Question

Wilson and Tom are stranded on a desert island. They spend their 30 hour working week producing coconuts and catching crabs, the two goods needed for survival. It takes Tom 1 hour to gather up a coconut and 2 hours to catch a crab. It takes Wilson 3 hours to open a coconut and 3 hours to catch a crab.

1. For each 30 hour week, draw separately the individual PPF for Tom and Wilson. (3 points). On your graph for Tom, show the production level if Tom spends 10 hours crab catching and 20 hours coconut gathering. For Wilson, show the production level if Wilson spends 12 hours crab catching and 18 hours coconut gathering.
2. Explain in which product each should specialize in producing.
3. If Wilson and Tom agree to trade after specializing, what would be the possible trading ratios (range of ratio) that crabs should trade for coconuts.
4. Draw a combined PPC for Tom and Wilson. Show on your graph the gains from trade and specializing and how much they gain.

Answer 1

Based on the information, if Wilson spends entire 30 hours on coconut, he can open 30/3 = 10 coconuts. Similarly, if he spends entire 30 hours to catch crab, he could catch 30/3 = 10 crabs. In other words, to open 10 coconuts, he needs to sacrifice catching of 10 crab. Hence, the opportunity cost of a coconut = 10/10 =1 crab for Wilson. And, the opporrtunity cost of catching a crab = 1 coconut for Wilson. The PPF is shown as the blue line in the diagram.

On the other hand, if Tom spends entire 30 hours on coconut, he can open 30/1 =30 coconuts. Similarly, if he spends entire 30 hours to catch crab, he could catch 30/2 = 15 crabs. In other words, to open 30 coconuts, he needs to sacrifice catching of 15 crabs. Hence, the opportunity cost of a coconut = 15/30 =0.5 crab for Tom. And, the opporrtunity cost of catching a crab = 30/15=2 coconuts for Tom. The PPF is shown as the orange line in the diagram.

If Tom spends 10 hours in crab catching, he will be able to catch 10/2=5 crabs and in rest 20 hours, he will be able to gather and open 20/1=20 coconuts. Hence, the point (20,5) is shown in the diagram as point T.

If Wilson spends 12 hours in crab catching, he will be able to catch 12/3=4 crabs and in rest 18 hours, he will be able to gather and open 18/3=6 coconuts. Hence, the point (6,4) is shown in the diagram as point W.

Since opportunity cost to gather and open coconut is lower for Tom as compared to Wilson, Tom has comparative advantage on coconut and he will specialize on cocnut gathering and opening. On the other hand, the opportunity cost of catching crab is lower for Wilson and he has comparative advantage in this and hence Wilson would specialize in crab catching.

Wilson will be willing to buy coconut if it costs less than 1 crab (his opportunity cost) to get a coconut and Tom will sell coconut if he gets more than 0.5 crab (his opportunity cost). Hence, the trade of coconut can happen with a price range 0.5 crab to 1 crab. In other words, the price of crab will be betwwn 1 coconut (Wilson's opportunity cost of a crab) and 2 coconuts (Tom's opportunity cost for a crab).

The overall PPF cab be derived by adding both the PPFs (Wilson and Tom) vertically as shown in the diagram.