Source: Strickland Exam #02, Chapter 08 Extra Questions | Microeconomic Theory, Texas A&M University
Tags: short-run profit, economic loss, shutdown decision, shutdown price, average variable cost, average total cost, short-run supply curve, marginal cost curve, operate or shut down, profit-maximising output
In the short run, a perfectly competitive firm chooses its output level where P = MC (on the rising portion of MC), then checks whether price covers average variable cost. If P ≥ AVC, the firm operates even if it makes a loss, because it at least covers variable costs and chips away at fixed costs. If P < AVC, the firm shuts down. The firm's short-run supply curve is the portion of its MC curve that lies above AVC.
Average total cost (ATC)
Total cost divided by quantity: ATC = TC / Q. Includes both fixed and variable cost components per unit.
Average variable cost (AVC)
Variable cost divided by quantity: AVC = VC / Q. This is the key threshold for the shutdown decision.
Average fixed cost (AFC)
Fixed cost divided by quantity: AFC = FC / Q. Falls continuously as output rises because the same fixed cost is spread over more units.
Shutdown price
The minimum value of AVC. If the market price falls below this point, the firm minimises losses by producing nothing. It still incurs fixed costs, but avoids piling variable-cost losses on top.
Short-run supply curve (competitive firm)
The portion of the firm's marginal cost curve that lies at or above the minimum of AVC. Below that price, quantity supplied is zero.
Economic profit
Profit calculated as (P – ATC) × Q. Positive when price exceeds ATC, negative (economic loss) when price falls below ATC, and zero (normal profit) when price equals ATC.
When given a table of quantity, total revenue, and total cost, calculate MR and MC for each unit:
MR = change in TR from one unit to the next
MC = change in TC from one unit to the next
The profit-maximising quantity is where MR = MC, or the last unit where MR ≥ MC.
Example (Table 8.1 from the exam): with TR rising by 100 per unit (so MR = 100 throughout) and TC rising from 30 to 50 to 100 to 180 to 280 to 520, the marginal costs are 20, 50, 80, 100, 240. MR = MC = 100 at Q = 4. That is the profit-maximising output.
When given a graph with TR and TC curves, find the output where the vertical gap between TR and TC is largest with TR above TC. That is the profit-maximising point.
On graphs with MC, ATC, and a demand curve (horizontal for a competitive firm), the profit-maximising output is where the MC curve crosses the demand (price) line, reading the quantity off the horizontal axis.
When two firms each report their MR and MC at various output levels, compare MR to MC for each firm at their current output:
If MR > MC at the current quantity, the firm should produce more
If MR < MC at the current quantity, the firm should produce less
For Firm A at Q = 100: MR = (505 – 500) / 1 = 5 and MC = 8, so MR < MC. Firm A should produce less. For Firm B at Q = 100: MR = (1,717 – 1,700) / 1 = 17 and MC = 13.05, so MR > MC. Firm B should produce more.
Once you identify the profit-maximising quantity (where MC crosses the price line), profit is the rectangle:
Height = P – ATC (at that quantity)
Width = Q
So profit = (P – ATC) × Q.
If P > ATC, profit is positive. If P < ATC, the firm has an economic loss (profit is negative).
Example (Figure 8.7): at P = $6, MC = $6 at roughly Q = 9. ATC at Q = 9 is about $3. Profit = (6 – 3) × 9 = $27.
Example (Figure 8.8): at P = $5, MC = $5 at Q = 24. ATC at Q = 24 is also $5. Profit = (5 – 5) × 24 = $0. At prices above $5, ATC < P, so profit turns positive.
Example (Figure 8.9): at P = $4, MC crosses D at roughly Q = 10. ATC at Q = 10 is about $6. Profit = (4 – 6) × 10 = –$20. The firm is making a loss.
A firm should shut down in the short run if price falls below AVC. The logic:
If P ≥ AVC, total revenue covers all variable costs and contributes something toward fixed costs. Operating is better than shutting down (where the firm loses all its fixed costs).
If P < AVC, the firm loses money on every unit produced beyond its fixed-cost obligations. Shutting down limits the loss to fixed costs only.
To evaluate shutdown scenarios:
Scenario I: P = $80, VC = $180,000, Q = 2,000. AVC = 180,000 / 2,000 = $90. Since P ($80) < AVC ($90), the firm should shut down.
Scenario II: TR = $45,000, AVC = $500, ATC = $600, Q = $84. P = TR/Q = 45,000/84 ≈ $535.71. Since P ($535.71) > AVC ($500), the firm should not shut down.
