appendix 3.2

OFFER CURVES AND THE TERMS OF TRADE

Appendix 3.2

Offer curves are an alternative way to represent the reciprocal demand that determines the terms of trade.

Figure A 3.2 shows A's desired trade for three different values of the terms of trade. As the TOT line gets steeper we see A's desired imports rise from T0 to T3, while desired exports rise from S0 to S3. As the TOT rises A is able to achieve a higher standard of living.

This change in the TOT is 'favorable' to A because it favors the good that A exports.

Figure 3.3 plots A's desired exports against A's desired imports.

If we think of the TOT as a price then as it rises A 'offers' a specific exchange of S for T.

The offer curve combines supply and demand behavior in one curve. It takes money prices out of the picture. Instead of offering to pay a certain number of dollars for a good, countries are going straight to making a barter offer.

In this approach money is a distraction and models that dispense with it get to the 'real' economics of trade.

Country B also has an offer curve.

Figure 3.4 puts the two offer curves on the same diagram.

There is only one TOT where the desired exports and imports all match. This is the equilibrium TOT.

At this equilibrium the two country's CICs must be tangent to each other.

Production choices, consumption choices, the terms of trade, goods prices and the exchange rate are all consistent with each other in general equilibrium. Unless there is some shock to the system the world will remain in this equilibrium state.

appendix 3.1

THE CLASSICAL MODEL WITH MANY GOODS

Appendix 3.1

Suppose:

• there are 5 goods
• all other classical assumptions hold especially fixed labor/output ratios

In Table 3.1 are the labor/output ratios.

Country A's comparative advantage is in good Y.

We guess that B will export T and A will export Y, but what about the other 3 goods?

We know that goods T and Y determine the range for relative wages.

1/3 < Wa/(E.Wb) < 1

Table 3.2 ranks the value of (labor hours per unit B produced/labor hours per unit A produced) for each good.

B's greatest comparative advantage good (its most competitive export) is on the left. To produce one unit of T, country B only requires one-third as much labor as country A does.

This ordering is called 'the chain of comparative advantage'.

Suppose the relative wage rate was 2/3. Then B would produce all the goods except Y.

Where do the wages rates actually get detemined? In theory the wage rates in each country should adjust so that trade is balanced. If the wage rate in one country is 'too high' then the price of its least competitive export will be too high to compete in the market. So the country will tend to do some combination of lowering the wage rate and cutting back production of its least advantageous good until trade is balanced.

topic 3.4

THE CLASSICAL MODEL OF INTERNATIONAL TRADE

Topic 3.4

Trade and wages

If labor is the only factor of production then in pretrade equilibrium the price of a good is simply the number of hours to produce it.

Psa = Wa x 3
Pta = Wa x 6
Psb = Wb x 12
Ptb = Wb x 8

Suppose both countries use the same currency.

Then for trade to occur the pretrade price of S must be lower in country A than in country B. And the opposite must be true for T.

Psa < E x Psb
Pta > E x Ptb

Where the exchange rate E converts country B currency into country A currency.


Then

Wa/(E x Wb) < 4
Wa/(E x Wb) > 4/3

that is 4/3 < Wa/(E x Wb) < 4

The middle term is the relative wage ratio.

Workers in A must earn more than in country B as measured in country A currency.

Differences in labor productivity explain the wage differences. Labor in A is 4/3 times as productive as labor in B (in textiles) and 4 times as productive in S production. These numbers set the limits for wage differences.

If the wage rate for labor in country A is more than four times the wage rate in country B then that would erase the advantage of buying goods from A. The extra high wage in A would erase any price advantage for S goods imported from A.

For good T, if wages in country B are more than ¾ the wages in A, it wipes out the productivity advantage of country B in the production of T.

To summarize, the wage rate in a country cannot be so high that it wipes out the natural comparative advantage that country has in its export good.

Another way of thinking about it: we know that productivity determines the standard of living in a country. It makes sense that relative productivity determines the relative wage rate between two countries. So the relative advantage A has in its export good sets the upper bound on its wage premium.

