Questions: Sophia grows Christmas trees. Her cost of production is shown in the table below. Christmas Trees Total Cost 1 60 2 90 3 162 4 246 5 342 6 450 7 570 Suppose the market for Christmas trees is perfectly competitive and that the market price for Christmas trees is 90 per tree. How many Christmas trees should Sophia grow? Sophia should grow trees. (Enter your response as an integer value.)

To determine how many Christmas trees Sophia should grow, we need to consider the concept of marginal cost (MC) and compare it to the market price. In a perfectly competitive market, a firm maximizes profit by producing up to the point where the marginal cost equals the market price.

Let's calculate the marginal cost for each additional tree:

1. MC for 1st tree = Total Cost for 1 tree - Total Cost for 0 trees = $60 - $0 = $60
2. MC for 2nd tree = Total Cost for 2 trees - Total Cost for 1 tree = $90 - $60 = $30
3. MC for 3rd tree = Total Cost for 3 trees - Total Cost for 2 trees = $162 - $90 = $72
4. MC for 4th tree = Total Cost for 4 trees - Total Cost for 3 trees = $246 - $162 = $84
5. MC for 5th tree = Total Cost for 5 trees - Total Cost for 4 trees = $342 - $246 = $96
6. MC for 6th tree = Total Cost for 6 trees - Total Cost for 5 trees = $450 - $342 = $108
7. MC for 7th tree = Total Cost for 7 trees - Total Cost for 6 trees = $570 - $450 = $120

The market price is $90 per tree. Sophia should produce up to the point where the marginal cost is less than or equal to the market price.

• For the 1st tree, MC = $60, which is less than $90.
• For the 2nd tree, MC = $30, which is less than $90.
• For the 3rd tree, MC = $72, which is less than $90.
• For the 4th tree, MC = $84, which is less than $90.
• For the 5th tree, MC = $96, which is greater than $90.

Therefore, Sophia should grow 4 trees, as the marginal cost of the 5th tree exceeds the market price.

Sophia should grow 4 trees.