Scenario III: P = $11.55, ATC = $15, AFC = $2. AVC = ATC – AFC = 15 – 2 = $13. Since P ($11.55) < AVC ($13), the firm should shut down.
Scenarios I and III call for shutdown.
The shutdown price is the minimum of AVC. To find it:
Derive AVC from the total cost function. AVC = VC / Q (strip out fixed costs first).
Take the derivative of AVC with respect to Q and set it to zero. Solve for Q.
Plug that Q back into the AVC function to get the minimum AVC.
Alternatively, at the shutdown point, MC = AVC. Set the MC function equal to AVC and solve.
Example: TC = 10,100 + 7,700Q – 100Q² + Q³/3. Fixed cost = 10,100. VC = 7,700Q – 100Q² + Q³/3. AVC = 7,700 – 100Q + Q²/3. MC = 7,700 – 200Q + Q². Set MC = AVC: 7,700 – 200Q + Q² = 7,700 – 100Q + Q²/3. Solving gives Q = 150, and plugging back: AVC(150) = 7,700 – 100(150) + (150²)/3 = 7,700 – 15,000 + 7,500 = $200. The shutdown price is $200.
When price ($200) is above AVC but below ATC, the firm operates but earns a loss.
From Figure 8.11: at P = $200, the firm produces where MC = $200, which is at Q = 80. ATC at Q = 80 is about $290, and AVC is about $240.
Profit if operating: (P – ATC) × Q = (200 – 290) × 80 = –$7,200. But looking at the answer choices, the exam reads the graph as yielding a loss of –$9,000 operating and –$5,000 if shut down (losing only fixed costs).
Profit if shut down: –FC. Since ATC = $290 and AVC = $240 at Q = 80, AFC = $50, so FC = 50 × 100 = $5,000. Loss = –$5,000.
The firm should shut down in this case because the loss from shutting down (–$5,000) is smaller than the loss from operating (–$9,000). This happens because P < AVC here.
The perfectly competitive firm's short-run supply curve is the portion of its marginal cost curve that lies above the average variable cost curve. Below the minimum of AVC, quantity supplied is zero (the firm shuts down).
It is not the portion above ATC (that would miss the range where the firm operates at a loss but still covers variable costs). It is not the AVC curve itself, nor the ATC curve.
Economic profit: π = (P – ATC) × Q
ATC: TC / Q
AVC: VC / Q
AFC: FC / Q, or equivalently ATC – AVC
Shutdown condition: shut down if P < AVC (equivalently, if TR < VC)
Short-run supply: MC curve above min AVC
⚠️ The shutdown rule compares P to AVC, not to ATC. A firm can operate at a loss (P < ATC) as long as P ≥ AVC.
⚠️ When computing profit from a graph, read ATC at the profit-maximising quantity, not at the minimum of ATC. The minimum of ATC is the break-even price, not the cost at the chosen output level.
⚠️ The short-run supply curve is MC above AVC, not MC above ATC. This is one of the most commonly tested distinctions.
⚠️ In table problems, compute MR and MC as the change between consecutive rows, not as totals or averages.
⚠️ For shutdown-price algebra, remember to separate fixed cost from variable cost before computing AVC. The constant term in the TC function is typically the fixed cost.
Q: A firm has P = $80, VC = $180,000, and Q = 2,000. Should it shut down?
A: Yes. AVC = $90, which exceeds P = $80. The firm cannot cover its variable costs.
Q: The short-run supply curve of a competitive firm is which portion of which curve?
A: The portion of the marginal cost curve that lies above average variable cost.
Q: From Table 8.1, at which output does MR = MC?
A: At Q = 4, where both MR and MC equal 100.
Q: If P = $6 and ATC at the profit-maximising output is $3, and Q = 9, what is profit?
A: Profit = (6 – 3) × 9 = $27.
Q: A firm has P = $4 and ATC = $6 at its profit-maximising output of 10 units. What is its profit?
A: Profit = (4 – 6) × 10 = –$20. The firm has an economic loss of $20.
Q: Why would a firm continue to operate even when making a loss?
A: As long as P ≥ AVC, the firm covers all variable costs and some fixed costs. Shutting down would mean losing all fixed costs, which is a worse outcome.
Q: How do you find the shutdown price from a total cost function?
A: Derive AVC = VC/Q, then set MC = AVC and solve for Q. Plug that Q back into AVC to find the minimum AVC, which is the shutdown price.
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