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I'm given this question. I'm not sure if I'm doing it right. Can any one help?

 Given the following short-run cost function: C=0.04q3 - 0.9q2 + 10q + 5
    
    And the constant price of the final commodity of $4 for the firm, determine: 
a. The best level of output for the firm; 
b. The level of profit the firm makes at this level of output;

My answer:

a) Best level of output would be: MR which is 4, since price is 4, perfect competition, MC is the derivative of total cost, which is 0.12q^2-0.18q+10, then equating, 4=0.12q^2-0.18q+10, so q=0.75

b) putting q=0.75 and multiplying price by quantity, level of profit would be 4*0.75

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    $\begingroup$ Verifying answers is not what we usually do here. Your post should include in detail the steps you took to arrive at your answers. $\endgroup$ Dec 13, 2020 at 18:05
  • $\begingroup$ @AlecosPapadopoulos- I edited using my steps in details. I hope its fine now. $\endgroup$
    – user31619
    Dec 13, 2020 at 19:01
  • $\begingroup$ I’m voting to close this question because it is poorly formulated with no effort $\endgroup$ Dec 16, 2020 at 18:41

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Your first answer would be correct conceptually if this was an interior solution. (The math is incorrect because 2*0.9=1.8 and not 0.18).

However, note that the price falls below the average variable cost. So the firm is better off not producing at all both in the short and long term.

As for your second question: you confuse revenue with profit. Revenue is $p*q$, profit is $p*q-c(q)$

For good measure here are two graphs: one depicts profit for q=0 to 20. Clearly it's negative for the full range profit

And here's one depicting average variable costs which you can see never falls below 4.

average variable costs

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