Question

Sophia grows Christmas trees. Her cost of production is shown in the table below

Christmas Trees	Total Cost
0	40
1	60
2	108
3	164
4	228
5	300
6	380

Suppose the market for Christmas trees is perfectly competitive and that the market price for Christmas trees is $68 per tree

How many Christmas trees should Sophia​ grow?

What is​ Sophia's profit

Answer 1

In perfect competition, profit is maximized when marginal cost equals marginal revenue. A profit-maximizing firm would produce at a point at which marginal revenue equals marginal cost or the difference between the marginal revenue and marginal cost is minimum.

Let us first calculate the marginal costs for different units of trees:

Trees	Total Cost	Marginal Cost
0	40	-
1	60	60 – 40 = 20
2	108	108 – 60 = 48
3	164	164 – 108 = 56
4	228	228 – 164 = 64
5	300	300 – 228 = 72
6	380	380 – 300 = 80

Therefore, Sophia should grow 4 Christmas trees as when 4 trees is grown, the difference between marginal revenue and marginal cost is minimum.

At this point, profit will be = Total Revenue - Total Cost = 4 * $68 - $228 = $272 - $228 = $44