Farmer Brian has 3 acres of land which he farms efficiently

Farmer Brian has 3 acres of land which he farms efficiently. Each acre can support 20 apple trees. However the 3 acres differ in their ability to support orange trees. He can grow 40 orange trees on the best land, 20 orange trees on the ok land, and 10 orange trees on the bad land. If he initially is growing oranges on two acres, what would be the opportunity cost of growing another orange tree? A. 60 apple trees B. 3 apple trees C. 2 apple trees D. 1 apple tree E. 1/2 of an apple tree F. 1/3 of an apple tree *The answer is 2 but can you explain how you got there

Solution

Tree

Best

Ok

Bad

Apple Tree

60

20

20

20

Orange Tree

70

40

20

10

For the last acre of land

No. of Apple tree = 20

No. of orange tree = 10

The farmer is already growing oranges in the Best and Ok land and hence

In the bad land

Portion of land required to grow 1 orange tree = 1/10 = .10

Portion of land required to grow 1 Apple Tree = 1/20 = .05

So, in the 0.10 portion of the land farmer can grow = 0.10/0.05 = 2 Apple tree

Hence the opportunity cost of growing 1 more orange tree are 2 Apple Trees.