Question

Assume that a competitive firm has the total cost function:

TC=1q3−40q2+710q+1700TC=

Suppose the price of the firm's output (sold in integer units) is $550 per unit.

By creating tables (but not using calculus) with columns representing cost, revenue, and profit to find a solution, what is the total profit at the optimal output level?

Please specify your answer as an integer

Answer 1

Q	Cost	Revenue	Profit
1	2371	550	-1821
2	2968	1100	-1868
3	3497	1650	-1847
4	3964	2200	-1764
5	4375	2750	-1625
6	4736	3300	-1436
7	5053	3850	-1203
8	5332	4400	-932
9	5579	4950	-629
10	5800	5500	-300
11	6001	6050	49
12	6188	6600	412
13	6367	7150	783
14	6544	7700	1156
15	6725	8250	1525
16	6916	8800	1884
17	7123	9350	2227
18	7352	9900	2548
19	7609	10450	2841
20	7900	11000	3100
21	8231	11550	3319
22	8608	12100	3492
23	9037	12650	3613
24	9524	13200	3676
25	10075	13750	3675
26	10696	14300	3604
27	11393	14850	3457
28	12172	15400	3228
29	13039	15950	2911
30	14000	16500	2500

Cost: TC=1q3−40q2+710q+1700

Revenue: TR = output * price

Note: Price = $550 per unit

We can see that profit is maximum at output level of 24 units.

The total profit at the optimal output level is 3676