University of Papua New Guinea International Economics Lecture 5: Trade Models II – The Specific Factors Model

University of Papua New Guinea

International Economics

Lecture 5: Trade Models II – The Specific Factors Model

The University of Papua New GuineaSlide 2

Lecture 5: Trade Models II – The Specific Factors Model Michael Cornish

Overview

• Introduction

• Setting up the Model

• Distributional effects of a change in price

• Adding trade to the Model

• Conclusions



Introduction

• The Ricardian Model proved the basics of

comparative advantage, but we need a more

complex model to understand the

distributional effects (effects on income

distribution)

• This is what the Specific Factors Model is for!



Capital goods0 1 2 3 4 5

5

10

15a

b

c

d

e

f

Co

nsum

er g

oods

Increasing (marginal)opportunity cost of capital goods

A bending-outwards PPF: increasing opportunity costs



Setting up the Model

Assumptions:

• Two products (just like in the Ricardian Model)

• But now we have three factors of production

– Can be any three, but convention is to use:

• L: Labour, the mobile, ‘non-specific’ factor

• K: Capital, a fixed and ‘specific’ factor

• T: Land, a fixed ‘specific’ factor

• All labour is employed

• We have perfectly competitive markets




• What is a ‘specific’ factor?

– A factor of production that is specific to a

particular product

– E.g. land for agriculture; or capital for

manufacturing




An example: cloth and food

• Our two products will be cloth and food

• Food requires land (T); cloth requires capital (K)

• Thus, our production functions are:

– QC = QC(K, LC)

– QF = QF(T, LF)

• Note, we assumed that all labour was employed,

thus: LC + LF = L

&



Graphing the production function

Note: The production

function for food has a similar shape!




• Why does the production function have

this shape?

– When the quantity of the specific factor is fixed, and

we increase labour, we expect to see diminishing

returns to labour

– This means that the marginal product of labour

(MPL) eventually decreases, and in fact, would

ultimately become negative!

MPL: The additional output produced by one additional worker

&



Graphing MPL

Note: MPL would eventually

become negative!

This is important! We’ll see why in a few

slides...






• Remember we saw that the MPL was equal to the

slope of production function?

• Using the graph from the previous page, we can

calculate that the slope of the PPF is:

– MPLF / MPLC

[Note: It is negative because of the negative slope]

&




• Now we know how much of each product

is produced, given how labour is allocated

• But how do we know how labour will be

allocated?

– For that, we need to know how high the wages

are in each of our two sectors…

&




• In the Ricardian Model, we assumed that

wages simply reflect the value of the work done

– It is the same for the Specific Factors Model!

• In the Ricardian Model, wages (per hour) were

determined by the price of the product divided by

how many hours it took to produce one unit

– Note: we fixed the quantity produced to one!

&




• In the specific factors model, we fix the

number of hours to one, and so it is the quantity

produced that changes

• Thus, if we set out MPL to reflect the value of

one additional (marginal) hour of labour:

w = MPL * P

E.g. wages in the food sector: wF = MPLF * PF

• Except, we assume labour can move freely –

thus wages should be identical in both sectors

&



Determining the equilibrium wage...

Note:The assumption is that the demand for labour in each sector is equal

to the value of the produce of labour

(P * MPL) [which is the willingness to pay a

certain level of wage]




• Looking at wages also helps us another way – it

tells us what the relative prices for our two

products should be

If: MPLC * PC = MPLF * PF = w

Then: – MPLF / MPLC = – PC / PF

• And since we know that – MPLF / MPLC is the slope

of our PPF…

&



Eureka!

In domestic equilibrium



Distributional effects of a change in price

• We’ve just established the relationship between

MPL, wages, prices, and the quantities produced

in autarky (an economy without trade)

• But before we add in the trade, let’s see what

happens if we change the domestic prices of

cloth and/or food…



A proportionally equal increase in both prices

It just increases the wage by the same proportion!

Therefore: • No change to

relative prices• No change to

the domestic PPF



An increase in one price only (e.g. cloth)

1. Labour shifts from the food sector into the cloth sector...



2. ...the relative price

changes

1. As labour shifts from the

food sector into the cloth

sector...



The effect on the PPF from an increase in one price only (e.g. cloth)

2. The relative price changes




• In our example, we saw that the absolute wage

increased by less than the increase in the price of

cloth (7% in our example)

– However, it still increased

• But the question is – are workers (L) better off??




• For this, we need to look at their real wage (w/p)

– That is, how much of the two different products

can they buy? Is it more or less than before?

• Their real wage in terms of cloth has fallen:

– w (less than 7%) < PC (7%) => w/PC

• Their real wage in terms of food has risen:

– w (less than 7%) > no Δ in PF => w/PF




• So the effect on workers (L) is ambiguous!

– It depends on what the relative preferences of

workers are for cloth and food...

• What about owners of capital (K) ?

– The price of their product has increased more

than the wage they pay workers

– So they are definitely better off!




• What about owners of land (T) ?

– The absolute price of their product has not

changed…

– …but the wages they must pay have increased

– So they are definitely worse off!

• And can show all of these distributional effects

diagrammatically!



Demand curve for Labour

Producer surplus

Consumer surplus

Distribution of income: consumer and producer surplus



Note: The effect on total wages paid [blue] is ambiguous:

(w/PC)1 * L1C => (w/PC)2 * L2

C

It depends!

[red]

Distribution of income: consumer and producer surplus



Adding trade to the Model

• Finally, let’s add the trade to our Model !

• Instead of considering two economies, we only look

at ‘Home’ and assume that they face a world price

• To do this, we again use general equilibrium analysis:

– Relative demand (RD) & relative supply (RS)

• Except we assume that producers are indifferent who

they supply to…

– So there is only the one RD with trade: RDWorld



But first: RD and RS in autarky



...and now with tradeNote: In this example, the world relative price of cloth just happens to be higher

This is only an assumption!But it is true that there is

only one RDWorld



Opening up to trade leads to a changes in Home’s relative price!

We can then track the effects from this change in relative price just like we did

before (Slides 20 – 28)

Note: In all our examples we tracked an increase in the relative price of cloth



Proving gains from trade



Conclusions

• The Specific Factors Model is very useful in

determining the winners and losers from trade

• Trade benefits the factor that is specific to

the export market, but hurts the factor that

is specific to the import market

• The effects upon the non-specific factor are

ambiguous

• It gives us a some understanding of how resource

endowments – the stock of specific factors (i.e. K, T)

and non-specific factors (i.e. L) – affect trade



Conclusions

• However, it still doesn’t tell us exactly how

differences in resource endowments are a

cause of trade

• For that we need our next trade model:

The Heckscher-Ohlin Model

» So stay tuned!

Documents

University of Papua New Guinea International Economics Lecture 5: Trade Models II – The Specific Factors Model