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Model 3.1: The Determination of Price in a Global Market When Countries Are Fully Specialised

Model 3.1: The Determination of Price in a Global Market When Countries Are Fully Specialised

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INTRODUCTION TO LOCATION 



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It is assumed to begin with that workers in country 1 can only produce

product 0 and that workers in country 2 can only produce product 1. In

effect, productivity in product 1 in country 1, and productivity in product

0 in country 2, are both zero. The assumption is therefore that b11 = b02 = 0.

This extreme assumption is relaxed in subsequent models.

The model is designed to explain the pattern of imports and exports

in each country. It is assumed to begin with that each product is perfectly

tradeable. There are no transport costs or tariffs. Global market equilibrium balances the total supply of each good with its total demand. Imports

and exports interact with local demands and supplies to maintain equilibrium in local markets.

Each worker sells their own production directly to customers. The customers are other workers, either at home or abroad. Because there are

many workers in each country, there are potentially many buyers and sellers for each product. The market is therefore competitive. Because both

products are homogenous, and buyers and sellers are well informed, all

units of the same product will sell for the same price. Nevertheless, the

process of negotiation between all these people is difficult to model in

detail. To simplify the analysis it is therefore usual to assume that the market is intermediated by a Walrasian auctioneer, named after the French

economist Walras, mentioned in Table 1.2.

The Walrasian auctioneer is a fictional personification of the process

of adjustment to equilibrium in a competitive market where there are no

transaction costs. The auctioneer announces a price, p, which individual

workers in both countries take as given (non-negotiable). If the price is too

high (supply exceeds demand), it is reduced, and if it is too low (demand

exceeds supply), it is increased, and this process continues until the equilibrium price is reached. Unlike the intermediator described in Chap. 2,

the auctioneer incurs no costs and sets no margin between buying price

and selling price and therefore makes no profit. As a consequence he does

not consume either. Monopolistic intermediation of trade, along the lines

discussed in Model 2, is considered later in Model 4.

Solution

Supplies

Let n1, n2 be the total hours of work in the respective countries. The supply per worker of product 0 in country 1 is b01n1 and the supply of product

1 in country 2 is b12n2.



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Budget Constraints

Let xhl represent consumption of product h (h = 0, 1) by an individual

worker in country l (l = 1, 2). The real budget constraints for workers in

country 1 and country 2 are respectively







x01 + px11 = b01 n1



x02 + px12 = pb12 n2



(4.1a)

(4.1b)



Equations (4.1a, 4.1b) require that in each country the sum of expenditure on product 0 and expenditure on product 1 is equal to the income

from production of the local product. The equations are not perfectly

symmetric because workers in country 1 earn income from product 0 and

those in country 2 from product 1, so that a change in price re-distributes

income between countries.

Market Equilibrium Conditions for the Global Economy

Equilibrium in the markets for products 1 and 2 requires that







x01 + x02 = b01 z1

x11 + x12 = b12 z2



(4.2a)

(4.2b)



Equations (4.2a, 4.2b) require that in each country, domestic consumption plus exports equal the supply of the local product.

These four conditions are not independent of each other. Any three

of them imply the fourth. This means, in particular, that if the market for

product 1 is in equilibrium then the market for product 0 is in equilibrium, and conversely. This is an example of Say’s Law, which too applies to

any market system where all traders exactly satisfy their budget constraints.

Demand for Product 1 in Each Country

Let the utility of a representative worker in each country be u1, u2 respectively. Consider the market for product 1. Maximising utility in country 1,

u1, subject to the real budget constraint (4.1a) shows that



INTRODUCTION TO LOCATION 







x11 = ( a11 – p ) / 2 a21 )



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(4.3a)







Similarly, maximising utility in country 2, u2, subject to (4.1b) gives





x12 = ( a12 – p ) / 2 a22 )



(4.3b)







where the preference parameters a11, a21 relate to country 1 and a12, a22

to country 2.

