Microeconomics Quiz: Profit Maximization
20 questions · exam conditions
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Profit MaximizationQuestion 1 of 20

A perfectly competitive firm is initially in a long-run equilibrium where it is earning zero economic profit. The government then imposes an annual lump-sum license fee on every firm in the industry. In the short run, how will this tax affect the firm's optimal output and profit?

Output will decrease and profit will become negative.
Output will remain the same and profit will remain zero.
Output will decrease and profit will remain zero.
Output will remain the same and profit will become negative.
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Microeconomics Quiz

Microeconomics Quiz: Profit Maximization

Practice Profit Maximization in Microeconomics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Profit Maximization, giving you a quick way to practice the rules, question types, and explanations that matter most for Microeconomics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A perfectly competitive firm is initially in a long-run equilibrium where it is earning zero economic profit. The government then imposes an annual lump-sum license fee on every firm in the industry. In the short run, how will this tax affect the firm's optimal output and profit?

  1. Output will decrease and profit will become negative.
  2. Output will remain the same and profit will remain zero.
  3. Output will decrease and profit will remain zero.
  4. Output will remain the same and profit will become negative. (correct answer)
Explanation: A lump-sum license fee is a fixed cost. An increase in fixed costs does not affect the firm's marginal cost (MC) or its average variable cost (AVC). Since the profit-maximizing rule in the short run is to produce where Price = MC, and neither P nor MC has changed, the firm's optimal output level will remain the same. However, the increase in fixed costs will raise the firm's total costs, and thus its average total cost. Since the firm was previously earning zero economic profit (P = ATC), the increase in ATC means that now P < ATC, and the firm will earn negative economic profit (a loss).

Question 2

The market demand in a perfectly competitive industry is QD=1,200−10PQ_D = 1,200 - 10P and market supply is QS=20P−300Q_S = 20P - 300. A typical firm has marginal cost MC(q)=10+5qMC(q) = 10 + 5q. What is the profit-maximizing output (q) for a typical firm?

  1. 8 units (correct answer)
  2. 10 units
  3. 50 units
  4. 900 units
Explanation: This is a two-step problem. First, find the market equilibrium price (P) by setting market demand equal to market supply. 1,200−10P=20P−3001,200 - 10P = 20P - 300. Solving for P: 1,500=30P1,500 = 30P, so P=50P = 50. Second, a competitive firm maximizes profit by producing the quantity (q) where price equals its marginal cost. Set the equilibrium price equal to the firm's MC: 50=10+5q50 = 10 + 5q. Solving for q: 40=5q40 = 5q, so q=8q = 8. The profit-maximizing output for a typical firm is 8 units.

Question 3

A competitive firm's marginal cost curve is given by MC=2Q+6MC = 2Q + 6. The firm faces a market price of $18. However, the firm also pays a monthly licensing fee of $100 regardless of output level. What is the firm's profit-maximizing output level?

  1. 6 units, because this is where MR equals MC regardless of the fixed licensing fee (correct answer)
  2. 9 units, because the firm must produce more to cover the additional fixed cost
  3. 3 units, because the licensing fee reduces the optimal output by increasing total costs
  4. 12 units, because the firm needs to maximize revenue to offset the licensing fee
Explanation: In perfect competition, profit maximization occurs where MR = MC, and MR = P = $18. Setting 18 = 2Q + 6 gives 2Q = 12, so Q = 6. Fixed costs (like the licensing fee) do not affect the profit-maximizing output level because they don't affect marginal cost or marginal revenue. Choice B incorrectly assumes fixed costs affect optimal output. Choice C incorrectly suggests fixed costs reduce optimal output. Choice D incorrectly focuses on revenue maximization rather than profit maximization.

Question 4

A perfectly competitive firm has a total cost function of TC=100+10q+q2TC = 100 + 10q + q^2. What is the equation of the firm's short-run supply curve?

