Q.A firm operating under perfect competition has the short-run total cost function $TC = Q^{2} + 5Q + 50$. The prevailing market price is Rs. 45 per unit. Find the firm's equilibrium output, its total revenue, total cost, and profit at that output, and state whether the firm should continue producing in the short run.

A firm is in equilibrium (maximum profit) where MC = MR, so the answer is option (b).

A firm reaches equilibrium at the output level where its profit is maximised. This requires two conditions:

1. Marginal Cost = Marginal Revenue (MC = MR) — the necessary condition.
2. MC cuts MR from below (MC is rising and its slope is greater than that of MR) — the sufficient condition.

If MR > MC, producing one more unit adds more to revenue than to cost, so the firm should expand. If MC > MR, the last unit costs more than it earns, so the firm should cut back. Profit is therefore largest exactly where MC = MR. (MR = Price is true only in perfect competition and is a special case, not the general equilibrium condition.)

Price and quantity supplied move in the same direction, so the relationship is positive (direct).

The law of supply states that, other things remaining constant, the quantity supplied of a commodity rises as its price rises and falls as its price falls. A higher price makes production and sale more profitable, encouraging firms to supply more; a lower price does the reverse. Because both variables move together, the supply curve slopes upward from left to right and the price–supply relationship is positive. (This is the opposite of the demand relationship, which is negative.)

A firm's equilibrium (profit-maximising) condition is MC = MR.

A firm keeps expanding output as long as each extra unit adds more to revenue than to cost (MR > MC), and it will not produce a unit that costs more than it earns (MC > MR). Profit is therefore maximised at the output where the two are equal, MC = MR (with MC rising, i.e. cutting MR from below). This is the first-order condition of firm equilibrium under all market structures and is central to price–output determination in the Tamil Nadu HSC Class 11 Economics syllabus.

Perfect competition assumes (a) homogeneous goods.

Perfect competition is a market with a very large number of buyers and sellers where firms have no control over price. A key assumption is that all firms produce a homogeneous (identical) product, so the goods of one seller are perfect substitutes for those of another. Because buyers cannot distinguish between sellers' products, a single uniform price prevails throughout the market and each firm is a price-taker.

Why the others are wrong:

• (d) Differentiated goods are a feature of monopolistic competition, not perfect competition.
• (b) Luxury goods and (c) Producer goods describe types of goods, not an assumption of the market form.

This is a standard assumption listed in the TN HSC Class-11 Economics market structure chapter.