Equilibrium in Market 1

Substituting Eq. (4.3a, 4.3b) into the equilibrium condition (4.2b) and

solving gives the equilibrium price





p = ( ( a11 a22 + a12 a21 ) – 2b12 a12 a22 z2 ) / ( a21 + a22 )







(4.4)



whence by back substitution into Eq. (4.3a, 4.3b):











x11 = ( a11 – p ) / 2 a21

x12 = ( a12 – p ) / 2 a22

x01 = b01 z1 – px11

x02 = p ( b12 z2 – x12 )











(4.5a)

(4.5b)

(4.5c)

(4.5d)



Thus, country 2 exports x12 units per worker of product 1 in exchange for

x02 units per worker of product 0 imported from country 1.

Comparative Statics

The comparative statics of even a simple trade model are quite complicated. This is because price changes not only alter opportunity costs but

influence incomes too. For this reason only the comparative statics of price

are examined. They are reported in Table 4.1. Increasing the intensity of

demand for product 1 in either country raises its price, whilst increasing



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Table 4.1  Comparative statics of price for Model 3.1

Exogenous variables



Endogenous price, p



a11

a21

a12

a22

b12

n1

n2



+

+

±

±



0





Comment



Positive if a12 < a22; negative if a12 > a22

Positive if a12 > a22; negative if a12 < a22



productivity in product 1, and the endowment of resources required to

produce it, both reduce price. However, changes in the rate of satiation

have ambiguous effects. The supply of product 0 is irrelevant so long as

the workers in country 1 who produce it can afford to purchase their

required amount of product 1.

Diagrammatic Analysis

As in Model 1, the equilibrium of the system can be illustrated using

both indifference curves and demand curves. As in Model 1, the demand

approach is most useful for analysing IB issues. However, the indifference

curve approach is illustrated first because it has played an important role in

the development of economic thinking and has been influential in popularising the notion of gains from trade.

Figure 4.1 illustrates the model using an ‘Edgeworth box’. It involves

two representative workers, one from each country. This ingenious diagram shows very clearly how trade can make people better off. The height

OA of the box OABC represents the production of product 0 by individual 1 and its width OC measures the production of product 1 by individual

2. The box is drawn tall and thin to ensure that worker 2’s production of

product 1 does not satiate their own demand for the product; no such

concern applies to product 0.

Worker 1’s consumptions are measured from the origin O and worker

2’s from the opposite corner B. The point B may be regarded as a mirror

image of O, obtained by flipping the axes across a diagonal line connecting A to C. Each point in the diagram therefore represents four different

quantities, which are measured off along the two axes emanating from

each of the two origins.



INTRODUCTION TO LOCATION 



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U13

U12



Consumption of

product 1

by individual 2

A



B



H



Individual 2



U11



F



U21

U22



K



L



E



Consumption

of product 0

by individual

2



G



U23



U21´



Consumption

of product 0

by individual

1



U13´



U12´



P



U11´



U22´



J

Individual 1



O



C

Consumption

of product 1

by individual

1



U23´



Fig. 4.1  The Edgeworth Box: international consumption patterns under complete specialisation of production



The no-trade situation is at the corner A. At A each worker consumes

what they produce; worker 1 consumes the total output of product 0 and

worker 2 the total output of product 1. The indifference curves associated

with the no-trade state are U11U11′ for worker 1 and U21U21′ for worker 2.



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Using the Edgeworth box it is possible to derive a ‘contract curve’

along which workers trade in an efficient manner. On the contract curve

no worker can become better off (attain higher utility) without the other

worker becoming worse off (accepting lower utility). The contract curve

equalises the marginal rates of substitution in consumption for the two

workers. This means that they both consume at a point where the slopes

of their indifference curves are equal. The points along the contract curve

correspond to points of tangency between worker 1’s indifference curves,

drawn with respect to the origin O, and workers 2’s indifference curves,

drawn with respect to the origin B.

To simplify the figure it is assumed that both workers have identical

preferences. Each is concerned solely with their own consumption, but as

consumers they value both products in the same way. The specific form of

the utility function (2.1) means that the contract curve is a straight line,

indicated by the thick vertical line FG. The length of the line represents

the scope for gains from trade. At F all gains are appropriated by worker

1; they attain the indifference curve U13U13′, whilst worker 2 remains

stuck on the curve U21U21′, with which they began. Conversely, at G all

gains are appropriated by worker 2; they attain the indifference curve

U23U23′, whilst worker 2 remains stuck on the curve U11U11′. This illustrates the existence of potential conflict over who gains most from trade.

