Question

Consider a firm with total costs represented by TC=8+1/2Q²

^{and a corresponding marginal cost of Q(MC=Q)}

^{1) Graph the ATC and MC, be certain to label the lowest point of the ATC}

Consider that the firm faces a price of $10

2) Find the optimal quantity

3) Using the ATC/MC graph, find and diagram, the total cost, total revenue, and any profit or loss at the optimal quantity.

Answer 1

1.

When TC = 8+1/2Q2 and MC = Q

Then, following ATC and MC curve are developed.

Q	ATC = 8/Q +1/2Q	MC = Q
1	8.5	1
2	5	2
4	4	4
6	4.333333333	6
8	5	8
10	5.8	10
12	6.666666667	12
14	7.571428571	14
16	8.5	16
18	9.444444444	18
20	10.4	20
22	11.36363636	22

2.

When P = $10, then graph is as follows. Optimal quantity is shown at E ( Q = 10)

3.

Total revenue = Gree area

Total cost = brownish green area

Profit = Gree area - brownish green area

Profit = total revenue - total cost = 10*10 - 58

Profit = $42