Question

Q3. Assume that a competitive firm has the total cost function: TC=1q3-40q2+890q+1800 Suppose the price of the firm's output (sold in integer units) is $600 per unit. Using tables (but not calculus) to find a solution, what is the total profit at the optimal output level? Please specify your answer as an integer.

Answer 1

ANSWER:

QUANTITY (Q)	TOTAL COST (Q^3 - 40Q^2 + 890Q + 1800)	PRICE
1	= (1^3 - 40 * (1) ^ 2 + 890 * 1 + 1800 = 2651	600
2	= (2^3 - 40 * (2) ^ 2 + 890 * 2 + 1800 = 3428	1200
3	= (3^3 - 40 * (3) ^ 2 + 890 * 3 + 1800 = 4137	1800
4	= (4^3 - 40 * (4) ^ 2 + 890 * 4 + 1800 = 4784	2400
5	= (5^3 - 40 * (5) ^ 2 + 890 * 5 + 1800 = 5375	3000
6	= (6^3 - 40 * (6) ^ 2 + 890 * 6 + 1800 = 5916	3600
7	= (7^3 - 40 * (7) ^ 2 + 890 * 7 + 1800 = 6413	4200
8	= (8^3 - 40 * (8) ^ 2 + 890 * 8 + 1800 = 6872	4800
9	= (9^3 - 40 * (9) ^ 2 + 890 * 9 + 1800 = 7299	5400
10	= (10^3 - 40 * (10) ^ 2 + 890 * 10 + 1800 = 7700	6000
11	= (11^3 - 40 * (11) ^ 2 + 890 * 11 + 1800 = 8081	6600
12	= (12^3 - 40 * (12) ^ 2 + 890 * 12 + 1800 = 8448	7200
13	= (13^3 - 40 * (13) ^ 2 + 890 * 13 + 1800 = 8807	7800
14	= (14^3 - 40 * (14) ^ 2 + 890 * 14 + 1800 = 9164	8400
15	= (15^3 - 40 * (15) ^ 2 + 890 * 15 + 1800 = 9525	9000
16	= (16^3 - 40 * (16) ^ 2 + 890 * 16 + 1800 = 9896	9600
17	= (17^3 - 40 * (17) ^ 2 + 890 * 17 + 1800 = 10283	10200
18	= (18^3 - 40 * (18) ^ 2 + 890 * 18 + 1800 = 10692	10800
19	= (19^3 - 40 * (19) ^ 2 + 890 * 19 + 1800 = 11129	11400
20	= (20^3 - 40 * (20) ^ 2 + 890 * 20 + 1800 = 11600	12000

The optimal output level are the no of units where total price equals or exceeds the total cost.

so in this case it happens when the quantity is 18.

Total profit at 18 units = total price at 18 units - total cost at 18 units = 10,800 - 10,692 = 108

so the total profit is $108.