But, and this is truly surprising – it is not absolute advantage that sets the (limits for) the wage premium. It is comparative advantage. Being the lowest cost producer of a good in terms of labor costs does not raise your relative wage. It is the structure of comparative advantage (lowest opportunity cost) that matters.

Another remarkable result: it is the trade sector that drives relative wages. Because trade in this model drives both countries to specialize completely (by assumption), the whole production pattern of an economy is determined by comparative advantage.

topic 3.3

THE CLASSICAL MODEL OF INTERNATIONAL TRADE

Topic 3.3

The Gains from International Trade

Consider Figure 3.4

The way we calculate the gains from trade is to compare the equilibrium CIC in autarky with the trade equilibrium CIC.

So moving from K to I is a gain from trade. Since I is above to the right of K it represents a welfare gain.

(But if consumption preferences were extreme (e.g. A residents only consumed S) then there would be no gain from trade.)

Another test of gains is: is the vertical intercept higher (GDP1/ PTO).

The further the TOT is from the PPF of country A, the greater are the gains to that country.

This model does not explicitly solve for the exact equilibrium TOT.

A small country could actually have greater relative trade gains than a larger country if the TOT was equidistant between the two PPFs because equal trade gains are being divided by a smaller base.

topic 3.3

THE CLASSICAL MODEL OF INTERNATIONAL TRADE

Topic 3.3

The Gains from International Trade

Consider Figure 3.4

The way we calculate the gains from trade is to compare the equilibrium CIC in autarky with the trade equilibrium CIC.

So move from K to I is a gain from trade. Since I is above to the right of K it represents a welfare gain.

If consumption preferences were extreme (eg A residents only consumed S) then there would be no gain from trade.

Another test of gains is the vertical intercept higher (GDP,/ PTO).

The further the TOT is from the PPF of country A, the greater are the gains to that country.

This model does not explicitly solve for the exact equilibrium TOT.

A small country could have greater relative trade gains than a larger country if the TOT was equidistant between the two PPFs.

topic 3.2

THE CLASSICAL MODEL OF INTERNATIONAL TRADE

Topic 3.2

The GE solution to the classical model.

Suppose we have the PPFs from figure 3.1.

In the test the two PPFs are not drawn to the same scale.

Figure 3.2 adds the CICs that are at a tangency with the PPFs.

If we allow trade to occur what will happen?

There will be only one would price. This price will be between the two autarky prices.

How much specialization will occur?

If we know what the new equilibrium will be we can say.

Comparative advantage determines specialization and trade.

Figure 3.3 illustrates an equilibrium.

The new world price is in between the autarky prices.

Suppose the new price is 3/4. This represents the ‘terms of trade’.

A will produce more S
B will produce more T

A will produce only S because this allows A to reach the highest CCI.

Similarly B will only produce T and reach its highest CCI.

How do we know that the new price is feasible? I.e. why should supply and demand be matched perfectly at that price? Because the price adjusts until it is at the equilibrium value (choosing ¾ is just a guess for illustration only).

This price is called the terms of trade: ‘TOT’

HIJ in Figure 3.3 is the ‘trade triangle’.

The trade triangle tells us how much S country A will export (J – H) and how much T it will import (all of its T consumption).

The trade triangles for the two countries must be congruent since the horizontal sections are equal and the hypotenuse has the same slope.

Walras Law

If there are n markets in a GE economy and (n-1) are in equilibrium then the last market must be in equilibrium.

topic 3.1

THE CLASSICAL MODEL OF INTERNATIONAL TRADE

Topic 3.1

Mercantilism aimed to limit imports and promote exports.

Adam Smith developed his ideas to refute mercantilism.

We shall continue to develop a model of international trade.

Factors of production cannot move between countries.

This keeps the PPF fixed (with static technology) and it also prevents wage equalization

There are no barriers to trade in goods.

So there are no tariffs or quotas.

Exports pay for imports.

This is balanced trade.
There are no flows of money or bonds (there are no ‘capital flows’).

Labor is the only factor of production

This is the ‘labor theory of value’.