  1. P=10+2qP = 10 + 2q for P≥10P \ge 10 (correct answer)
  2. P=100/q+10+qP = 100/q + 10 + q for all P>0P > 0
  3. P=10+qP = 10 + q for P≥10P \ge 10
  4. P=10+2qP = 10 + 2q for P≥30P \ge 30
Explanation: A competitive firm's short-run supply curve is its marginal cost (MC) curve above its average variable cost (AVC) curve. First, find MC: MC=dTC/dq=10+2qMC = dTC/dq = 10 + 2q. Next, find AVC: The variable cost is VC=10q+q2VC = 10q + q^2, so AVC=VC/q=10+qAVC = VC/q = 10 + q. The firm will only produce if price is greater than or equal to the minimum AVC. The minimum of AVC=10+qAVC = 10 + q occurs at q=0, where AVC=$10. This is the shutdown price. Therefore, the supply curve is given by P = MC for all prices at or above the minimum AVC. The supply curve is P=10+2qP = 10 + 2q for P≥10P \ge 10.

Question 5

A competitive firm discovers that at its current output of 12 units, marginal revenue is $40, marginal cost is $35, and average total cost is $45. The firm is considering three options: maintain current output, increase to 13 units (where MC = $42), or decrease to 11 units (where MC = $33). Which option maximizes profit?

  1. Increase to 13 units, because marginal cost at 13 units remains relatively close to marginal revenue despite slightly exceeding it
  2. Maintain 12 units, because the firm is already earning positive marginal profit at this level of output
  3. Decrease to 11 units, because this reduces the loss from high average total cost relative to market price
  4. Increase to 13 units, because moving toward the point where MC = MR increases total profit (correct answer)
Explanation: The firm should produce where MC = MR = 40.Currentlyat12units,MC(40. Currently at 12 units, MC (35) < MR (40),sothefirmshouldincreaseoutput.At13units,MC(40), so the firm should increase output. At 13 units, MC (42) is closer to MR ($40) than at 12 units, so moving to 13 units increases profit even though MC slightly exceeds MR. The 12th unit adds $5 to profit (MR - MC = $40 - $35). Choice A uses imprecise reasoning. Choice B stops short of the optimum. Choice C incorrectly focuses on ATC rather than marginal analysis.

Question 6

Two identical competitive firms each have marginal cost curves of MC=4+2QMC = 4 + 2Q. Firm A operates in a market where price is $16, while Firm B operates in a market where price is $20. If both firms are profit maximizing, what is the difference in their output levels?

  1. 1 unit, because each $2 increase in price increases optimal output by 1 unit given this MC function
  2. 4 units, because the $4 price difference translates directly to a 4-unit output difference
  3. 2 units, because Firm B produces 8 units while Firm A produces 6 units (correct answer)
  4. 6 units, because Firm A produces 6 units while Firm B produces 12 units
Explanation: When you encounter profit maximization problems for competitive firms, remember that firms always produce where marginal cost equals market price (MC=PMC = P). This fundamental rule allows you to solve for optimal output levels. For both firms with MC=4+2QMC = 4 + 2Q, you set marginal cost equal to their respective market prices. For Firm A: 16=4+2QA16 = 4 + 2Q_A, so 12=2QA12 = 2Q_A and QA=6Q_A = 6 units. For Firm B: 20=4+2QB20 = 4 + 2Q_B, so 16=2QB16 = 2Q_B and QB=8Q_B = 8 units. The difference is 8−6=28 - 6 = 2 units. Answer A incorrectly suggests a mechanical relationship where each $2 price increase yields 1 additional unit of output. While this happens to work here due to the specific slope of the marginal cost curve (coefficient of 2), this reasoning misses the underlying economic principle and wouldn't apply to different cost functions. Answer B assumes price differences translate directly into output differences, ignoring how marginal cost curves determine the actual relationship between price and quantity. A $4 price difference doesn't automatically mean a 4-unit output difference. Answer D makes calculation errors, incorrectly stating that Firm B produces 12 units when the correct calculation shows 8 units. Study tip: Always solve $MC=PMC = P $ algebraically rather than looking for shortcuts or assuming direct proportional relationships. The shape of the marginal cost curve determines how price changes affect output, and this varies across different cost functions.

