nAnswers to Textbook Problems
1. a. The first step is to compute the opportunity cost of both cloth and food. We are given the
following resource constraints:
Solve these two constraints for the quantity of food produced:
This gives us two budget constraints for food production that must both be met. The production
possibilities frontier traces out these budget constraints for food and cloth production.
Looking at the diagram, we see that production of both food and cloth will take place when the
relative price of cloth is between the two opportunity costs of cloth. The opportunity cost of cloth
is given by the slopes of the two components of the production possibilities frontier above, 2/3
and 2. When cloth production is low, the economy will be using relatively more labor to produce
cloth and the opportunity cost of cloth is 2/3 a unit of food. However, as cloth production rises,
the economy runs scarce on labor and must take capital away from food production, raising the
opportunity cost of cloth to 2 units of food.
b. Note the input requirements for each good. One unit of cloth can be produced using 2 units of
capital and 2 units of labor. One unit of food is produced using 3 units of capital and 1 unit of
labor. In a competitive market, the unit cost of each good must be equal to the output price.
c. Looking at the two expressions above, we see that an increase in the price of cloth will cause the
d. The capital stock increases to 4,000. The labor constraint will remain unchanged, keeping the
maximum price of cloth at 2 units of food. The new capital constraint is given by:
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