Long Run Supply Curve In Perfect Competition

Long Run Supply Curve in Perfect Competition

In a perfectly competitive market, firms are price takers and can freely enter or exit the industry. On the flip side, because of these conditions, the long run supply curve in perfect competition reflects how total output supplied by the industry changes when all inputs, including the number of firms, are variable. Worth adding: unlike the short‑run curve, which may slope upward due to fixed factors, the long‑run curve is typically horizontal at the market price that equals the minimum point of each firm’s long‑run average cost (LRAC). This article explains why the curve takes that shape, how it is derived, and what it implies for market equilibrium and welfare.

Introduction to the Long Run Supply Curve

When economists talk about the long run supply curve in perfect competition, they refer to the relationship between the market price and the quantity supplied after firms have had enough time to adjust all of their inputs, including plant size and the number of firms operating in the market. In the long run:

• Entry and exit are costless – firms will enter if they can earn positive economic profit and exit if they suffer losses.
• All factors are variable – there are no fixed inputs that constrain production.
• Firms operate at the minimum of their LRAC – any firm producing elsewhere would incur higher average costs and could not survive competition.

So naturally, the market price in long‑run equilibrium settles exactly at the minimum LRAC. At that price, each firm earns zero economic profit (normal profit only), and there is no incentive for further entry or exit. The industry supply curve therefore becomes a perfectly elastic (horizontal) line at that price, indicating that any quantity demanded at that price can be supplied without changing the market price And that's really what it comes down to..

Deriving the Long Run Supply Curve: Step‑by‑Step

Below is a concise, step‑by‑step outline of how the long‑run supply curve is constructed for a perfectly competitive industry Worth keeping that in mind..

1. Identify each firm’s long‑run cost functions

   • Derive the long‑run total cost (LRTC) as a function of output q.
   • Obtain the long‑run average cost (LRAC) = LRTC / q.
   • Find the long‑run marginal cost (LRMC) = d(LRTC)/dq.

2. Locate the minimum point of LRAC

   • Set LRMC = LRAC and solve for q (the output where LRAC is lowest).
   • Denote this output as q* and the corresponding cost as P* = LRAC(q*).

3. Determine the firm’s supply decision

   • In perfect competition, a firm produces where price = LRMC, provided price ≥ minimum LRAC.
   • At price P*, the firm is indifferent between producing q* or shutting down because profit = 0.
   • For any price > P*, the firm would want to expand output indefinitely (if LRMC is upward sloping) or produce more until LRMC equals the higher price.
   • For any price < P*, the firm would incur losses and exit.

4. Aggregate individual supplies to market supply

   • If price = P*, each existing firm can supply any quantity up to its capacity (theoretically infinite if constant returns to scale).
   • Because firms can freely enter, the number of firms N adjusts so that total market quantity supplied equals market quantity demanded at price P*.
   • Hence, the market supply curve is horizontal at P*:
     [ Q_s(P) = \begin{cases} 0 & \text{if } P < P^\ \text{any } Q \ge 0 & \text{if } P = P^\ \infty & \text{if } P > P^* \end{cases} ]

5. Interpret the result

   • The horizontal segment reflects perfect elasticity of supply in the long run.
   • Shifts in demand change equilibrium quantity but not price, as long as the shift does not push the price below the minimum LRAC (which would trigger exit) or above it (which would trigger entry until price returns to P*).

Scientific Explanation: Why the Curve Is Horizontal

The horizontal shape of the long‑run supply curve stems from two core assumptions of perfect competition:

Constant Returns to Scale (CRS) Scenario

When firms experience constant returns to scale, doubling all inputs exactly doubles output, leaving LRAC unchanged across all output levels. In this case:

• LRAC is a flat line; its minimum equals its value at any output.
• The market price that yields zero profit is the same regardless of how many firms operate.
• So, the industry can expand or contract output without affecting the price—producing a perfectly elastic supply curve.

Increasing or Decreasing Returns to Scale

If the industry exhibits increasing returns to scale (economies of scale) at low output and decreasing returns (diseconomies) at high output, the LRAC curve is U‑shaped. The long‑run supply curve remains horizontal at the minimum of that U‑shape because:

• Any price above the minimum invites entry, which drives price back down as new firms increase total output.
• Any price below the minimum causes exit, reducing total output and pushing price back up.
• The entry/exit process continues until the market price exactly equals the minimum LRAC, at which point firms earn zero profit and the quantity supplied adjusts to meet demand.

Thus, irrespective of the underlying returns to scale, the long run supply curve in perfect competition is horizontal at the price that corresponds to the lowest achievable average cost Practical, not theoretical..

Market Equilibrium and Welfare Implications

Because the long‑run supply curve is perfectly elastic, the equilibrium in a perfectly competitive market has distinctive features:

If demand shifts rightward (increase), the equilibrium quantity rises while price stays at P*. New firms enter until the extra output is absorbed. Conversely, a leftward demand shift leads to exit and a lower equilibrium quantity, again with unchanged price It's one of those things that adds up..

Frequently Asked Questions (FAQ)

Q1: Can the long‑run supply curve ever slope upward?
A: In the strict perfect‑competition model with free entry and exit, the long‑run supply curve is horizontal. Upward slopes appear only when there are barriers to entry, fixed factors that cannot be varied in the long run, or when input prices rise as industry output expands (e.g., due to scarcity of a key resource).

Q2: What happens if input prices increase as the industry grows?
A: Rising input prices shift each firm’s LRAC upward, raising the minimum LRAC. The new long‑run supply curve becomes a higher horizontal line, reflecting a higher equilibrium price. This scenario is sometimes called an **increasing‑