2

(a12— c12)/4a22

(a11— c12)/4a21

Total cost of production

of product 1

O2

Consumption of product 1

Fig. 4.4  Monopoly equilibrium with international price discrimination

of product 1. In the absence of transport costs, the unit opportunity cost of

production is the same in both countries. This is represented by the supply

curve SS′. The marginal revenue schedules are D1R1 and D2R2 respectively.

They intersect SS′ at E1 and E2 respectively. This determines consumptions

OF1, O2F2, and prices OP1, O2P2 respectively. Profit per worker generated in

country 1 is measured by the area of the rectangle SE1H1P1 and profit per

worker in country 2 by the area S´E2H2P2. Total profit is the sum of these

areas. Consumers’ surplus generated in country 1 is measured by the area of

the triangle D1H1P1 and in country 2 by D2H2P2.

Total production of product 1 is measured along the horizontal axis

by the length O1F1 + O2F2. The total opportunity cost of production, in

terms of product 0 foregone, is measured by the area O1F1E1S + O2F2E2S´.

The value of exports from country 2 to country 1 is measured by the area

O1F1H1P1. The value of imports of product 1 into country 2 depends on

where the intermediator is located. If the intermediator is located in country 2 (where production takes place) then profits are remitted to country

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M. CASSON

2. In this case the amount of product exported to country 2 is equal to

the value of product 1 exported to country 1, namely O1F1H1P1. This has

two components. One is compensation for the reduction in production

of good 1 in country 2 on account of the diversion of resources to export

production in product 1, and the other is product 0 to be consumed by

the intermediator out of their profit. If, on the other hand, the intermediator is located in country 2, then that part of the payment for exports

accounted for by profit is remitted back from country 2 to country 1. The

net export of product 1 from country 1 is therefore only O1F1E1S, which is

equivalent to the wage bill for the exports and not their total price.

Discussion

Profits will be higher under price discrimination than under uniform pricing. Uniformity is a constraint on pricing policy; if uniform prices maximised profit unconditionally then uniformity would be selected as the

optimal policy when discrimination was possible. The uniform price lies

between the limits set by the discriminatory prices. As a result, consumer

surplus is lower in the high-price market, and higher in the low-price market, than under uniform pricing.

Consumer’s surplus is equal to one half of the profit under both systems

of pricing. Since profit is higher under discrimination, consumer surplus

is higher too. Thus consumers gain on average; the loss of surplus in the

high-price market is less than the gain of surplus in the low-price market.

If country 1 is a developed country and country 2 a developing country

then profits will accrue to the developed country and potentially widen

international economic inequality. Price discrimination may, however,

benefit the developing country, even though it increases profits. If demand

for product 1 is stronger in the developed country than the developing

country then the monopolist will discriminate against consumers in their

home country. So far as the developing country is concerned, therefore,

international price discrimination may be the lesser of two evils.

Bibliography

On welfare analysis applied to IB see

Casson, M. (2007). Multinational enterprises: Their private and social benefits and

costs. World Economy, 30(2), 308–328.

MacDougall, G. D. A. (1960). The benefits and costs of private investment from

abroad: A theoretical approach. Economic Record, 36, 13–35.

Chapter 5

Division of Labour and Modularisation

Abstract  The division of labour is a central concept in international business (IB), although it is sometimes known by other names. Its significance

was first noted by the eighteenth-century-economist Adam Smith. He

defined it as the sub-division of a complex task into a set of simpler tasks

that can be performed by unskilled labour or machines. In IB different

tasks are often carried out at different locations. Marketing and research

and development can be separated from production, and upstream and

downstream production can be separated too. Separate activities can be

carried out in different countries. This chapter examines the gains from

the international division of labour and shows how the optimal division of

labour in any sector or industry can be analysed in economic terms.

Keywords  Division of labour • Modularisation • Transport cost

• Product development • Technology transfer

Introduction

The division of labour is one of the oldest concepts in economics. In the

Wealth of Nations, Adam Smith argued that the division of labour encourages the employment of specialised workers and the mechanisation of certain jobs, and thereby increases productivity. He described the division

© The Editor(s) (if applicable) and the Author(s) 2016

M. Casson, The Theory of International Business,

DOI 10.1007/978-3-319-32297-1_5

71

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M. Casson

of labour in terms of the modularisation of production. Modularisation

replaces a single complex task requiring a scarce combination of skills

with a set of simpler tasks requiring skills that are much easier to acquire.

Simple tasks can be performed more quickly; they are therefore repeated

more often and so are easier to learn. They can also become monotonous,

however; workers are sometimes rotated between tasks to help them maintain concentration.

The division of labour can also be defined in terms of occupational

specialisation. Modularisation and specialisation are distinct but related.

Modularisation provides opportunities for specialisation, but specialisation can also occur through product differentiation. Medical services, for

example, have become highly differentiated; for example, surgeons specialise in different organs of the body. Hospital operations are also modularised; they involve not only surgery but also anaesthetic, recovery and

aftercare. Product differentiation generates ‘horizontal’ specialisation,

whilst modularisation generates ‘vertical’ specialisation.

The following chapters are concerned with the vertical specialisation

within a modular supply chain. The process of supply is resolved into the

following activities:

.Production, as described above

1

2. Marketing and distribution

3.Transport—especially international transport of wholesale product

from production to distribution.

4. Development, including product design and research and development

(R&D)

5. Knowledge transfer—especially international technology transfer

6.Headquarters operation, where coordination activities are

concentrated.

Modularisation is applied only to product 1. Product 0 is still present

in the models, but its role is to act as a unit of account—not a nominal

unit of account like money but a real unit of account instead. From now

on subscripts identify modular activities and their locations, but not the

product involved.

It was noted in Chap. 1 that neoclassical economists used to treat the

firm as a black box. Production was analysed as a single activity that simply

supplied a product to a market. We are now opening up the black box

to take a look inside. What we find is a web of linkages between distinct

activities. These activities now become the subject of investigation.

Division of Labour and Modularisation

73

There is a problem, however. Each of these activities, in turn, is composed

of component activities, for example, marketing comprises advertising, storage, shop display, delivery and so on. However, this finer-grained division of

labour lies outside the scope of this book. Whenever we open up a black box

we find a set of other black boxes, and so the process goes on. We have to

stop somewhere, and this is the place at which we stop in this book.

Model 5: Marketing

and Distribution

Model 5.1. Marketing with No International Transport Costs

The focus is on local marketing services in the country where the product is consumed. Marketing requires labour and therefore incurs costs.

Product is exported from a factory to a wholesaler, or possibly direct to

a retailer. It is therefore necessary to distinguish between the wholesale

price at which goods leave the factory and the retail price at which they

are supplied to the customer. Retail product is not tradeable. It is assumed

to begin with that there are no international transport costs. Domestic

transport costs (where applicable) are included within the overall cost of

local distribution.

Local marketing is identified as activity 2. Let b21, b22 be labour productivity in marketing in countries 1 and 2 respectively. The output of

marketing services at each location is measured by the amount of product

distributed and consumed.

Let c2l represent the opportunity cost of marketing and distribution in

country l (l = 1, 2); then

c21 = b01 / b21 ; c22 = b02 / b22

(5.1)

It is assumed, as in Model 4, that all production takes place in country 2.

Let x1 be consumption in country 1 and x2 consumption in country 2.

With international price discrimination, profit per worker is

p = ( p1 – c12 – c21 ) x1 + ( p1 – c12 – c22 ) x2

(5.2)

Demand schedules are the same as before (Eqs. 4.12a, 4.12b). Maximising

(5.2) with respect to p1, p2 determines the monopoly prices