1. Specific Factors and Income Distribution
© Prof. J. Peter Neary Economics Department, Oxford

2. Specific-Factors Model
Ricardian model has nothing to say about domestic income distribution
BUT: In reality, trade has important effects on distribution
One major reason: Factors cannot move immediately or costlessly between sectors
An interesting alternative model, which focuses clearly on this issue, is the Specific-Factors model
Difference in assumptions: 3 factors instead of 1
Labour (L) is mobile between sectors
Capital (K) and Land (T) are immobile or “sector-specific”
Similar to 2-sector Ricardian model in other respects:
2 goods: Manufacturing and Food
Full Employment; perfect competition

3. Fig. 3-1: The Production Function for ManufacturesQM
QM = QM(K, LM)
Fig. 3-1: The Production Function
for Manufactures LM
MPLM
Fig. 3-2: The Marginal Product
of Labour in Manufactures
Equals the slope of the prod. func.
Downward-sloping: Reflecting Diminishing Returns
As more labour is added to fixed amount of capital, its marginal return falls LM

4. Fig. 3-3: The PPF in the Specific-Factors ModelQF
PPF: Production
Possibility
Frontier
Production Function
For Food LF QM
Production Function
For Manufactures
Full-Employment Locus:
LM+LF=L
Exercise: repeat this slide and last
for 2-good Ricardian model LM
Fig. 3-3: The PPF in the Specific-Factors Model

5. Equilibrium Allocation of Labour
Profit maximisation in each sector =>
w = Value of marginal product of labour
i.e., w = P x MPL
For given price, VMPL curve is just the MPL curve
i.e., it is the demand curve for labour
e.g., in manufacturing:
VMPLM w
PM x MPLM LM LM

6. Equilibrium Allocation of Labour (cont.)
VMPLF
Similarly in food: w LF LF
Now, flip this diagram around:
VMPLF w LF LF

7. Equilibrium Allocation of Labour (cont.)
Finally, combine the two labour demand curves:
VMPLM
VMPLF w LF LM LM LF L
Horizontal axis measures L: i.e., full employment
Intersection of two demand curves determines equilibrium wage and allocation of labour between sectors
Note: w is exogenous in partial equilibrium, endogenous in general equilibrium: follow the arrows!

8. Effects of a Rise in the Relative Price of Manufactures
VMPLM
VMPLF B w A LF LM LM LF
Curve shifts upwards: equilibrium shifts from A to B
Employment and hence output of manufactures increase (intuitive)
Wage rises BUT by less than the price increase
i.e., wage-earners gain in terms of food, lose in terms of manufactures
Owners of capital gain, owners of land lose (in terms of both goods)

9. Effects of price rise in PPF diagram:
Effects of a Rise in the Relative Price of Manufactures (cont.)
Effects of price rise in PPF diagram:
Initial equilibrium at A
Price = MC in each sector => slope of price line = slope of PPF QF A B QM
Higher world price of M => steeper price line
=> New equilibrium at B: QM rises, QF falls

10. Effects of a Rise in the Capital Stock
VMPLM
VMPLF B w A LF LM LM LF
Curve shifts rightwards: equilibrium shifts from A to B
(Looks very like last VMPL diagram, though interpretation is different)
Employment and hence output of manufactures increase (intuitive)
Wage rises relative to both goods prices: i.e., wage-earners definitely gain
Owners of capital lose per unit, owners of land lose

11. Implications for Trade Patterns
N.B. This diagram is similar to the 2-good Ricardian case; differences:
Countries have identical technology, and differ in factor endowments
The supply curves are smooth
Foreign has less capital:
So lower relative supply of M
p=pM/pF
World supply curve
an average of the two
p*A pF
Assume Home has more capital:
So higher relative supply of M pA
Relative demand curve
determines equilibrium
in both autarky and free trade

12. Distributional Conflict versus Aggregate GainsQF A B QM
Move from autarky at A to free trade at B:
Since some factors gain and some lose, what can we say?
At least, we can say that the economy as a whole could do better than its initial total consumption
i.e., starting from B, economy could consume along red portion of new price line
As in Ricardian model, trade expands the economy’s consumption possibilities
So, losers could be compensated and still leave gainers better off
BUT: In practice, compensation is rarely carried out

13. Specific Factors: General Conclusions
Differences in resources: a source of comparative advantage
[Topical, with oil at $120 a barrel! (April 2008)]
Trade (and any other change) has both winners and losers
Winners are factors specific to export sectors; losers are factors specific to import-competing sectors
Winners could compensate losers …
BUT: In practice, such compensation is rarely carried out fully
Though there are examples of partial compensation
e.g., adjustment assistance, retraining subsidies, temporary subsidies, etc.
Case study: Repeal of the Corn Laws in 1846
See:
Overall: A very neat, simple model:
Rationalises partial equilibrium intuition, in a fully specified GE model
Highlights effects on distribution
But: Naïve theory of trade [Samuelson: “tropical countries export tropical products because of the abundance of tropical products there”!]

14. Reconciling the HOS and Specific-Factors Models
So far: Two interesting but very different models: Are they necessarily in conflict?
Not necessarily - One way of reconciling them: Interpret each as applying to a different time frame.
SF: Describes short-run responses
HOS: Describes longer-run responses (after capital stock has had time to adjust)
Mechanism driving this adjustment can be seen by looking at full effect of a price change in SF model:
Note: There is a magnification effect on the rentals (though not on the wage)
Compare this with the effects in the HOS model

15. Reconciling the HOS and Specific-Factors Models (cont.)
This rise in rM relative to rF encourages capital to flow (reallocate) over time out of sector F into sector M
As a result:
Long-run response to price change is greater than short-run response: i.e., declining sector declines by more
Economy converges in longer run towards the equilibrium predicted by the HOS model
Finally: An alternative (though related) difference in interpretation between the two models concerns the different kinds of shocks they illustrate:
SF: Describes response to unanticipated shocks
HOS: Describes response to anticipated shocks: Capital will have already begun to move