The Theory of the Firm Under Perfect Competition

A competitive firm maximizes economic profit when TWO simultaneous conditions are satisfied:
1. Condition 1 (Necessary Condition): $MR = MC$ (or $P = MC$):
As long as $MR > MC$, producing an additional unit adds more to revenue than to cost, increasing total profit. If $MR < MC$, the firm incurs a loss on that unit. Therefore, profits are maximized where $MR = MC$.
2. Condition 2 (Sufficient Condition): $MC$ must be RISING at the point of intersection (cuts $MR$ from below):
If $MC$ is falling when it equals $MR$, producing further units will lower marginal costs below $MR$, yielding even higher profits. That first intersection represents a point of minimum profit. Only when $MC$ cuts $MR$ from below (rising $MC$) is profit at its absolute maximum peak.

• Why Price Taker: In a perfectly competitive market, there are thousands of sellers producing an identical (homogeneous) product. Each individual firm produces an infinitesimal fraction of total industry output. If a firm tries to charge a higher price, buyers will instantly abandon it and purchase identical goods from other sellers. The firm cannot alter market price and must accept the price determined by industry supply and demand.
• Why Horizontal Demand Curve: Because the firm can sell any desired quantity of output at the prevailing market price ($P$), the price remains constant ($P = AR = MR$). A constant price yields a horizontal straight-line demand curve parallel to the X-axis with infinite price elasticity of demand ($E_d = \infty$).

The Short-Run Supply Curve represents the quantities of output a competitive firm is willing to supply at different market prices.
1. A competitive firm produces output where $P = MC$ on the rising portion of its $MC$ curve.
2. Case 1 ($P \ge \min AVC$): As long as market price is equal to or greater than the minimum of Average Variable Cost ($AVC$), the firm covers all its variable operating costs and a portion of fixed costs. It produces output where $P = SMC$.
3. Case 2 ($P < \min AVC$): If price falls below minimum $AVC$, the firm cannot even cover its daily variable expenses (labor, raw materials). It shuts down completely and supplies zero output ($Q = 0$).
Conclusion: The Short-Run Supply Curve of a competitive firm is the rising segment of its Short-Run Marginal Cost ($SMC$) curve that lies on or above the minimum point of its Average Variable Cost ($AVC$) curve.

• Break-Even Point: The point of output where market price equals minimum Average Cost ($P = \min AC$, or $TR = TC$). At this point, the firm earns zero economic profit (Normal Profit)—covering all explicit accounting costs plus implicit opportunity costs.
• Shut-Down Point: The point of output where market price equals minimum Average Variable Cost ($P = \min AVC$, or $TR = TVC$). If price drops below this point, the firm ceases operations immediately because continuing production incurs operating losses greater than its Total Fixed Cost ($TFC$).

In the short run, a firm must pay its Total Fixed Cost ($TFC$) (factory rent, debt interest) even if output is completely zero. Therefore:
• If it shuts down, its loss is exactly equal to $TFC$.
• If market price is above Average Variable Cost ($P > AVC$), every unit sold covers 100% of its variable costs and provides a surplus to pay off a portion of $TFC$.
Its total loss from producing is less than $TFC$. Hence, continuing production minimizes short-run losses compared to shutting down!

Free entry and exit ensures that in the long run, competitive firms can earn only Normal Profit ($P = AC$):
1. If existing firms earn Supernormal Profits ($P > AC$): New firms are attracted into the industry. Total market supply shifts to the right, driving the market price down until supernormal profits are completely wiped out.
2. If existing firms incur Losses ($P < AC$): Unprofitable firms exit the industry. Total market supply contracts, driving market price up until remaining firms break even at normal profits.

Given:
$P_1 = 20, \quad P_2 = 25 \implies \Delta P = 25 - 20 = +5$
$Q_1 = 100, \quad Q_2 = 150 \implies \Delta Q = 150 - 100 = +50$
Formula:

$$E_s = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$

Substitute values:

$$E_s = \frac{50}{5} \times \frac{20}{100} = 10 \times 0.20 = \mathbf{2}$$

Conclusion: Price elasticity of supply is highly elastic ($E_s = 2 > 1$).

The Market Supply Curve is derived through the horizontal summation of the individual short-run supply curves of all existing competitive firms in the industry. At each given market price, the quantities supplied by every individual firm are added together horizontally: $Q_{\text{market}} = \Sigma q_i$.