Question

Suppose that you are on a desert island and possess exactly 20 coconuts. Your neighbor, Friday, is a fisherman, and he is willing to trade 2 fish for every 1 coconut that you are willing to give him. Another neighbor, Kwame, is also a fisherman, and he is willing to trade 3 fish for every coconut.

1. On a single figure, draw budget lines for trading with Friday and for trading with Kwame. (Put coconuts on the vertical axis.)
2. What is the slope of the budget line from trading with Friday?
3. What is the slope of the budget line from trading with Kwame?
4. Which budget line features a larger set of attainable combinations of coconuts and fish?
5. If you are going to trade coconuts for fish, would you rather trade with Friday or Kwame? Why?

Short answer

(a) The budget lines for both Friday and Kwame are as follows.

(b) The slope of the budget line from trading with Friday is 1/2.

(c) The slope of the budget line from trading with Friday is 1/3.

(d) The budget line from trading with Kwame features a larger set of attainable combinations of coconuts and fish.

(e) To trade coconuts for fish, you will deal with Kwame as he can provide more fish for one coconut, and your overall consumption of both commodities will increase.

Step-by-step solution

Explanation for part (a)

The maximum number of coconuts is 20. For each coconut, Friday will give 2 fish. So, for 20 coconuts, Friday can trade 40 fish. Similarly, Kwame can trade 60 fish for 20 coconuts.

Therefore, on the vertical axis, the corner solution is (0,20), and on the horizontal axis, the corner solution for trade with Friday is (40,0), and that for Kwame is (60,0).

Explanation for parts (b) and (c)

The slope of the budget line is the ratio of the units of y commodity sacrificed for a gain of x commodity. As on trading with Friday, you will gain 2 fish in exchange for one coconut each time, the slope of the budget line for trade with Friday is

$Slope=\frac{∆y}{∆x}=\frac{1}{2}$

Similarly, the slope of the budget line for trade with Kwame is

$Slope=\frac{∆y}{∆x}=\frac{1}{3}$

Explanation for part (d)

Kwame has a maximum of 60 fish to offer to the business, while Friday has only 40 fish to offer to the business.So, the budget line from trade with Friday lies inside the attainable area of the budget line from trade with Kwame.

Therefore, the budget line from trade with Kwame covers a broader area of the attainable combination.

Explanation for part (e)

As Kwame can give more fish in exchange for one coconut, the budget line covers a larger portion of attainable combinations. So, the consumption of fish will increase.

Also, the budget line from trade with Kwame shows that the trade will help you to consume more coconuts out of 20, which were previously unused. Therefore, trade with Kwame helps to increase consumption for both the goods. So, you will trade with Kwame to achieve a higher amount of both the goods.