Production exhibits constant returns to scale between labor and output.

Proportional changes in imports lead to proportional changes in outputs when labor is the only factor of production this means that there is a fixed ratio of output to input.

The constant returns assumption allows us to derive formulas that are independent of the absolute level of output.


Absolute advantage can be illustrated by tables.

There are two variations of these tables. One version assumes that each country has the same amount of labor and then presents the maximum output of each good that is possible for each country. The other version holds the production levels the same for each country the same and then presents the different amounts of labor required within each country.

Both variations are equivalent – they are different approaches to presenting the same information. Tables are only useful for presenting linear PPFs.

Table 3.1 is the second type of table.

From table 3.1 we see than country A has an absolute advantage in producing S and country B has the absolute advantage in producing T.

Diagram 3.1


If each country had 12 hours of labor A has the absolute advantage in T (it can produce more units of T) and B has the absolute advantage of S (if can product more units of S).

In order to know where each country would be in autarky and where they would change production if trade was allowed we need information about consumption preferences (not in diagram 3.1).

Under reasonable consumption preferences (the best we can do without being given the ‘true’ CICs) and assuming that both countries consume both goods it is likely that A will specialize in T and B will specialize in S.



Table 3.3 represents a situation where A has the absolute advantage in both good.

Diagram 3.2

A has the absolute advantage in both goods, but its comparative advantage is S.

There is potential for A to specialize in production of S while B specializes in production of T.

topic 2.4

TOOLS OF ANALYSIS FOR INTERNATIONAL TRADE MODELS

topic 2.4

Can we devise a better measure of national welfare than community indifference curves? Ideally we would like to create a GDP measure. Then we can answer question like ‘does trade make a country better off?’

formula for GDP

GDP = Ps S + Pt T


GDP/Pt = (Ps / Pt) . S + T

converts our GDP measure into units of T

Figure 2.7 shows how this equation allows us to convert a production point into a measure of real GDP.


We are going to convert everything into ‘T’ units.

What about tastes? Don’t they matter?

They do matter, and they enter in via the market prices Ps, Pt.

For example, it consumers hade a low preference (on the margin) for good S, then Ps would be low relative to Pt, and the line in figure 2.7 would be flat. Then GDP would increase little in response to greater S production, but it would increase a great deal is T production increased.

We are using T as the ‘numeraire’ good.

The concept of standard of living uses the measure per capita GDP.

An alternative but equivalent approach to national welfare is to use national demand and supply curves.

We will derive these curves from PPFs and CICs.

Figure 2.8 shows how to derive the curves.

Recall that a demand curve is a representation of a function.

‘call out’ a => quantity
market price demanded

Likewise, for supply

‘call out’ a => quantity
market price supplied

So be rotating the line representing different relative prices we can generate demand and supply quantities.

Ps / Pt = ($ /units of S) / ($ /units of T)

Cancel out the $

Ps / Pt = units of T / units of S

The vertical axis is the ‘price’ of S in terms of the numeraire T

Rotating the price line about the PPF generates the supply curve.

As we rotate Ps / Pt about the PPF we find the point of tangency with a CIC. This generates a demand curve.

The position of the PPF ‘anchors’ the consumers so they are only allowed to consume quantities consistent with what they can produce this period. There is no borrowing from the future in this model.

Nwo introduce a second country, country ‘B.’

Figure 2.10 shows the two demand and supply curve diagrams, each one representing the situation in autarky.

If we allow trade between the countries we expect that the new global market price Ps / Pt will be intermediate between the autarky prices.

Because country A has the lower autarky price of S it has the comparative advantage in S. Trade will start out with consumers in country B importing S, and country B producers will export T. Trade will begin by following the pattern of comparative advantage.

