Ch4. Producer Theory — Cost Structure and Profit Maximization

The Production Function and Marginal Product

Production Function: Q = f(K, L)
  K = capital, L = labor

Marginal Product of Labor (MPL):
  MPL = ΔQ / ΔL
  (additional output from one more unit of labor)

Law of Diminishing Marginal Returns (Short Run):
  Holding capital (K) fixed, adding more labor
  eventually causes MPL to fall

Relationship of TP, AP, and MP:
  MP > AP → AP is rising
  MP = AP → AP is at its maximum
  MP < AP → AP is falling

Cost Concepts

Short-Run Cost Breakdown:
  Total Fixed Cost (TFC): does not vary with output
    (e.g., rent, insurance, depreciation)
  Total Variable Cost (TVC): rises with output
    (e.g., labor, raw materials)
  Total Cost (TC) = TFC + TVC

Average Costs:
  AFC = TFC / Q  (always falling)
  AVC = TVC / Q  (U-shaped)
  ATC = TC / Q = AFC + AVC  (U-shaped)

Marginal Cost (MC):
  MC = ΔTC / ΔQ = ΔTVC / ΔQ

MC–ATC Relationship:
  MC < ATC → ATC is falling
  MC = ATC → ATC is at its minimum
  MC > ATC → ATC is rising
  → MC curve passes through the minimum of ATC

Shape of Short-Run Cost Curves

AVC and ATC: U-shaped
  Initially fall (increasing returns to labor)
  Then rise (diminishing marginal returns)

AFC: continuously declining
  (fixed cost spread over more units)

MC: U-shaped
  Intersects both AVC and ATC at their minima

Note: AVC minimum is to the LEFT of ATC minimum
  because ATC = AVC + AFC and AFC > 0 always

Long-Run Costs and Economies of Scale

Long Run: all inputs are variable
  Long-Run Average Cost (LAC) = envelope of
  short-run ATC curves (one for each plant size)

Economies of Scale:
  Expanding output → LAC falls
  Reason: specialization, spreading fixed costs,
    bulk purchasing (e.g., Amazon, Boeing)
  → Leads to natural monopoly in some industries

Diseconomies of Scale:
  Expanding output → LAC rises
  Reason: bureaucracy, coordination problems,
    management inefficiencies

Minimum Efficient Scale (MES):
  Output level at the minimum point of LAC

Profit Maximization

Profit (π) = TR − TC

Profit-Maximization Rule:
  MR = MC

Intuition:
  MR > MC → produce one more unit (profit rises)
  MR < MC → produce one less unit (profit rises)
  MR = MC → profit is maximized

Perfectly Competitive Firm:
  P = MR (price taker: horizontal demand curve)
  → Maximize profit where P = MC

Break-Even Point:
  P = ATC → economic profit = 0
  (firm covers all costs, including normal profit)

Short-Run Shutdown Condition:
  P < AVC → shut down (can't cover variable costs)
  P > AVC but P < ATC → operate at a loss
    (covers variable costs; loss < TFC)

MC Passes Through the Minimum of ATC ★★★★★ : When MC < ATC, the average is being pulled down. When MC > ATC, the average is being pulled up. They cross exactly at the minimum of ATC. Memory hook: MC = ATC at the bottom of the U

Profit Maximization: MR = MC ★★★★★ : Every firm — competitive, monopolist, or oligopolist — maximizes profit at the output where MR = MC. Competitive firms have P = MR. Memory hook: MR = MC = profit peak

Shutdown vs. Operate at a Loss ★★★★☆ : Shut down if P < AVC (can’t cover variable costs). Continue operating if P > AVC even if P < ATC (loss is smaller than TFC). Memory hook: P < AVC → close; P < ATC but > AVC → stay open and cut losses

Practice Questions

Q. A perfectly competitive firm faces P = $20, MC =$ 18, ATC = $22. What should it do?

MR (= P = $20) > MC ($ 18) → increase output to reach MR = MC. However, P ( $20) < ATC ($ 22) → the firm is making a loss. As long as P > AVC, the firm should continue in the short run to minimize losses. The firm should produce where MR = MC and re-evaluate whether to exit in the long run.

Q. Why should a firm in the downward-sloping region of its long-run average cost curve expand production?

It is operating in the region of economies of scale. Expanding output lowers LAC → reduces cost per unit → improves competitiveness. The firm should expand until it reaches its minimum efficient scale (MES), the bottom of the LAC curve.