Q.A perfectly competitive firm has $TFC = Rs.\,80$ and $TVC = Q^{2}+10Q$. If the market price falls to Rs. 12 per unit, should the firm continue producing or shut down in the short run? Show your reasoning with the relevant cost figures at the firm's best available output.

Find the output where P=MC, then compare the given price with AVC at that output to decide continue vs. shutdown.

$TC=80+Q^{2}+10Q$, so $MC=2Q+10$. Setting $P=MC$: $12=2Q+10 \Rightarrow Q=1$. $AVC=TVC/Q=(1+10)/1=11$. Since $P(12)>AVC(11)$, continue producing (though the firm makes an overall loss since $ATC=(80+11)/1=91$).

$TC=TFC+TVC=80+Q^{2}+10Q$, so $MC=\dfrac{d(TC)}{dQ}=2Q+10$.

Setting $P=MC$ at the given price of Rs. 12:

At $Q=1$: $TVC=1^{2}+10(1)=11$, so $AVC=TVC/Q=11/1=Rs.\,11$. $TC=80+11=91$, so $ATC=91/1=Rs.\,91$.

Comparing the given price to AVC: $P=12 > AVC=11$, so the firm should CONTINUE producing — it earns Rs. 1 per unit over and above variable cost, which goes toward covering part of its fixed cost. However, since $P=12$ is far below $ATC=91$, the firm is making a substantial overall LOSS ($TR-TC=12-91=-79$) — continuing is still the loss-MINIMISING choice, not a profitable one, because shutting down would mean losing the entire Rs. 80 fixed cost instead of only Rs. 79.

Students sometimes conclude "shut down" purely because the firm is making an overall loss — the correct test is always whether price covers AVC, not whether price covers full ATC; a firm covering AVC but not ATC should still continue in the short run.