Question 7

A perfectly competitive firm faces a market price of $12 per unit. Its total cost function is $TC=50+4Q+0.5Q2TC = 50 + 4Q + 0.5Q^2 $. If the firm currently produces 8 units and is considering whether to increase production to 10 units, what should the firm conclude about this change?

  1. The firm should increase production because marginal revenue exceeds marginal cost at 10 units
  2. The firm should not increase production because marginal cost exceeds marginal revenue at 10 units (correct answer)
  3. The firm should increase production because total profit increases by $6 when moving from 8 to 10 units
  4. The firm should not increase production because average total cost exceeds price at 10 units
Explanation: For a perfectly competitive firm, MR = P = $12. The marginal cost function is MC = dTC/dQ = 4 + Q. At Q = 10, MC = 4 + 10 = 14.SinceMC(14. Since MC (14) > MR ($12) at 10 units, the firm should not increase production to 10 units. Choice A is incorrect because MC > MR at 10 units. Choice C is incorrect because the change in profit from 8 to 10 units is negative (each additional unit beyond optimal adds negative marginal profit). Choice D focuses on average cost rather than the marginal analysis needed for profit maximization.

Question 8

A firm in a perfectly competitive market is currently producing an output level where its Average Total Cost (ATC) is $40 and its Average Variable Cost (AVC) is $25. The market price for its product is $30. Which of the following describes the firm's optimal strategy?

  1. Shut down immediately as it is incurring an economic loss.
  2. Increase its price to $40 to cover its average total cost.
  3. Continue to operate in the short run but plan to exit in the long run if the price persists. (correct answer)
  4. Decrease output to the point where average total cost is minimized.
Explanation: The firm's decision-making involves two stages. In the short run, the firm should continue to operate as long as the price (P) covers the average variable cost (AVC). Here, P=30isgreaterthanAVC=30 is greater than AVC=25, so the firm is covering its variable costs and contributing 5perunittoitsfixedcosts.Shuttingdownwouldresultinalargerloss(equaltototalfixedcosts).Inthelongrun,thefirmmustcoverallcoststobeviable.SinceP=5 per unit to its fixed costs. Shutting down would result in a larger loss (equal to total fixed costs). In the long run, the firm must cover all costs to be viable. Since P=30 is less than ATC=$40, the firm is making an economic loss. If this price is expected to persist, the firm should plan to exit the market.

Question 9

A manufacturer of widgets in a perfectly competitive market invested $500,000 in specialized machinery that cannot be resold or used for other purposes. The average variable cost to produce a widget is $15. If the current market price for widgets is $12, the firm should:

  1. continue to produce in the short run to recover a portion of the machinery's cost.
  2. shut down production in the short run to minimize its losses. (correct answer)
  3. exit the industry because the price is below the cost of production.
  4. increase production until marginal cost equals the market price.
Explanation: The $500,000 investment is a sunk cost; it cannot be recovered and is irrelevant to the short-run production decision. The firm should decide whether to produce based on a comparison of the market price (P) and the average variable cost (AVC). In this case, P = $12 and AVC = $15. Since the price is less than the average variable cost (P < AVC), the firm loses an additional $3 on every widget it produces. To minimize its losses, the firm should cease production immediately (shut down). Its loss will be limited to its fixed (sunk) costs.

Question 10

A competitive firm has a marginal cost of MC=4qMC = 4q and faces a market price of P=$40. The firm is subject to a production quota and cannot produce more than 8 units. What is the firm's profit-maximizing output?

  1. 0 units
  2. 8 units (correct answer)
  3. 10 units
  4. 12 units
Explanation: First, we determine the unconstrained profit-maximizing quantity by setting P = MC: 40=4q40 = 4q, which yields q=10q = 10. However, the firm is constrained by a quota and cannot produce more than 8 units. For any quantity less than the unconstrained optimum of 10, the price (40)isgreaterthanthemarginalcost(e.g.,atq=8,MC=40) is greater than the marginal cost (e.g., at q=8, MC=32). This means that each additional unit of production up to 10 adds to profit. Since the firm cannot produce 10 units, it should produce as much as it is allowed to, which is 8 units. Producing the 8th unit adds $40 in revenue and only $32 in cost, so it is profitable.

