Economics: Class 12 (Part 2) — Chapter 4: The Theory of the Firm under Perfect Competition

• Large Number of Buyers and Sellers: No single buyer or seller is large enough to influence the market price. Each agent is a price-taker.
• Homogenous Product: The products of all firms are identical in terms of quality, size, and features. Buyers are indifferent about which firm they purchase from.
• Free Entry and Exit: Firms can easily enter or leave the industry in the long run without facing legal or financial barriers.
• Perfect Information: All buyers and sellers have complete and instantaneous knowledge of prices, product quality, and market conditions.

Because of these features, a firm must accept the prevailing market price:

• If a firm sets a price above the market price, it loses all its buyers to competitors.
• There is no incentive to set a price below the market price because the firm can sell any quantity it wants at the market price.

Total Revenue is the total money receipt of a firm from the sale of its output. It is calculated as:

Where $p$ is the market price and $q$ is the quantity sold. Since $p$ is constant, the TR curve is an upward-sloping straight line passing through the origin.

• Average Revenue (AR): Revenue earned per unit of output. Under perfect competition, AR equals the market price:
  $$AR = \frac{TR}{q} = \frac{p \times q}{q} = p$$
• Marginal Revenue (MR): The change in total revenue resulting from selling one additional unit of output:
  $$MR = \frac{\Delta TR}{\Delta q} = p$$

Thus, for a perfectly competitive firm, MR = AR = p. The demand curve facing the firm is a horizontal straight line at the market price, representing a perfectly elastic demand.

For a firm to maximize profits at an output level $q_0$, three conditions must be satisfied:

1. Condition 1: The market price $p$ must equal the marginal cost ($MC$):
   $$p = MC$$
2. Condition 2: Marginal cost must be non-decreasing (i.e., the MC curve must be upward-sloping) at $q_0$.
3. Condition 3:
   • In the short run, price must be greater than or equal to the average variable cost ($p \ge AVC$).
   • In the long run, price must be greater than or equal to the average cost ($p \ge AC$).

The short run supply curve of a firm is divided into two parts:

• For prices equal to or greater than the minimum of $AVC$, the supply curve is the rising part of the Short-run Marginal Cost ($SMC$) curve.
• For prices strictly less than the minimum of $AVC$, the firm produces zero output.

The long run supply curve of a firm is divided into two parts:

• For prices equal to or greater than the minimum of $LRAC$, the supply curve is the rising part of the Long-run Marginal Cost ($LRMC$) curve.
• For prices strictly less than the minimum of $LRAC$, the firm produces zero output.

• Shut Down Point: The minimum point of the $AVC$ curve in the short run (or $LRAC$ in the long run) below which the firm stops production.
• Normal Profit: The minimum level of profit required to keep a firm in its current business. It is treated as an opportunity cost and is included in total cost.
• Super-normal Profit: Profit earned over and above normal profit.
• Break-even Point: The point on the supply curve where the firm earns only normal profits (where $p = \text{minimum } AC$).

• Technological Progress: Organizational or technological innovations lower marginal costs, shifting the $MC$ curve rightward (downward). This shifts the supply curve to the right, meaning more output is supplied at any given price.
• Input Prices: An increase in input prices (e.g., wages, raw materials) raises production costs, shifting the $MC$ curve leftward (upward). This shifts the supply curve to the left.
• Unit Tax: A tax imposed per unit of output sold increases the firm's marginal and average costs by the tax amount $t$. This shifts the supply curve to the left.

It is obtained by the horizontal summation of the individual supply curves of all firms in the market.

For a market with $n$ firms, the market supply $S_m(p)$ at price $p$ is:

Where $\Delta Q$ is the change in quantity supplied, and $\Delta P$ is the change in price.

The elasticity of a straight-line supply curve depends on where it intersects the axes:

• If the supply curve cuts the price-axis (Y-axis) in its positive range, $e_s > 1$.
• If the supply curve passes through the origin, $e_s = 1$.
• If the supply curve cuts the quantity-axis (X-axis) in its positive range, $e_s < 1$.