Question

Sophia grows Christmas trees. Her cost of production is shown in the table below. Christmas Trees VOOR WN Total Cost $80 $120 $216 $328 $456 $600 $760

Suppose the market for Christmas trees is perfectly competitive and that the market price for Christmas trees is

​$120 per tree.

a) How many Christmas trees should Sophia​ grow?

b) What us Sophias profit?

Answer 1

Christmas   Trees	Total Cost	MC	P = MR	TR=P*Q	Profit=TR-TC
1	$80	-	$120	$120	$40
2	$120	$40	$120	$240	$120
3	$216	$96	$120	$360	$144
4	$328	$112	$120	$480	$152
5	$456	$128	$120	$600	$144
6	$600	$144	$120	$720	$120
7	$760	$160	$120	$840	$80

Formulas used in calculation:

1. Marginal cost = Total cost of (n) – Total cost of (n-1)

2. In perfect competition, price = marginal revenue

3. Total revenue = Price * Quantity

4. Profit = Total revenue – Total cost

Answer:

a. Sophia should grow 4 trees to maximize her profits.

When growing 4 trees, marginal cost is less than marginal revenue. If she produces beyond that marginal cost exceeds marginal revenue.

b. Sophia’s Profit = $152

At 4 unit of output, profit is maximum.

Profit = Total revenue – Total cost

Profit = $480 - $328

Profit = $152