Chapter 3
3.2 Smith's argument for free trade
Summarizing Smith's argument for free trade, it runs roughly as follows.
First, he emphasizes the opportunity costs in regulations in general: Regulations, for
example promoting the interests of shoemakers, imply that resources, such as capital and
labour, are drawn away from other sectors of the economy. Smith pointed out that there were
costs to this increase, now known as opportunity costs, because the extra capital and labour
used for shoe production might have been more advantageously employed in some other
sectors.
Third, he applies the same opportunity cost principle to international commercial policy:
International trade flows reflect the fact that goods and services can sometimes be imported
at lower cost from abroad than they can be produced at home. This increases the
consumption opportunities for a nation, and is, therefore, beneficial for the nation as a
whole, just as the specialization of the artificers, the shoemaker and the tailor, is
advantageous at the individual level.
3.3 Ricardo's contribution
How can a country that is less efficient than another country in all sectors of production still trade
with other countries?
Theory of comparative advantage: When a country can either import a commodity or produce it at
home, it compares the cost of producing at home with the cost of procuring from abroad; if the
latter cost is less than the first, it imports. The cost at which a country can import from abroad
depends, not upon the cost at which the foreign country produces the commodity, but upon what the
commodity costs which it sends in exchange, compared with the cost which it must be at to produce
the commodity in question, if it did not import it.
3.4 Technology as a basis for comparative advantage
Theory of comparative advantage, assumptions:
Assume that there are two countries (EU and Kenya)
Producing two goods (food and chemicals)
Using one factor of production (labour)
The production function in both countries and for both goods exhibits constant returns to
scale, indicating that if we double the amount of inputs (labour), the output level
(production) will also double.
We assume that there are many firms in both countries, each behaving perfectly
competitively; each firm wants to maximize profits, taking the price levels in the output and
input markets as given.
Taken together, the assumption of constant returns to scale and perfect competition imply
that if a good is produced in equilibrium, the price level in the output market must be equal
to the unit cost of production.
The productivity table summarises the state of technology in both countries. As the
production functions use only one input (labour) and exhibit constant returns to scale, they
can be summarized using a table specifying how much labour is required to produce one
unit of either good in either country.
These two extra units of food reflect the potential gains from specialization if both countries
concentrate in the production of the good for which they have a comparative advantage, that is the
good they produce relatively most efficiently, namely chemicals for the EU and food for Kenya. In
principle, there is room for both countries to gain from trading with each other.
,3.5 Production possibility frontier and autarky
Start the analysis of trade between two Ricardian-type countries from a situation of autarky, that is,
if the two countries are not trading any goods. This is done most easily using the production
possibility frontier:
Production possibility frontier (PPF): All possible combinations of efficient production points
given the available factors of production and the state of technology.
As there are constant returns to scale and there is only one factor of production, all we really have to
do is calculate the maximum production points and connect these with a straight line. We can now
determine the equilibrium price of chemicals in terms of food (which we take as our measurement
unit, known as the numéraire) for both countries.
Thus, the autarky price ratio in a Ricardian model is exclusively determined by the technical
coefficients of the productivity table; the price of chemicals in terms of food equals 4 in the EU and
6 in Kenya. Opportunities for trade between nations arise whenever the relative, or comparative,
productivity ratios differ. They do not depend on absolute productivity levels.
3.6 Terms of trade and gains from trade
Determining the price of chemicals in terms of food in autarky in both countries does not allow us
to determine exactly the terms of trade if the two countries decide to open up opportunities to trade
with each other, as this requires more detailed information. We can, however, determine the range
within which the terms of trade can vary, and we can demonstrate that both countries may gain from
trade. To start, the autarky price of chemicals in terms of food is four units in the EU and six in
Kenya. The terms of trade can only vary within this range, endpoints included.
Gains from trade, three seperate cases/possibilities:
If the terms of trade is strictly in between four and six units of food, both countries will gain.
Assume price 4.8, at that price, Kenya will produce only food (30) and will purchase abroad
the required amount of chemicals at a price of 4.8 (to maximum 30/4.8=6.25). Similarly, at
that price the EU will produce only chemicals (25) and will purchase the amount of food it
wants (to maximum 25x4.8=120). Both countries gain because at those terms of trade the
production decisions of the entrepreneurs allow the consumers to choose a consumption
point beyond the old autarky optimum, because the budget line has pivoted outwards. So, if
(can only be equilibrium if combined consumers of EU and Kenya at that price want to
consume the total world production of both goods) a price of 4.8 is a trading equilibrium,
both countries will gain from trade.
