0. International Economics
Lecture 5: Trade Models II –
The Specific Factors Model

1. Overview Introduction Setting up the Model
Distributional effects of a change in price
Adding trade to the Model
Conclusions

2. 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!

3. A bending-outwards PPF: increasing opportunity costs
Capital goods 5 10 15 a b c d e f
Consumer goods
Increasing (marginal)
opportunity
cost of capital goods

4. 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

5. Setting up the Model 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

6. Setting up the Model & 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

7. Graphing the production function
Note:
The production function for food has a similar shape!

8. MPL: The additional output produced by one additional worker
&
Setting up the Model
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

9. Graphing MPL Note: MPL would eventually become negative!
This is important!
We’ll see why in a few slides...

11. &
Setting up the Model
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]

12. Setting up the Model & 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…

13. Setting up the Model & 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!

14. Setting up the Model & 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

15. 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]

16. &
Setting up the Model
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…

17. In domestic equilibrium
Eureka!

18. 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…

19. 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

20. An increase in one price only (e.g. cloth)
1. Labour shifts from the food sector into the cloth sector...

21. 2. ...the relative price changes
1. As labour shifts from the food sector into the cloth sector...

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

23. Distributional effects of a change in price
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??

24. Distributional effects of a change in price
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

25. Distributional effects of a change in price
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!

26. Distributional effects of a change in price
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!

27. Distribution of income: consumer and producer surplus
Demand curve for Labour
Consumer surplus
Producer surplus

28. Distribution of income: consumer and producer surplus
Note:
The effect on total wages paid [blue] is ambiguous:
(w/PC)1 * L1C => (w/PC)2 * L2C
It depends!
[red]

29. 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

30. But first: RD and RS in autarky

31. This is only an assumption!
Note: In this example, the world relative price of cloth just happens to be higher
...and now with trade
This is only an assumption!
But it is true that there is only one RDWorld

32. 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

33. Proving gains from trade

34. 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

35. Conclusions So stay tuned! The Heckscher-Ohlin Model
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!