Question

1) Katie and Dena find themselves on a deserted island. The only two activities available are fishing and picking apples. In a full day, Katie can catch 5 fish or find 15 apples or some linear combination of the two; in the same time, Dena can catch 8 fish or find 16 apples or some linear combination of the two. When left on their own, without trade, Katie decides to consume 4 fish per day and Dena also decides to consume 4 fish per day.

a) When Katie and Dena specialize and trade, would trading fish for apples on a 1 for 1 basis be acceptable to Katie without making her worse off? Briefly explain your answer. What is the most that Katie would be willing to pay in order to trade for the good that she does not have a comparative advantage in producing? (assume she would be willing to trade as long as she is not made worse off by the trade)

b) Suppose that, after specialization and trade, Katie ends up consuming 4 fish and 5 apples each day and Dena ends up consuming 4 fish and 10 apples each day. Are either Katie or Dena capable of producing these consumption bundles on their own without trade (i.e. are these consumption bundles outside of their individual PPF)? Briefly explain. (2 points)

c) When Katie and Dena specialize and trade, would trading fish for apples on a 1 for 1 basis be acceptable to Dena without making her worse off? Briefly explain your answer. What is the most that Dena would be willing to pay in order to trade for the good that she does not have a comparative advantage in producing? (assume she would be willing to trade as long as she is not made worse off by the trade)

Answer 1

1) Katie can get 5 fish or 15 apples whereas, Dena can get 8 fish or 16 apples.

Plotting fish on vertical axis and apples on the horizontal axis, PPF curve for Katie has a vertical intercept of 5 and horizontal intercept of 15. Similarly, PPF curve for Dena has a vertical intercept of 8 and horizontal intercept of 16.

Without trade, both Katie and Dena are consuming on their PPF curves, i.e, Katie consumes 4 fishes and 3 apples whereas, Dena consumes 4 fishes and 8 apples.

Now, opportunity cost of getting fish for Katie = number of apples sacrificed/number of fish caught = 15/5 = 3

and opportunity cost of getting apples for Katie = number of fishes sacrificed/number of apples caught = 5/15 = 0.33

Similarly, opportunity cost of getting fish for Dena = number of apples sacrificed/number of fish caught = 16/8 = 2

and opportunity cost of getting apples for Dena = number of fishes sacrificed/number of apples caught = 8/16 = 0.5

As opportunity cost of catching fishes is lower for Dena, Dena has comparative advantage in catching fishes, whereas, as opportunity cost of catching apples is lower for Katie, Katie has comparative advantage in catching apples.

a. With trade Katie must specialize in apples only and Dena must specialize in fish only .

Terms of trade must lie in between the relative price for both of them

i.e., relative price in terms of fish for Dena < Terms of trade < relative price in terms of fish for Katie

or, 16/8 apples per fish < TOT < 15/5 apples per fish

or, 2 apples per fish < TOT < 3 apples per fish.

Here, Katie will trade a maximum of 3 apples per fish whereas, Dena will trade a minimum of 2 apples per fish.

Now, Katie will be better off with trade if exchange rate is 1 apple per unit of fish. However, at this rate Dena will not trade as she will be worse off.

b. Both Katie and Dena cannot produce these consumption levels of their own without trade. This is because the new consumption points lie above their individual PPF curves.

c. As Dena has a comparative advantage in the production of fish, it will trade a minimum of 2 apples per unit of fish. Thus, Dena will be worse off at 1 fish to 1 apple exchange rate.