If the terms of trade is four units, only Kenya will gain while welfare in the EU will not
change. A plausible outcome in this set-up in which the production levels of the EU are
much larger than in Kenya is, therefore, that the terms of trade will be the same after
opening up to trade as the autarky equilibrium price in the EU (4 units). This implies that the
EU budget line does not change, such that the EU welfare does not change. Kenya, however,
completely specializes in the production of food and can trade this at the most beneficial
terms of trade with the EU (to maximum of 30/4=7.5 units of chemicals. The entrepreneurs
in the EU simply adjust their production decisions along the production possibility frontier
to accommodate the Kenyan wishes and clear world markets. Note, in particular, that
Kenyan welfare rises as a result of trading with the EU, while the EU welfare remains
unchanged, even though Kenya is less efficient in the production of both goods.
If the terms of trade is six units, only the EU will gain while welfare in Kenya will not
change. Similar reasoning as possibility two.
3.7 Application: Kenya and the EU
Differences in comparative costs are crucial for determining international trade flows and gains
from trade.
Absolute cost advantages, however, are crucial for determining a country's per capita welfare level,
and thereby explain differences in international wages.
,Example:
Assume that EU specializes in production of chemicals; Kenya in food; exchange rate is one; wage
rate in Kenya as the numéraire.
In a perfectly competitive economy with constant returns to scale, the price of a product is equal to
the cost of production. As food is produced in Kenya, the Kenyan wage is one (numéraire), and it
takes four units of Kenyan labour to produce one unit of food, the price of food must be 4 (4x1). As
the EU produces chemicals and it requires 8 units of EU labour to produce, the price of chemicals
must be 8xWeu.
If the EU would produce food, the price would be 2xWeu. As we have assumed that only Kenya
produces food, this price must be higher than the actual food price (=4). We conclude therefore that
2xWeu < 4, or Weu < 2. Similarly, Kenya can also produce chemicals. If it did, the price would be
24 (24x1), as it requires 24 units of Kenyan labour to produce one unit of chemicals and the Kenyan
wage is one. As Kenya does not actually produce chemicals, this price must be higher than the price
currently prevailing (8, see above). We conclude, therefore, that 8xWeu < 24, or Weu < 3.
Combining this information, we can conclude that the EU wage rate is at least twice as high as the
Kenyan wage rate, and at most three times.
If the differences in relative productivity are very large, the net trade flow is generally in accordance
with the comparative cost advantage.
3.8 More countries and world PPF
So far we have restricted ourselves with two final goods and two countries. Both restrictions can be
relaxed quite easily, as long as we continue to restrict ourselves to the analysis of only one
production factor:
More goods. Analyse a setting with many goods ranked from high to low in terms of
comparative advantage, say for the EU. If we use the index i to identify a good and there are
N goods, i = 1, … , N, then the EU will have the highest comparative advantage for good
one, second highest for good two, etc. There is a crucial good, say n, such that the EU will
produce the goods 1, … , n and the other country produces the goods n+1, … N. Each
country therefore produces the range of goods for which its comparative advantage is
highest.
More countries. Suppose there are four countries, each able to produce two goods (food and
chemicals). First illustrate the production possibility frontiers for each of the four individual
countries. Then draw the world production possibility frontier; that is, all combinations of
efficient production points for the world as a whole.
The maximum world production level of food, Fmax say, obtains if all four countries only produce
food. As country A has the flattest slope of its production possibility frontier, indicating that its
opportunity costs for producing food are highest, it will be the first country to stop producing food;
that is, close to Fmax the slope of the world PPF is equal to the slope of country A's PPF. Once
point E0 is reached, country A will have completely specialized in the production of chemicals. As
country B has the second flattest slope of its PPF, country B will be the second country to start
producing chemicals. This process continues until all countries specialize in the production of
chemicals at Cmax.The various dashed lines connecting Fmax and Cmax depict the world PPF.
Once we have derived the world PPF it is easy to determine the world production point in a free
trading equilibrium. Suppose, for example, that the relative price of chemicals is equal to Pc0/Pc0.
Then, the maximum value of world production is obtained at point E0; that is, country A will
produce chemicals and the other three countries will produce food. Country A will, therefore, export
chemicals in exchange for food with the other three countries. Next, suppose that the relative price
of chemicals is equal to Pc1/Pf1. Then, the maximum value of world production is obtained at point
E1; that is, country D will produce food an the other three countries will produce chemicals.
Country D will, therefore, export food in exchange for chemicals with the other three countries, and
similarly for other relative prices.
