The total cost function for a firm in a perfectly competitive market is TC = 350 + 15q + 5q2. At its profit maximizing quantity in the short-run, each firm is making a loss but chooses to stay open. Which of the following is/are necessarily true at the profit maximizing quantity?
MR = 15 + 5q
AR > 350/q + 15 + 5q
Both A and B are true.
Both B and C are true.
All of the above are true.
Answer is option B)
since firm is having loss, so price is less than ATC at all output levels , thus ATC = TC/Q = 350/q + 15 + 5q
So price = AR , should be < ATC for losses.
Option c is false.
In perfect competition, P= MC & P = MR = MC
So MC = derivative of TC = 15+ 10 q
Thus P = MR = 15+10q, so option a is false
Hence d & e, f are wrong too.
So to remain in business , price should be at least equal to minimum of AVC = 15
So P should be > 15
AVC = 15+5q, & minimum AVC = 15
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