**Draw an example of a production possibilities frontier for Robinson Crusoe, a shipwrecked sailor who spends his time gathering coconuts and catching fish. Does this frontier limit Crusoe's concumption of coconuts and fish if he lives by himself? Does he face the same limits if he can trade with natives on the island?**

Suppose Robinson spends 8 hours working in a day and he can catch 1 fish or gather 1 unit of coconut in every hour. Then the quantity of coconuts produced in 1 day + the quantity of fish produced in 1 day = 8.

Figure 3-1 shows Robinson Crusoe's production possibilites frontier for gathering coconuts and catching fish. If Crusoe lives by himself, this frontier limits his consumption of coconuts and fish, but if he can trade with natives on the island, he will possibly be able to consume at a point outside his production possibilities frontier.

**Since Crusoe lives by himself, the quantity produced equals to the quantity consumed. This frontier does limit Crusoe's consumption of coconuts and fish because for each unit of fish he consumes he has to give up 1 unit of coconut. However, he won't face the same limits if he can trade with natives on the island simply because trade can make everyone better off, allowing his consumption to reach a point outside the PPF.**

Robinson Crusoe can gather 10 coconuts or catch 1 fish per hour. His friend Friday can gather 30 coconuts or catch 2 fish per hour. What is Crusoe's opportunity cost of catching one fish? What is Friday's? Who has an absolute advantage in catching fish? Who has a comparative advantage in catching fish?

Crusoe's opportunity cost of catching one fish is 10 coconuts. Friday's opportunity cost of catching one fish is 30 coconuts. Friday has an absolute advantage in catching fish. Crusoe has a comparative advantage in catching fish.

Crusoe's opportunity cost of catching one fish is 10 coconuts, since he can gather 10 coconuts in the same amount of time it takes to catch one fish. Friday's opportunity cost of catching one fish is 15 coconuts, since he can gather 30 coconuts in the same amount of time it takes to catch two fish. Friday has an absolute advantage in catching fish, since he can catch two per hour, while Crusoe can catch only one per hour. But Crusoe has a comparative advantage in catching fish, since his opportunity cost of catching a fish is less than Friday's.

**Suppose that the world's fastest typist happens to be trained in brain surgery. Should he do his own typing or hire a secretary? Expain.**

To finish the workload of typing, he can either type himself or hire a secretary. Suppose typing by himself takes him x hours, spending which on brain sugery will bring him $Y, and hiring a secretary to do the same workload costs him $Z. Now the marginal cost of hiring a secretary is $Z while the marginal benefit is $Y.

If Y > Z, then he should hire a secretary.

If Y < Z, then he shouldn't.

If the world's fastest typist happens to be trained in brain surgery, he should hire a secretary because the secretary will give up less for each hour spent typing. Although the brain surgeon has an absolute advantage in typing, the secretary has a comparative advantage in typing because of the lower opportunity cost of typing.