,3.9 Measuring trade advantages: the Balassa index
The index used to establish a country's 'revealed comparative advantage' is known as the Balassa
index:
Many countries are, for example, producing and exporting cars. To establish whether a country, say
Japan, holds a particularly strong position in the car industyr, Balassa argued that one should
compare the share of car exports in Japan's total exports with the share of car exports in a group of
reference country's total export. More specifically, if BIaj is country A's Balassa index for industry
j, this is equal to:
BIaj = share of industry j in country A exports
share of industry j in reference country exports
If Bia(j-1), country A is said to have a revealed comparative advantage in industry j, as this industry
is more important for country A's exports than for the exports of the reference countries.
In general, sectors with a high comparative advantage tend to sustain this advantage for a fairly long
time. Changes over extended period of time are, however, also possible.
Chapter 4
4.2 Neoclassical economics
There are four main results of neoclassical trade theory, namely:
The factor price equalization proposition. International free trade of final goods between
two nations leads to an equalization of the rewards of the factors of production in the two
nations.
The Stolper-Samuelson proposition. An increase in the price of a final good increases the
reward to the factor of production used intensively in the production of that good.
The Rybczynski proposition. An increase in the supply in a factor of production results in
an increase in the output of the final good that uses this factor of production relatively
intensively.
The Heckscher-Ohlin proposition. A country will export the good that intensively uses the
relatively abundant factor of production.
4.3 General structure of the neoclassical model
General assumptions:
There are two countries, Austria (A) and Bolivia (B), two final goods, manufactures (M) and
food (F), and two factors of production, capital (K) and labour (L).
Production in both sectors is characterized by constant returns to scale. The two final goods
sectors have different production functions.
The state of technology is the same in the two countries, such that the production functions
for each sector are identical in the two countries. Any trade flows arising in the model,
therefore, do not result from Ricardian-type differences in technology.
The input factors capital and labour are mobile between the different sectors within a
country, but are not mobile between countries.
All markets are characterized by perfect competition. There are no transport costs for the
, trade of final goods between nations.
The demand structure in the two countries is the same.
The available amounts of factors of production, capital and labour, may differ between the
two nations. These differences in factor abundance will give rise to international trade flows.
4.4 Production functions
If there are two or more inputs needed to produce a final good, we call the set of all efficient input
combinations an isoquant:
The isoquant can be derived from the production function. The same level of output can be
produced using many different combinations of capital and labour. See figure 4.2 (p. 79). Note that
if very little of an input is used it becomes harder to substitute this input for another input. The
extent to which additional capital is needed to substitute for labour depends, of course, on the value
of the parameter (a)m. For higher levels of the capital intensity parameter (a)m the isoquant is tilted
towards the capital axis.
4.5 Cost minimization
In our model the best a firm can do is to ensure that it does not make a loss.
The problem facing an entrepreneur in the manufacturing sector trying to minimize the costs for
producing one unit of output is illustrated in figure 4.5 (p. 84). As the entrepreneur can choose
between two different inputs, we first have to determine the level of costs associated with a certain
input combination before we can determine how to minimize the level of these costs. The
entrepreneur takes the price level of labour, the wage rate w, and the price level of capital, the rental
rate r, as given. If the firm hires Lm labour and Km capital, total costs with this input combination
are:
costs = wLm + rKm
Obviously, different input combinations of capital and labour can give rise to the same cost level.
Such isocost combinations are straight lines in labour-capital space, with a slope equal to -w/r, this
is illustrated by the isocost line.
Graphically, the cost minimization problem facing the entrepreneur is quite simple: move the
dashed isocost line down to the south-west as far as possible, with the restriction that at least one of
the input combinations on the isocost line is able to produce one unit of manufactures (M=1). This
gives the optimal input combination, using Km(w,r) units of capital and Lm(w,r) units of labour.
Figure 4.5 also illustrates the optimal relative input combination Km/Lm. This corresponds to the
following optimal relative input combination (capital-labour ratio) for manufactures and food:
Km = (a)m x w ; Kf = (af) x w
Lm (1-a)m r Lf (1-a)f r
The optimal capital-labour ratio depends on two factors:
The ratio is higher if the capital intensity parameter (a) rises;
The ratio is higher if the wage-rental ratio w/r rises
4.6 Impact of wage rate and rental rate
The optimal input of labour and capital depends on the wage-rental ratio. Three issues are
important:
First, the cost-minimizing input combination depends only on the wage-rental ratio, not on
their absolute levels; an equiproportional change in the wage rate and the rental rate does not
change the slope of the isocost lines, and therefore does not affect the cost-minimizing input
combination. An equiproportional change in input prices does, however, change the cost
level.
