Producer's Equilibrium under Perfect Competition

• Producer’s equilibrium is the level of output at which the firm maximises its profit.
• Under perfect competition, the firm is a price taker; its price, average revenue (AR) and marginal revenue (MR) are equal and constant.
• The firm’s equilibrium output is where MR = MC and MC is rising.
• Total variable cost (TVC) is the sum of marginal costs (MC) of all units produced.

Consider the following (illustrative) cost schedule:

• TVC at 4 units of output = 80.
• Sum of MC for 1 to 4 units = 20 + 20 + 15 + 25 = 80.
• Therefore:

TVC = ∑MC

(from the first unit up to the given level of output).

• X-axis: Output (O to L).
• Y-axis: Cost.
• Draw a U-shaped MC curve:
  (i) Initially downward sloping (MC falling).
  (ii) Then bottoming out (MC at minimum).
  (iii) Finally, upward sloping (MC rising).
• Shade the area under the MC curve from O to L units of output.
• Label the area OLSK as TVC.

Key point:

• TVC is equal to the sum of marginal costs of all units produced, which is represented by the area under the MC curve between O and L.

Due to the law of variable proportions:

• At first, when a variable factor (like labour) is increased with a fixed factor (like machinery), the firm uses resources more efficiently. Output rises more than proportionately, so marginal cost falls.
• After a certain point, too much of the variable factor with the same fixed factor leads to overcrowding, pressure on machines, and inefficiency. Output from each extra unit of input rises less and finally falls, so marginal cost rises.

Therefore, MC curve first falls, then remains roughly constant, and finally rises, giving it a U-shape.
This shape results from production technology and is common in all market forms (perfect competition, monopoly, etc.).

Under perfect competition:

• A firm is a price taker. It accepts the market price determined by the industry where market demand equals market supply.
• Price (P) remains constant for the firm, whatever quantity it sells.

Therefore, for an individual firm:

P = AR = MR

and the AR and MR curves are horizontal straight lines at the level of the market price.

A firm reaches equilibrium (profit is maximised) when both of these conditions are satisfied:

1. First condition: MR = MC
2. Second condition: MC is rising at the point of equality

• TVC is the sum of marginal costs of all units produced; graphically, it is the area under the MC curve between the origin and the chosen output.
• The MC curve is U-shaped due to the law of variable proportions (initial increasing returns followed by diminishing returns).
• Under perfect competition, the firm is a price taker; hence P = AR = MR and the MR curve is horizontal.
• Producer’s equilibrium (profit-maximising output) is attained where:
  MR = MC, and
  MC is rising and cuts MR from below.
• At this equilibrium output, the difference between total revenue and total cost (profit) is maximum, and the firm has no incentive to change its level of output.