Question

Robinson is stranded on an island. He only has 24 labor hours in a day, but must sleep for 8 of these hours. The remaining time can be divided between two tasks: fishing (F) and harvesting coconuts (C) . Let Lf and Lc represent time spent allocated to fishing and coconuts respectively. The production of fish and coconuts correspond to the functions C = sqrt(Lc) and F = sqrt(Lf)

Which of the following allocations of (C, F) are Pareto efficient? (check all that apply)

1. (3, 3)

2. (4, 0)

3. (0, 4)

4. (2, 2)

Answer 1

The correct options are B and C

Reason

Since he has 24 hours in a day and he sleeps for 8 hours, thus he has (24-8) = 16 hours for fishing and collecting coconuts.

So, for option A, number of hours required for (3,3) is 3^2+3^2=18 hours which can not be allocated.

For option B, number of hours required for (4,0) is 4^2=16 hours which is exactly the time he can use at max.

For option C, number of hours required for (0,4) is 4^2=16 hours which is exactly the time he can use at max.

For option D, number of hours required for (2,2) is 2^2+2^2=8 hours which is lower than the 16 hours he can allocate.

Thus, the pareto efficient ourcomes are B and C only.