Source: Strickland Exam #02, Chapter 08 Extra Questions | Microeconomic Theory, Texas A&M University
Tags: long-run equilibrium, long-run average total cost, long-run marginal cost, zero economic profit, free entry, LATC, LMC, economic rent, long-run supply, technological innovation
In the long run, free entry and exit drive economic profit to zero for every firm in a perfectly competitive industry. Each firm produces at the minimum of its long-run average total cost (LATC), where price equals both LMC and LATC. Technological innovation initially lowers costs and creates temporary profit, but entry of new firms pushes the price back down. Firms with lower costs than the marginal (highest-cost) producer earn economic rent.
Long-run equilibrium
The state where no firm has an incentive to enter or exit the industry. Price equals the minimum of LATC, economic profit is zero, and each firm produces where P = LMC = minimum LATC.
Long-run average total cost (LATC)
The per-unit cost when all inputs (including plant size) are adjustable. Its minimum defines the long-run equilibrium price.
Long-run marginal cost (LMC)
The additional cost of one more unit when all inputs can be varied. In long-run equilibrium, LMC = LATC = P at the firm's chosen output.
Economic rent
The earnings a low-cost producer receives above what is needed to keep it in the industry. Calculated as the difference between the market price (set by the highest-cost producer still in the market) and the low-cost firm's own average total cost, multiplied by its output.
Zero economic profit
The condition where total revenue exactly covers total cost, including the opportunity cost of all resources. The firm earns a normal return but nothing above that. This is the long-run outcome for every firm in perfect competition (assuming identical cost structures).
In long-run equilibrium for a competitive firm, three conditions hold simultaneously:
P = LMC (the firm is maximising profit)
P = minimum LATC (economic profit is zero)
The demand curve (horizontal) is tangent to the LATC curve at its lowest point, and LMC passes through that same point
On a four-panel graph, the correct panel shows the demand line touching the LATC curve exactly at its minimum, with LMC crossing through the same point. Panels where demand intersects LATC above its minimum (positive profit) or below it (losses), or where MR diverges from D (not a competitive firm), do not represent long-run equilibrium.
Given a long-run total cost function LTC and its corresponding LMC:
Derive LATC = LTC / Q.
Find the minimum of LATC by taking its derivative, setting it to zero, and solving for Q.
Plug that Q back into LATC (or equivalently into LMC) to find the equilibrium price.
Example: LTC = 100Q – 10Q² + (1/3)Q³. LATC = 100 – 10Q + (1/3)Q². Taking the derivative: dLATC/dQ = –10 + (2/3)Q. Set to zero: Q = 15. LATC(15) = 100 – 10(15) + (1/3)(225) = 100 – 150 + 75 = $25. The long-run equilibrium price is $25.
Alternatively, set LMC = LATC. LMC = 100 – 20Q + Q². Setting 100 – 20Q + Q² = 100 – 10Q + Q²/3 and solving yields Q = 15. Plugging into either function gives $25.
If the current long-run equilibrium price is $12 and a technological innovation lowers production costs:
Initially, firms adopting the technology earn positive economic profit because their costs fall below $12 while price is still $12.
Positive profit attracts new entrants (or existing firms adopt the cheaper technology).
Increased industry supply pushes the market price down.
Entry continues until economic profit returns to zero, at a new, lower equilibrium price.
The long-run equilibrium price falls below $12 and stays there. It does not return to $12 unless costs revert to their original level.
When firms in an industry have different cost structures (some are low-cost, some are high-cost), the long-run equilibrium price is set by the highest-cost firm that remains in the market.
In Figure 8.19 from the exam, three firms have different LMC curves. The key observations:
Firm 1 has the highest costs (steepest LMC), meaning it produces the least output
Firm 3 has the lowest costs (flattest LMC), meaning it produces the most output
In the long run, each firm does not produce the same quantity, because their cost structures differ
The statement "Firm 1 is the highest-cost producer and Firm 3 is the lowest-cost producer" is true
The statement "Firm 3 will produce the most output in the long run" is also true
Economic rent for a low-cost producer = (Market price – Firm's own LATC at its output) × Firm's output.
