Question

 Since Wakanda has no access to ocean, fish is a rare commodity there. Fish can be produced by either fishing it from the lake (wild catch), or faming from the ponds. The quality of fish caught in the like is equal to farm-raised fish. However, the productivity of workers in the ponds is always 2 fishes per hour. The productivity of fishermen depends on how many fisherman are currently fishing:

 if there is just one fisherman on the lake, his productivity is 6 fishes per hour per fisherman:

 if there are two fishermen on the lake, their productivity is 5 fishes per hour per fisherman;

 if there are three fishermen on the lake, their productivity s 4 fishes per hour per fisherman;

 if there are four fishermen on the lake, their productivity is 3 fishes per hour per fisherman;

 if there are five fishermen on the lake, their productivity is 2 fishes per hour per fisherman;

 if there are six fishermen on the lake, their productivity is one fish per hour per fisherman.

 There are only 6 fishermen in Wakanda. What is the socially-optimal allocation of fishermen between the lake and ponds? How many fishes will be caught? Briefly explain.

Answer 1

Lake		Pond
Fishermen	Fishes	Fishermen	Fishes	Total Fishes
0	0	6	12	12
1	6	5	10	16
2	10	4	8	18
3	12	3	6	18
4	12	2	4	16
5	10	1	2	12
6	6	0	0	6

Socially optimum allocation will be 3 fishermen to the lake and 3 in pond or 2 in the lake and 4 in the pond
Total fishes caught = 18