Sample Trade and Specialization Problems

Example Problem

Food / Clothing
Person A / 10 / 20
Person B / 15 / 10

(i) Draw the production possibilities curve for both A and B.

(ii) Find the marginal cost of food for A. Find the marginal cost of clothing for A.

(iii) Find the marginal cost of food for B. Find the marginal cost of clothing for B.

(iv) Who has the comparative advantage in food? Who has the comparative advantage in clothing?

(v) Find the price for which A will produce his comparative advantage good. Find the price for which B will produce his comparative advantage good.

(vi) Find the range of prices for which trade will occur.

(vii) Choose a price in that range and draw the consumption possibilities curve for both A and B.

Problem 1

Food / Clothing
Person A / 40 / 20
Person B / 15 / 30

(i) Draw the production possibilities curve for both A and B.

(ii) Find the marginal cost of food for A. Find the marginal cost of clothing for A.

(iii) Find the marginal cost of food for B. Find the marginal cost of clothing for B.

(iv) Who has the comparative advantage in food? Who has the comparative advantage in clothing?

(v) Find the price for which A will produce his comparative advantage good. Find the price for which B will produce his comparative advantage good.

(vi) Find the range of prices for which trade will occur.

(vii) Choose a price in that range and draw the consumption possibilities curve for both A and B.

Problem 2

Food / Clothing
Person A / 30 / 20
Person B / 20 / 10

(i) Draw the production possibilities curve for both A and B.

(ii) Find the marginal cost of food for A. Find the marginal cost of clothing for A.

(iii) Find the marginal cost of food for B. Find the marginal cost of clothing for B.

(iv) Who has the comparative advantage in food? Who has the comparative advantage in clothing?

(v) Find the price for which A will produce his comparative advantage good. Find the price for which B will produce his comparative advantage good.

(vi) Find the range of prices for which trade will occur.

(vii) Choose a price in that range and draw the consumption possibilities curve for both A and B.

Costs of Trading

Consider Problem 2 again, but now we will impose a cost to trading; or a transaction cost. The production possibilities remain the same. That is,

Food / Clothing
Person A / 30 / 20
Person B / 20 / 10

As before the marginal cost are given by

MC of 1 Food / MC of 1 Clothing
Person A / 2/3 C / 3/2 F
Person B / ½ C / 2 F

In this case, A has the comparative advantage in clothing and B has the comparative advantage in food. And the range of prices for specialization and trade, if there is no transaction cost, is given by

½ C < 1F < 2/3 C

But now suppose the seller of food (person B) must pay a transaction cost of ¼ C for every unit of clothing sold. Then the price he sells at must cover not only his cost of production but also the transaction cost. That is, person B must have a price such that ½ C+ ¼ C < 1F, or ¾ C < 1F. So we have

A’s Condition:1F < 2/3 C

B’s Condition: 1F > ¾ C

Notice there is no way for both conditions to hold. Any price satisfying A cannot satisfy B. Hence trade will not occur because the transaction cost was larger than the gains from trade.

Of course the transaction cost could be small enough that trade is still possible. For example, suppose B’s transaction cost is only 0.1 C. Then B’s condition to trade is ½ C + 0.1 C < 1 F, or 0.6 < 1F. We then have

A’s Condition:1F < 2/3 C

B’s Condition: 1F > 0.6 C

Both conditions can be met and the range of prices is thus given by

0.6C < 1F < 0.67C

Hence the size of the transaction cost is what matters. If it is less than the gains from trade, then trade will occur. If it is greater than the gains from trade then trade will not occur.

Problem 3

Consider the production possibilities from Problem 1, repeated below.

Food / Clothing
Person A / 40 / 20
Person B / 15 / 30

Assume the seller of food must pay a transaction cost of 1C. Will trade occur? What if the transaction cost is 2C?