Question 11

A perfectly competitive firm is producing a positive output level, q*, where market price equals marginal cost. For q* to be the profit-maximizing output, which of the following conditions is also required?

  1. Average total cost must be at its minimum at q*.
  2. The marginal cost curve must be upward sloping at q*. (correct answer)
  3. The firm must be earning zero or positive economic profit at q*.
  4. Price must be greater than average variable cost at all output levels.
Explanation: The condition P = MC is the first-order condition for profit maximization; it identifies a point where profit is at a local maximum or minimum. To ensure it is a maximum, the second-order condition must be satisfied. This condition states that the marginal cost curve must be rising (i.e., its slope must be positive) at the point of intersection with the price line. If MC were falling, producing more would lead to MC falling further below the price, increasing profit and implying the current point is not a maximum.

Question 12

A competitive firm's marginal cost is MC=15+2qMC = 15 + 2q, and the market price is $55. The government introduces a per-unit subsidy of $10 paid to the firm for each unit it produces. After the subsidy is introduced, the firm's output will:

  1. increase by 5 units. (correct answer)
  2. increase by 10 units.
  3. decrease by 5 units.
  4. remain unchanged.
Explanation: Without the subsidy, the firm sets P=MC: 55=15+2q55 = 15 + 2q, which means 40=2q40 = 2q, so q1=20q_1 = 20. A per-unit subsidy can be viewed in two ways: it either reduces the firm's marginal cost or increases its marginal revenue. Viewing it as a reduction in MC, the effective marginal cost becomes MC′=MC−subsidy=(15+2q)−10=5+2qMC' = MC - subsidy = (15 + 2q) - 10 = 5 + 2q. The firm sets P = MC': 55=5+2q55 = 5 + 2q, which means 50=2q50 = 2q, so q2=25q_2 = 25. The output increases from 20 to 25, which is an increase of 5 units.

Question 13

A perfectly competitive firm has been producing 15 units at a market price of $30. Due to a change in input costs, the firm's marginal cost at 15 units increases from $30 to $35, while marginal cost at 14 units becomes $32 and at 13 units becomes $29. Assuming the market price remains $30, how should the firm adjust its production?

  1. Continue producing 15 units because the firm has already committed to this output level
  2. Reduce production to 14 units and accept the $2 loss per unit on marginal production
  3. Reduce production to 13 units where marginal cost is closest to but below the market price (correct answer)
  4. Increase production beyond 15 units to spread the higher marginal costs over more units
Explanation: When a perfectly competitive firm faces changing costs, you need to apply the fundamental profit-maximization rule: produce where marginal cost equals marginal revenue (which equals market price in perfect competition). Initially, the firm was optimally producing 15 units where MC = MR = $30. After the cost increase, you must find the new quantity where MC equals the $30 market price. Looking at the new marginal costs: at 15 units, MC = $35; at 14 units, MC = $32; at 13 units, MC = $29. Since the firm should produce where MC equals price ($30), and the closest match is 13 units where MC = $29 (just below the market price), the firm should reduce to 13 units. Producing beyond this point would mean MC > MR, reducing profit on additional units. Answer A incorrectly suggests sunk cost thinking - there's no "commitment" to previous output levels in competitive markets. Answer B misunderstands the optimization rule by focusing on the loss per unit rather than finding where MC = MR. The "$2 loss per unit" language also confuses marginal analysis with average cost thinking. Answer D reflects a common misconception about spreading costs - this is irrelevant for short-run profit maximization and would actually worsen the situation since MC > MR for units beyond 13. Remember: in perfect competition, always produce where MC = MR (market price). When costs change, immediately recalculate this optimal point rather than sticking with previous decisions or trying to "spread" costs.

Question 14

A competitive firm's short-run supply curve is derived from its marginal cost curve above the shutdown point. If a firm's marginal cost function is MC=Q2−8Q+20MC = Q^2 - 8Q + 20 and its average variable cost is minimized at Q = 4 with AVCmin=4AVC_{min} = 4, at what price will the firm supply exactly 6 units?