The market price is set by the marginal (highest-cost) producer's minimum LATC.
Example: High-cost producers have minimum ATC = $150. Low-cost producers have LTC = 150Q – 15Q² + 0.4Q³, so LATC = 150 – 15Q + 0.4Q². LMC = 150 – 30Q + 1.2Q².
Step 1: Find the low-cost firm's profit-maximising Q. Set LMC = P = $150 (the market price set by high-cost firms): 150 – 30Q + 1.2Q² = 150, so 1.2Q² – 30Q = 0, giving Q(1.2Q – 30) = 0, so Q = 25.
Step 2: Find the low-cost firm's LATC at Q = 25: LATC = 150 – 15(25) + 0.4(625) = 150 – 375 + 250 = $25.
Step 3: Economic rent = (150 – 25) × 25 = 125 × 25 = $3,125.
Figure 8.3 shows a perfectly competitive market for walnuts with an equilibrium price of $1.73.
For an individual walnut grower:
The demand curve facing the grower is perfectly elastic at $1.73 (a horizontal line at the market price)
If a grower sells 80,000 pounds, total revenue = $1.73 × 80,000 = $138,400
Selling one more pound increases total revenue by exactly $1.73, because MR = P for a price taker
Statement I ("demand curve is perfectly elastic at $1") references the wrong price. The equilibrium price from the graph is $1.73, not $1. So statement I is false. Statement II ($138,400) is true, and statement III ($1.73 marginal revenue) is true. The correct combination is II and III.
LATC: LTC / Q
Long-run equilibrium condition: P = LMC = minimum LATC
Economic rent: (P – LATC at firm's Q) × Q
To find min LATC: set dLATC/dQ = 0, or set LMC = LATC
⚠️ In long-run equilibrium, price equals the minimum of LATC, not just any point on the LATC curve. Economic profit is zero.
⚠️ On graph questions, the correct long-run equilibrium panel has the demand line tangent to LATC at its minimum, with LMC passing through the same point. If demand is above the minimum of LATC, the firm earns positive profit and the industry is not yet in long-run equilibrium.
⚠️ Technological innovation permanently lowers the long-run equilibrium price. It does not temporarily lower it and then bounce back. Free entry ensures the new, lower cost structure becomes the standard.
⚠️ When firms have different costs, the market price is pinned to the highest-cost firm still operating. Low-cost firms earn economic rent, which is the reward for having a cost advantage.
⚠️ The walnut-market question is a careful reading exercise. Check the actual equilibrium price on the graph before evaluating statements about TR or the demand curve's position.
⚠️ When computing economic rent, use the market price (set by the marginal producer), not the low-cost firm's own minimum LATC.
Q: In long-run equilibrium for a perfectly competitive firm, what is the relationship between P, LMC, and LATC?
A: P = LMC = minimum LATC. The firm earns zero economic profit.
Q: If LTC = 100Q – 10Q² + (1/3)Q³, what is the long-run equilibrium price?
A: $25. LATC = 100 – 10Q + Q²/3. Minimise by setting the derivative to zero: Q = 15. LATC(15) = 25.
Q: If the long-run equilibrium price is $12 and a technological innovation lowers costs, what happens to the equilibrium price in the long run?
A: It falls below $12. Lower costs create temporary profits, entry follows, supply increases, and the price settles at a new, lower level.
Q: High-cost producers have minimum ATC of $150. A low-cost producer has LATC = $25 at its profit-maximising output of 25 units. What is the low-cost firm's economic rent?
A: (150 – 25) × 25 = $3,125.
Q: Which panel shows long-run equilibrium: one where D is above min LATC, tangent to min LATC, below min LATC, or where MR diverges from D?
A: The panel where D is tangent to LATC at its minimum point, with LMC passing through that same point.
Q: In Figure 8.19 with three firms of different costs, do all firms produce the same output in the long run?
A: No. Lower-cost firms produce more output than higher-cost firms. Firm 3 (lowest cost) produces the most.
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