Chapter 4: The Theory of the Firm under Perfect Competition

4.1 Perfect Competition: Defining Features

Price-taking behavior: An individual firm accepts the market price as given because its output is small relative to the market. The firm faces a horizontal demand curve at that price, so its average and marginal revenue are equal to price. This is a model assumption; real markets may depart from it.

• If a firm sets price > market price → sells nothing
• If price ≤ market price → can sell any quantity

4.2 Revenue

In perfect competition: AR = MR = p

Revenue Curves

TR Curve: Straight line through origin with slope = p

AR/MR Curve: Horizontal line at market price (perfectly elastic demand)

4.3 Profit Maximization

Profit Maximization Conditions

Short Run: Choose the output where price (marginal revenue) equals marginal cost on its rising portion. Then compare price with average variable cost: if price is below minimum AVC, shutting down minimizes the loss; if price is at least minimum AVC, producing can cover variable cost and contribute toward fixed cost. A firm can produce at a loss when price is below average total cost.

1. p = SMC (Price equals short run marginal cost)
2. SMC must be non-decreasing at equilibrium output
3. p ≥ AVC (Price ≥ average variable cost)

Long Run: Choose output where price equals long-run marginal cost on its rising portion, provided price covers long-run average cost. If price is below minimum LRAC, exit is preferable in the long run. With free entry and exit in competitive long-run equilibrium, price is driven to minimum LRAC and firms earn normal profit, which is included in economic cost.

1. p = LRMC (Price equals long run marginal cost)
2. LRMC must be non-decreasing at equilibrium output
3. p ≥ LRAC (Price ≥ long run average cost)

4.4 Supply Curve of a Firm

4.4.1 Short Run Supply Curve

A competitive firm short-run supply is the rising portion of its SMC curve at or above minimum AVC. Below that shutdown price, the firm supplies zero. This rule assumes the firm chooses output to maximize profit and treats market price as given.

• For p ≥ min AVC: Supply = quantity where p = SMC
• For p < min AVC: Supply = 0 (shutdown point)

4.4.2 Long Run Supply Curve

In the long run, the firm supplies where price equals rising LRMC when price covers LRAC. Below minimum LRAC, it exits rather than continue indefinitely. Do not mix this long-run exit decision with the short-run shutdown rule, which compares price with AVC.

• For p ≥ min LRAC: Supply = quantity where p = LRMC
• For p < min LRAC: Supply = 0 (exit point)

4.4.3 Shut Down Point

Short Run: Minimum point of AVC curve

Long Run: Minimum point of LRAC curve

4.4.4 Normal Profit and Break-even Point

4.5 Determinants of a Firm's Supply Curve

4.5.1 Technological Progress

Shifts supply curve to the right (more output at each price)

4.5.2 Input Prices

Increase in input prices shifts supply curve to the left (less output at each price)

Impact of Unit Tax

A tax per unit sold shifts supply curve left by amount of tax

4.6 Market Supply Curve

Horizontal summation of individual firms' supply curves

Factors affecting market supply:

• Number of firms (more firms → rightward shift)
• Technology
• Input prices
• Taxes and subsidies

4.7 Price Elasticity of Supply

Calculating elasticity:

e_s = (ΔQ/Q) / (ΔP/P) = (ΔQ/ΔP) × (P/Q)

Elasticity for Straight-line Supply Curves

1. Supply curve intersecting price axis: e_s > 1
2. Supply curve through origin: e_s = 1
3. Supply curve intersecting quantity axis: e_s < 1