Question

Imagine an island with many people on it, each of whom can catch some number of fish or pick some number of coconuts (each person's numbers being different from the rest). Now imagine that they discover a new invention--the ladder! The ladder allows every person to pick twice as many coconuts as before.

a. What happens to the marginal cost of fish for each person and what happens to the marginal cost of coconuts?

b. Sketch the PPF and show how it shifts with the new invention. (There are no numbers in this problem, but I want it to have the proper shape. Make sure to clearly indicate which is the old one and which is the new one.)

c. Assume that on the island is a market where people trade fish for coconuts? What do you think will happen to the price of fish and the price of coconuts after this new invention? Show this on a graph of the coconut market and also on another graph of the fish market. (Hint: Who buys fish on this island?)

Note: There is no money on the island. The price of fish is measured in coconuts and the price of coconuts is measured in fish. This means that in some sense there is only one price. And in fact, there is only one market. But we can look at it from two different angles (fish market or coconut market)!

d. Does this new invention make coconut producers better off or worse off? What about fish producers?

Answer 1

Answer: It is given that in the island, people surive on two goods: Fish and Coconuts. A new invention allows the people to be twice as productive in coconut production (i.e coconut picking) than they were before.

(a): The marginal cost of fish for each person is the cost incured by the islanders in catching fish. Since there is no invention to enhance the fish catching and the current invention does not stymie the fish catch, the marginal cost of fish for each person does not change. The marginal cost of coconuts of each person is the cost incured by the islanders in picking coconuts. Since the new invention allows the producers (or, pickers) to double their productivity, the marginal cost of coconut picking falls by half.

(b): PPF measures the maximum output an economy can produce while utilising all its resources and given the production technology. The intercepts of the PPF represents maximum of each goods produced when all the resources available are devoted to production of that unit.

The invention shifts the PPF's horizontal intercept by twice (since MC is halved) while it does not change the vertical intercept (since MC does not change). The horizontal intercept measures the output of Coconuts while the vertical intercept measures the output of Fishes.

The shape of the PPF is linear since the opportunity costs are constant. The red line in the dagram is the new PPF and the black line is the initial PPF.

(c): Since there is no money on the island, and the price of fish is measured in coconuts and the price of coconuts is measured in fish. With the new invention, the production and supply of coconuts doubles in the market (assuming the people produce the commodities they specialize in, i.e. a person either produces fish or coconuts) which, with no change in demand, leads to a fall in price of coconuts and increase in quantity consumed. This implies that the producers of coconuts will have to accept lower amount of fishes for each unit of coconut exchanged.

The diagram given below presents the market for coconuts: The red line indicates the new supply curve. The quantity consumed increases from C₀ to C₁ while the price falls from P₀ to P₁.

Since, there is no change in the technology or the marginal cost of fish, the market for demand or supply of fish does not change and the prices and quantity changed remains same. The below diagram show the market for fishes:

The above diagram represents the partial equilibrium analysis (since there is not explicit mention of general equilibrium analysis). In case of a general equilibrium analysis, the demand curve for fishes would shift left and raise the price of coconut (or lower the price of fish) which, in turn, would shift the demand curve for coconuts to the left. This process would go on until the markets (both of them) reach a point where both the markets are simultaneously in equilibrium.

(d): The new invention makes the coconut producers worse off, since it lowers the amount of fishes recieved in exchange for a unit of coconut.

The new invention makes the fish producers better off, since it raises the amount of coconuts recieved in exchange for a unit of fish.