Competitive equilibrium can resolve this conflict. When the Walrasian

auctioneer announces a price, the workers must trade at a point inside

the box corresponding to that price. This point must lie on a straight line

emanating from the point A. The point where the indifference curves

are simultaneously tangent to each other and to the straight line determines the equilibrium. The relevant line is the line AP; the point where

AP intersects the contract curve determines the Walrasian equilibrium E.

Under the assumed conditions this is unique. Projecting this equilibrium

onto the sides of the box at H, J, K, L determines the consumption pattern under trade. In the figure the two workers consume the same amount

of product 1; this is a consequence of the assumption that their preferences are the same, OJ = HB; in general these amounts will be different.

The equilibrium is price is measured by the slope of AP. This price not

only determines the terms of exchange, but also allocates income between

workers 1 and 2. Under the trade equilibrium worker 1 attains the indifference curve U12U12′ and worker 2 the curve U22U22′.



INTRODUCTION TO LOCATION 



61



Demand Analysis

The demand analysis is shown in Fig. 4.2. It focuses on the market for

product 1. Say’s Law implies that if the market for product 1 is in equilibrium then the market for product 0 is in equilibrium too. Production of

product 1 (entirely by worker 2) is measured by the interval OC along the

horizontal axis. D1D1′ and D2D2′ are the worker demand curves for product 1. Worker 2’s demand curve on the right-hand side is drawn backwards, from right to left, whilst worker 1’s demand curve, on the left, is

drawn in the conventional way, from left to right. Reversing a demand

curve is a useful technique in the geometrical analysis of trade. When trade

takes place worker 2 exports product 1 to worker 1, and so worker 2’s

demand for the exported product limits its supply. So far as worker 1 is



Price of product 1

relative to product 0



Increase in individual 1’s

utility from substituting

consumption of product 1

for product 0

by individual 1



D1



Equilibrium price

P



D2



E







Increase in individual 2’s

utility from substituting

consumption of product 0

for product 1

by individual 1



F

D2´



J

O



D1´



Consumption

Consumption C

of product 1

of product 1

by individual 1 by individual 2



Fig. 4.2  Determination of consumption under complete specialisation in

­production: demand analysis



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M. CASSON



concerned, therefore, worker 2’s demand curve appears as a supply curve,

and this is the way that it is interpreted in the figure.

The initial no-trade position is represented by the point F, where all product 1 is consumed by worker 2. The height OF measures the minimum price

at which worker 2 would be willing to exchange some product 1 for product

0 if trade were possible. The outcome when trade is possible is indicated

by the intersection of the demand curves at E. At E the sum of the worker

demands is equal to the fixed total production. Worker 2 exports product 1

to worker 1 in return for imports of product 0 of equivalent value.

The equilibrium determines the price (measured by OP) and the quantities of product 1 consumed (measured by OJ for worker 1 and JB for

worker 2). With identical demand curves these quantities are equal.

The gain in utility by worker 1 is measured by the area of the triangle

D1EP. This gain arises because worker 1 purchases the all units of their

imports of product 1 at the value they attach to the marginal unit. The gain

in utility to worker 2 is measured by the area of the triangle PEF. This gain

arises because worker 2 receives the same amount of product 0 in return

for intra-marginal units of product 1 as they receive for the marginal unit.

It is customary to add these two areas together to form an estimate

of the total gains from trade, measured by the area of the triangle D1EF.

Note, however, that this involves a value judgement that equal weight

should be given to the utilities of the two workers.



Model 3.2: Specialisation in Trade According

to Comparative Advantage in Production

Model 3.1 took an extreme position on specialisation in production.

Each worker could only produce one of two goods. Suppose now that

each worker can produce both goods. Suppose that one worker, say

worker 2, is uniformly more productive than the other. Does this mean

that this worker should produce everything and the other nothing?

While superficially plausible, on careful examination this proposition is

nonsense. Worker 1’s hours of work cannot be transferred to worker

2; they are inalienable. If worker 2 does all the work, then worker 1 is

simply idle, and so long as worker 2’s productivity is positive, it is better

that they produce something rather than nothing. But in this case what

should they produce?



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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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Model 3.1: The Determination of Price in a Global Market When Countries Are Fully Specialised

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