  1. $8, because this equals the marginal cost at Q = 6 units and exceeds the shutdown price (correct answer)
  2. $4, because this equals the minimum average variable cost required to stay in operation
  3. $12, because this equals the average total cost needed to break even at Q = 6 units
  4. $16, because this reflects both the marginal cost and the fixed cost component at Q = 6 units
Explanation: A competitive firm's supply curve shows the quantity supplied at each price, which corresponds to the MC curve above the shutdown point. At Q = 6, MC = 6² - 8(6) + 20 = 36 - 48 + 20 = 8. Since $8 > $4 (the shutdown price), the firm will supply 6 units when price equals $8. Choice B gives the shutdown price, not the supply price for 6 units. Choice C incorrectly references average total cost. Choice D incorrectly adds fixed cost considerations to marginal cost.

Question 15

A competitive firm has a marginal cost function MC=6+0.5QMC = 6 + 0.5Q and faces a market price of $18. The firm also has the option to invest in new technology that would change its marginal cost function to $MC=8+0.4QMC = 8 + 0.4Q $. Should the firm adopt the new technology, and why?

  1. No, because the new technology increases marginal cost at every output level
  2. Yes, because the new technology reduces marginal cost at the profit-maximizing output level
  3. No, because the firm's profit-maximizing output decreases with the new technology
  4. Yes, because the new technology allows the firm to produce more units profitably (correct answer)
Explanation: When analyzing technology adoption decisions, you need to compare how the change affects profit at the optimal output level, not just look at marginal cost in isolation. First, find the profit-maximizing output under each technology. A competitive firm maximizes profit where price equals marginal cost. With the original technology: 18=6+0.5Q18 = 6 + 0.5Q, so Q=24Q = 24 units. With the new technology: 18=8+0.4Q18 = 8 + 0.4Q, so Q=25Q = 25 units. The key insight is that "profitably" means producing units where price exceeds marginal cost. Under the original technology, the 25th unit would cost MC=6+0.5(25)=18.5MC = 6 + 0.5(25) = 18.5, which exceeds the $18 price. Under the new technology, the 25th unit costs exactly $18, making it profitable to produce. The new technology allows production of one additional profitable unit. Option A incorrectly focuses only on the intercept increase from 6 to 8, ignoring that the slope decreased from 0.5 to 0.4. Option B is wrong because at the original profit-maximizing output of 24 units, the new technology actually increases marginal cost from $18 to $17.6 - but this misses the point that optimal output changes. Option C incorrectly states that output decreases when it actually increases from 24 to 25 units. Remember: technology adoption decisions depend on how changes affect profit at the new optimum, not just marginal cost comparisons at arbitrary output levels. Always recalculate the profit-maximizing quantity under each scenario.

Question 16

A price-taking firm is maximizing profit by producing 500 units. The market price is $80 per unit, and the firm is earning $10,000 in economic profit. What is the firm's average total cost (ATC) at this level of production?

  1. $20
  2. $40
  3. $60 (correct answer)
  4. $80
Explanation: Economic profit is calculated as (Price - Average Total Cost) × Quantity, or π=(P−ATC)×q\pi = (P - ATC) \times q. We are given (\pi = 10,000\), P = $80, and q = 500. We can plug these values into the formula and solve for ATC: 10,000 = (80 - ATC) \times 500.First,dividebothsidesby500:. First, divide both sides by 500: 10,000 / 500 = 80 - ATC,whichgives, which gives 20 = 80 - ATC. Rearranging the equation to solve for ATC yields \(ATC = 80 - 20 = 60).

