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 arewilling to give him. Another neighbor, Kwame, is also a fisherman, and he is willing totrade 3 fish for every 1 coconut.
A. On a single figure, draw budget lines for trading with Friday and for trading withKwame. (Put coconuts on the vertical axis.)
B. What is slope of the budget line from trading with Friday?
C. What is slope of the budget line from trading with Kwame?
D. Witch budget line features a larger set of attainable combinations of coconuts andfish?

Answer 1

Answer:

• A. See the figure attached

• B. 1/2

• C. 1/3

• D. Both budget lines have the same number of combinations of coconuts and fish.

Explanation:

A. See the figure attached

To draw the buget line for trading with Friday you can enter some points.

Note that for every coconut you give, Friday will give you 2 fish. Hence:

• number of fish = 2 × number of coconuts
• number of coconuts = number of fish / 2

Fish (horizontal axis)    Coconuts (vertical axis)

            0                                    0

            2                                     1

            4                                     2

            6                                     3

          40                                   20

The range is from 0 coconuts to 20 coconuts, which limits the number of fish to the even umbers bwetween 0 and 40.

B. See the figure attached

For every coconut you give, Kwame will give you 3 fish. Hence:

• number of fish = 3 × number of coconuts
• number of coconuts = number of fish / 3

Fish (horizontal axis)    Coconuts (vertical axis)

            0                                    0

            3                                     1

            6                                     2

            9                                     3

          60                                   20

The range is also from 0 coconuts to 20 coconuts, but now the number of fish is limited to mulitples of 3 between 0 and 60.

B. What is slope of the budget line from trading with Friday?

The slope is the trading rate:

• slope = rise / run = Δy / Δx = 1 coconut / 2 fish

It means that you will give 1 coconut per each 2 fish you receive from Friday.

C. What is slope of the budget line from trading with Kwame?

Again, the slope is the trading rate:

• slope = rise / run = Δy / Δx = 1 coconut / 3 fish

It means that you will give 1 coconut per 3 fish that you receive from Kwame.

D. Witch budget line features a larger set of attainable combinations of coconuts and fish?

Both buget lines have the same number of combinations of coconuts and fish.

For Friday:

• (0,0), (2,1), (4,2), (6, 3), ..... (40, 20), which are 21 combinations if you include (0,0).

For Kwame:

• (0,0), (3,1), (6, 2), (9, 3), . . . (60, 20), which also are 21 combinations.