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Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1900 Suppose the price of the...

Assume that a competitive firm has the total cost function: TC=1q3−40q2+740q+1900 Suppose the price of the firm's output (sold in integer units) is $550 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.

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Answer #1
Q TC MC P = MR Total profit
0 1900 550 -1900
1 2601 701 550 -2051
2 3228 627 550 -2128
3 3787 559 550 -2137
4 4284 497 550 -2084
5 4725 441 550 -1975
6 5116 391 550 -1816
7 5463 347 550 -1613
8 5772 309 550 -1372
9 6049 277 550 -1099
10 6300 251 550 -800
11 6531 231 550 -481
12 6748 217 550 -148
13 6957 209 550 193
14 7164 207 550 536
15 7375 211 550 875
16 7596 221 550 1204
17 7833 237 550 1517
18 8092 259 550 1808
19 8379 287 550 2071
20 8700 321 550 2300
21 9061 361 550 2489
22 9468 407 550 2632
23 9927 459 550 2723
24 10444 517 550 2756
25 11025 581 550 2725

Profit = P x Q - TC

MC (nth unit) = TC (n units) - TC ((n-1) units)

Profit is maximized when MR > = MC for the last unit produced (MC must be increasing)

optimal output = 24

Total profit = 2756

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