Question

Farmer Brian has 3 acres of land which he farms efficiently. Each acre can support 10 apple trees. However the 3 acres differ in their ability to support orange trees. He can grow 60 orange trees on the best land, 40 orange trees on the ok land, and 20 orange trees on the bad land.

If he initially is using 2 acres to grow apples, what would be the opportunity cost of growing another orange tree?

At first I assumed that since he already used 2 acres to grow apples, that means that the best land for orange is the only land left. My logic was since in this last land he can either grows 10 apple trees or 60 orange trees, that means if he grow another orange tree, his opportunity cost would be 1/6 or 10/6?

Answer 1

Answer: The correct answer will be 1/6 of an apple tree.

Explanation: Here we first need to find which are the two plots of land where the farmer will actually grow apple and the plot of land in which he will grow oranges.

Given that the farmer initially uses 2 acres of land for growing apple trees he will use those two lands where the opportunity cost of growing apple trees to oranges is the lowest. Now since the farmer will have to give up 60 oranges if he grows apples in best field which is higher than 40 and 20 oranges if he grows apples in okay and bad land respectively, he would use the best field for growing oranges and okay and bad land to grow apples.

Considering the best land first, 60 orange trees will have to be given up for 10 apple trees. So for an extra orange tree the number of apple trees that will have to be given up will be 10/60= 1/6.

Next, if the land is ok land then 40 orange trees will have to be given up for 10 apple trees. As a result for an extra orange tree the number of apple trees that will have to be given up will be 10/40= 1/4.

Next, talking about the bad land, we can see that 20 Orange trees will have to be given up for 10 apple trees. So for one more orange tree, the number of apple trees that will have to be given up will be 10/20=1/2.

So the opportunity cost of growing another orange tree is 1/6 of an apple tree.