Question 17

A competitive firm has the total cost function TC=27+3q+(1/3)q2TC = 27 + 3q + (1/3)q^2. In the long run, this firm will exit the market if the price falls below:

  1. $3
  2. $6
  3. $9 (correct answer)
  4. $12
Explanation: In the long run, a firm will exit the market if the price falls below the minimum of its average total cost (ATC). The exit point is P = min(ATC). First, find ATC: ATC=TC/q=27/q+3+(1/3)qATC = TC/q = 27/q + 3 + (1/3)q. To find the minimum of ATC, set MC equal to ATC. First, find MC: MC=dTC/dq=3+(2/3)qMC = dTC/dq = 3 + (2/3)q. Now, set MC = ATC: 3+(2/3)q=27/q+3+(1/3)q3 + (2/3)q = 27/q + 3 + (1/3)q. This simplifies to (1/3)q=27/q(1/3)q = 27/q, which gives q2=81q^2 = 81, so q=9q = 9. This is the output level where ATC is minimized. To find the exit price, plug q=9 into the ATC or MC function: (P = MC(9) = 3 + (2/3)(9) = 3 + 6 = $9).

Question 18

A perfectly competitive firm has a total cost function TC=20+15q+q2TC = 20 + 15q + q^2. The market price falls to $25. What is the firm's profit (or loss) in the short run if it produces the optimal quantity?

  1. A loss of $5 (correct answer)
  2. A loss of $20
  3. Zero profit
  4. A profit of $5
Explanation: First, find the optimal quantity by setting P = MC. The marginal cost is MC=dTC/dq=15+2qMC = dTC/dq = 15 + 2q. So, 25=15+2q25 = 15 + 2q, which gives 10=2q10 = 2q, or q=5q=5. Next, check the shutdown condition. AVC = (15q+q2)/q=15+q(15q+q^2)/q = 15+q. At q=5, AVC = 20. Since P=25>AVC=25 > AVC=20, the firm should produce. Finally, calculate profit at q=5: Profit = TR - TC = (P×q)−(20+15q+q2)(P \times q) - (20 + 15q + q^2) = (25×5)−(20+15(5)+52)(25 \times 5) - (20 + 15(5) + 5^2) = 125−(20+75+25)125 - (20 + 75 + 25) = 125−130=−5125 - 130 = -5. The firm incurs a loss of $5.

Question 19

A perfectly competitive firm's total cost function is TC=100+5Q+Q2TC = 100 + 5Q + Q^2. If the market price falls from $25 to $15, how does this affect the firm's profit-maximizing output and total profit?

  1. Output decreases by 5 units, and profit decreases by exactly $50
  2. Output decreases by 5 units, and profit decreases by $75 (correct answer)
  3. Output decreases by 10 units, and profit decreases by $100
  4. Output decreases by 5 units, and profit decreases by $25
Explanation: MC = dTC/dQ = 5 + 2Q. At P = $25: 25 = 5 + 2Q, so Q = 10. Profit = 25(10) - (100 + 5(10) + 10²) = 250 - 250 = $0. At P = 15:15=5+2Q,soQ=5.Profit=15(5)−(100+5(5)+52)=75−150=−15: 15 = 5 + 2Q, so Q = 5. Profit = 15(5) - (100 + 5(5) + 5²) = 75 - 150 = -75. Output decreases by 5 units, profit decreases by $75. Choice A uses incorrect profit calculation. Choice C incorrectly calculates the output change. Choice D underestimates the profit decrease.

Question 20

A firm's marginal cost function is given by MC(q)=q2−18q+90MC(q) = q^2 - 18q + 90. If the market price is $18, what is the firm's profit-maximizing level of output?

  1. 6 units
  2. 9 units
  3. 12 units (correct answer)
  4. 18 units
Explanation: To find the profit-maximizing output, set price equal to marginal cost: 18=q2−18q+9018 = q^2 - 18q + 90. Rearranging gives the quadratic equation q2−18q+72=0q^2 - 18q + 72 = 0. Factoring the quadratic yields (q−6)(q−12)=0(q - 6)(q - 12) = 0, so the possible output levels are q=6 and q=12. Profit is maximized only when the marginal cost curve is upward-sloping. The MC curve is a U-shaped parabola with its minimum at q=−b/(2a)=−(−18)/(2∗1)=9q = -b/(2a) = -(-18)/(2*1) = 9. Therefore, at q=6, MC is downward-sloping (profit is minimized at this point relative to its surroundings), and at q=12, MC is upward-sloping. The profit-maximizing output is 12 units.