Question

1. Let there be an island with 18 acres of land and 12 people. Each acre of land can be used for farming, forestry, or mining. A farm will provide food worth 25 utility to one person. A forest will provide energy to 1 person, worth 5 utility. A mine will provide energy to 3 people, worth 15 utility total, but will create pollution that will do 1 utlity worth of harm to each person. In the optimal allocation of resources, how much land will be used for mining?

   		0 acres
   		1 acres
   		2 acres
   		3 acres

Answer 1

the answer is (c) 3 acres

the optimal allocation is such that each of the 12 people has food and energy

Now, since 1 farm provides food for only 1 person, 12 farms are needed to provide food for 12 people.

Thus, we are left with 18-12 = 6 acres of land.

In order to provide energy to all 12 people, 3 acres of mine can be used to give energy to 3*3 = 9 people

Remaining acres = 3 and remaining people to provide energy = 3

Thus, 3 forests can be used to give the remaining people energy

Thus, the allocation is optimal and using lower than 3 acres for mines will not provide energy to all the people.