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While studying, I came across the solution that in some cases only the produces surplus, PS, needs to be positive, however not the profit, $\pi$. That means that if $PS \geq 0; p \geq AVC$, whereas, e.g. in long-run, $\pi \geq 0; p \geq AC$ to supply a positive amount.

I wonder, why the fixed costs need not to be covered in some cases (e.g. $R(Y) \geq VC(y) \Leftrightarrow PS \geq 0)$.

thebilly
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Your question is somewhat wrong in the sense that a firm needn't cover its unavoidable costs (sunk costs). If there are fixed costs that are somewhat avoidable or recoverable (for instance selling an old machine for a salvage value), we need to cover them.

Now coming back to the main question. We can express the profit of a firm using the following equation $$\pi = R-VC-FC$$

Assume that a firm has already incurred an unavoidable FC of \$5000. The VC that the firm is incurring is \$2000 and the revenue (R) of the firm is \$2500. If the firm continues to operate, its net loss from the business will be \$4500, however, if the firm ceases its operation, its loss would amount to \$5000. Thus as long as a firm has a positive contribution ($R-VC$), the firm must continue its operations.

All in all, Microeconomics says that there is no use crying over a spilt milk. If you have already incurred a sunk cost, it is better to get whatever you can.

Harsh Sharma
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  • I can see that for the case of contractually fixed costs, however, for technological fixed costs (TFC), on the other hand, not so much. The conditions for supply change especially in the case of TFC from $p \geq AVC$ in the short-run to $p \geq AC$ in the long-run. – thebilly Jan 17 '20 at 16:20