Specific factor and Income Distribution

The Repeal of the Corn Law

An effort to reduce food price (up to 80% tariff)
Repealed under Robert Peel ruling in 1846.
pivotal for UK manufacturing transformation.
Birth of the economist magazine

Last week

We learned Ricardian model, the earliest of trade model.
gains from trade(in a purely economic sense) comes from specialization and comparative advantage.
This model has strong assumptions: free movement of factor between industry.
- Today we’re relaxing this assumption a bit.

Specific factor model

2 Sectors i: Cloth (C) and Food (F)
3 factors j: Labor (L), Terrain (T), and Capital (K).
- Labor can move between sectors
- T can only used to produce F, K only C.

$\begin{align} Q_F=F(L_F,T) \\ Q_C=C(L_C,K) \\ L_F+L_C=L \end{align}$

PPF

Now that we have 2 factors each industry, we need to rethink our PPF.
Since L is the only moving factor, the only way to increase industrial production is to increase $L$ .
since total number of labour is fixed, the only way to increase $L$ in one industry is to decrease the other industry’s $L$

PPF

However, since other factors ain’t moving, we have a diminishing returns to labour.
- Imagine your office increase no. of employee but not computers.
- Increase no. of farmers but not land.
Meaning, labour productivity (i.e., marginal product of labour, MPL) goes down as $L_i$ goes up.
- Consequently, MPL goes up in the other sector.

PPF dan MPL

PPF dan MPL sektor C

Note: F industry is identical.

PPF

Another 1 unit of $L_C$ increases $Q_C$ by $MPL_C$ unit.
- as $L_C$ goes up, $MPL_C$ goes down.
- $Q_C$ will keep increasing albeit in decreasing amount.
As $L_C$ up by 1 unit, $L_F$ down by 1 unit.
- Consequently, an increase in $Q_C$ is accompanied by decrease in $Q_F$ .
- The rate, however, varies.

$L_C+L_F=L$

PPF

To increase $Q_C$ by 1 unit, $Q_F$ must decrease by $\frac{MPL_F}{MPL_C}$
From here, we can express $Q_C$ as the function of $Q_F$ :

$\text{Slope of PPF}=-\frac{MPL_F}{MPL_C}$

PPF

Firm problem

A profit maximizing firms will want to employ until:

$MPL_C \times P_C = w$

At that place, an increase in $L_C$ decreases $MPL_C$
If $P_C$ does not change, then $MPL_C \times P_C < w$
- That is, cost will be higher than revenue since both prices and wage are fixed.

Firm problem

Since F also has the same employment rule, the labour market dynamics become:

$\begin{align} MPL_C \times P_C = MPL_F \times P_F = w \\ \\ -\frac{MPL_F}{MPL_C}=-\frac{P_C}{P_F}=w=\text{slope PPF} \end{align}$

MPL reflects productivity / technology.
Prices is also set by preferences.
- Preference (by extension, prices) is given.

Production status quo

diminishing return leads to a non-linear ppf.
production ended-up at dot 1, where PPF tangents price ratio.
This is a bit different compared to ricardian with a linear PPF and a constant MPL.
4-quadrant grafik is an excellent tool to visualize QF/QC relationship.

Labor market

The labour market movement depends on MPL of the two industries
An equilibrium exists where $MPL_i \times P_i$ , where employment settles at some level $w$ .
The labour market dynamics changes when MPL or price ratio changes

$\left(\frac{P_C}{P_F}\right)$ .

Labor market

Note that L is fixed, $L_C$ is the left one.

Increase in both price

Say an inflation leads to both prices increase by 10% $P_C^*=1.1P_C$ and $P_F*=1.1P_F$
With a fixed MPL, increase of both curves $MPL_i \times P_i$ is in-line with increase in $P$ s.
Since both prices go up at the same pace, labour dynamics does not change.
Prices up by also 10%, negates the impact of the inflation. No welfare changes.

Increase in both price

Change in relative price

Let this country trades, and in the global market, $P_C$ is 10% more expensive while $P_F$ is the same.
Then price ratio changes, i.e., $\frac{P_C}{P_F} \uparrow$
Labour market will shift toward C, where $L_C \uparrow$ while $L_F \downarrow$
- Remember, total labour is fixed.
Wage goes up, but not as much as increase in $P_C$ .

Change in relative price

New production allocation

CHanges in price ratio leads to changes in production allocation.
Remember that production will be done such that its slope equals to price ratio.
When price ratio changes, production allocation follows.
- It will be biased toward the higher good.

New production allocation

Understanding income distribution

new allocation bear consequences: changes in income distribution.
This is a consequence of disproportional changes: $\Delta P_C > \Delta w > \Delta P_F$

$\frac{w}{P_C} < \frac{w}{P_F}$

Income distribution

Does labour better off? Depends on the preference:
- Both receives the same wage
- Workers benefit if C is less important in their basket.
However, specific factor owner is decisive:
- Capital owners win, Land owners lose.
- We can show this from surplus dynamics.

Cloth Sector

Increase in textile price

Food sector

Landlord surplus

Gains from trade

Trade benefits the factor that is specific to the export sector of each country but hurts the factor specific to the import-competing sectors, with ambiguous effect on mobile factors.

Results from trade is ambiguous in this case. Can we show that trade ALWAYS better in general?
- if this is the case, then theoretically, we can compensate the loser.

Gains from trade

Without trade, consumption = production

$D_C=Q_C \ and \ D_F=Q_F$

with trade, consumption does not need to equal production, as long as:

$P_C \times D_C + P_F \times D_F = P_C \times Q_C + P_F \times Q_F$

Gains from trade

We can rearrange the budget constraint as such:

$D_F - Q_F = \left(\frac{P_C}{P_F}\right) \times (Q_C-D_C)$

That is, import of F = price ratio times C export.

How much we can import depends on how much we can export.

Gains from trade

Grey area is the better set

Gains from trade

Without trade, consumption = production = at the PPF.
With trade, we have a bit more option. Of course the option that makes sense is what makes us better off: unambiguously if we can have more of both goods.
As long as the better set is always reachable, compensation is always an option.

Gains from trade

With trade, we have option as long as it’s in the budget constraint.
- obviously this allocation includes the old set.
- the option comes from the ability to export and import.
we can reach allocation even previously unfeasible.
- theoretically, the result can be unambiguously good.
That said, just because everyone CAN benefit doesn’t mean everyone WILL.

Political economy of trade

International trade can possible make immobile factor owners worse off.
- in the real world, even workers can be somewhat immobile!
However, this issue isn’t the worse to economists:
- income distribution changes happen all the time: tech changes, pandemics, etc.
- compensation always better than trade restriction.

Political economy of trade

In a democratic country, mobilization of the masses is extremely important.
Government intervention happens in concentrated industries.
- Large economy with small numbers of players, SOEs, etc.
When cornered, industries will have the same interest thus easier to organize.
Those who benefits from trade usually consumers who are badly organized.

Short run model

It’s good to note that this model can be seen as a short-run model.
In the long-run, investment will increase the immobile factors: capital accumulations, land reclamations, deforestation, etc.
Factor may moves in the long run:
- if mining is sustainably large, people will pursue degrees in mining.
- Sell land, buy factories.

Next week

The new trade theory.