Comparative advantage can only be assessed by looking at the countries’ relative autarky positions. But in the real would we don’t observe the autarky state. This is a great challenge for testing trade theories based on comparative advantage.

topic 2.3

TOOLS OF ANALYSIS FOR INTERNATIONAL TRADE MODELS

Topic 2.3

Let’s try applying a little calculus

Π = Pt T + Ps S

where Π = profit
Pt, Ps = prices of T, S
T, S = outputs of T, S

this is an endowment model so costs are zero, the firm is simply trying to maximize revenue

dΠ = Pt ∆T + Ps ∆S

at the profit maximization point dΠ = O

so Pt ∆T + Ps ∆S = O

so Ps/Pt = - ∆T/ ∆S (1)


(by the way firms act competitively and so they treat prices as parameters, not variables)


(1) says that production will be chosen so that the point on the PPF will have the same slope as the ratio of prices.

another way of describing this:

· Ps/Pt is outside the control of the firm because it is determined by consumers
· the firm wants (1) to be true
· the firm will increase T and decrease S or the opposite (moving along the PPF) until (1) is true
· once (1) is true the firm will stop and remain at that point on the PPF forever until there is a change in Ps/Pt
· the firm is reacting to price changes, not attempting to influence them


what if we are at a point like ‘U’ on the PPF where

-Ps/Pt < ∆T/ ∆S (assuming CIC0 determines prices via tangency)

(when we are looking at negative slopes the steeper slope has a lower numerical value)

to rephrase, the CIC curve has a steeper slope than the PPF at U


so 0 < ∆T/∆S + Ps/Pt (2)

given that we are at U, let us consider what would happen if we increased S production

so ∆ S > 0

Multiply both sides of (2) by Pt ∆S

then Ps ∆S + Pt ∆T > 0


so we will increase Π if we increase S


If we were starting on the PPF to the right of X (at a point like Y) similar reasoning would show that we could increase Π by decreasing S production.

Intuitively, the ‘U’ point is a situation where the price of S is relatively high compared to the price of T and the opportunity cost of increasing S production (T sacrificed) is low. So the firm figures that it will make more profit by ↑ S and selling it at the ‘high’ price of S, even after factoring in the loss of revenue from decreasing production of T.

At this point it’s worth pointing out that the model does not really have a mechanism for determining what prices will actually be at ‘U’ We are just assuming that somehow the prevailing market price will be close to the slope of CIC0 at ‘U’ because of ‘consumer demand’

topic 2.2

TOOLS OF ANALYSIS FOR INTERNATIONAL TRADE MODELS

Topic 2.2

The basic model

When measuring welfare gains the reference point is autarky.

Consider Figure 2.5

It represents a closed economy.

There are two goods:
· Soybeans (S)
· Textiles (T)

EF is the PPF

CIC0 ,CIC1 ,CIC2 are I.C.s

Producing at ‘Z’ allows the country to reach the highest I.C.

The point (Sz, Tz) is determined by the production opportunities and tastes.

Note that this model has no mechanism to explain how the economy gets to Z. There is no explicit market, no dynamics.

But we can say that if agents behave rationally and there is a competitive market we should reach Z eventually.

The key assumption is that if this is a competitive market [That is, agents take prices as given and do not try to strategize.] Then we think that this will be the solution. There is an enormous literature in microeconomics (general equilibrium) theorizing about when an economy will be at the competitive and welfare maximizing equilibrium solution. We are not getting into this theory. But we can do some experiments testing weather these solutions are at least plausible.

In the competitive equilibrium at Z we can say that certain conditions must hold.
One condition is that the relative price of the two goods must equal the ratio of marginal utilities at the tangency point on the indifference curve CIC1.

Equivalently, the MRS (marginal rate of substitution ) (along CIC1) at Z must equal the ratio of prices.

MRS=Ps/Pt

MUs /MUy=Ps /Pt

MUs /Ps= MUy / Pt

Where Ps, Pt =dollar prices of S, T
MU =marginal utility
(By the way we are ignoring all the negatives of these slopes)

The argument for which we expect to reach Z is a sort of proof by contradiction. We look at a point that is not Z and show that agents will move in the correct direction.

Consider point Y.

There is an argument that consumers will move in the ‘correct ‘direction. What is it?

Figure 2.6

Figure 2.6 represents a situation with increasing opportunity costs in production

If the economy is at a point like ‘U’ then producers will move in the correct direction. Why?