Questions: Short-Run Cost Structure: Fixed and Variable Costs

Question 1

A firm has fixed costs of $600 and produces 100 units with total variable costs of $400. It then produces one more unit (101st), bringing total variable costs to $412. What is the marginal cost of the 101st unit, and what is the average total cost at 100 units?

• A. MC = $12; ATC = $10.00
• B. MC = $4; ATC = $10.00
• C. MC = $12; ATC = $4.00
• D. MC = $6; ATC = $7.00

Answer: (A)

Marginal cost = ΔTCC/ΔQ = ($412+$600) - ($400+$600) / 1 = $12. Since ΔFC = 0, MC = ΔVC/ΔQ = $12 - $0 (the change in VC only) = $12. ATC at 100 units = TC/Q = ($600 + $400)/100 = $1000/100 = $10.00. This shows the key relationship: MC reflects only the change in variable costs, not the fixed overhead, while ATC includes both components divided by output.

Question 2

At the minimum point of the average total cost (ATC) curve, which of the following must be true?

• A. ATC equals average variable cost (AVC), since fixed costs are zero at the minimum
• B. Marginal cost (MC) equals ATC, because when MC is below ATC it pulls the average down and when above it pulls the average up
• C. MC is at its own minimum, since cost curves reach their lowest point simultaneously
• D. ATC equals average fixed cost (AFC), as the overhead is fully spread at the minimum

Answer: (B)

The MC curve always passes through the minimum of the ATC curve — this is a mathematical identity, not a coincidence. When MC < ATC, adding one more unit costs less than the average, pulling ATC down. When MC > ATC, the additional unit costs more than average, pulling ATC up. They must be equal exactly at the minimum. The same logic applies to the AVC curve: MC passes through AVC's minimum too. MC and ATC do NOT reach their minima at the same output level — MC typically turns upward before ATC does.

Question 3

An increase in a firm's fixed costs will raise its marginal cost curve.

• T. True
• F. False

Answer: False

Marginal cost measures how total cost changes as output changes by one unit: MC = ΔTC/ΔQ = ΔVC/ΔQ (since ΔFC = 0). Fixed costs, by definition, do not change with output — so they contribute nothing to ΔTC. An increase in fixed costs shifts the ATC and AFC curves upward but leaves the MC curve and the AVC curve completely unchanged. This is why fixed costs are called 'sunk' in the short run — they don't influence how much it costs to produce one more unit.

Question 4

Average fixed cost (AFC) declines continuously as output increases, because a fixed overhead cost is spread over more and more units.

• T. True
• F. False

Answer: True

AFC = FC/Q. Since FC is a constant, dividing by larger and larger Q drives AFC toward zero — it falls throughout the entire output range and never turns upward. This is the 'spreading the overhead' effect. It is one reason ATC declines at first even when AVC is relatively stable — the falling AFC pulls ATC down. Eventually, as AVC starts rising (due to diminishing returns), AVC's increase more than offsets AFC's decline, and ATC reaches its minimum and then rises.

Question 5

Why is MC = ΔVC/ΔQ even though TC = FC + VC? What does this tell you about the relationship between fixed costs and short-run production decisions?

Model answer: Because fixed costs don't change with output, ΔFC = 0 for any change in quantity. So ΔTC = ΔFC + ΔVC = 0 + ΔVC = ΔVC. Therefore MC = ΔTC/ΔQ = ΔVC/ΔQ — marginal cost is determined entirely by variable costs. For short-run production decisions (should we produce this unit?), only variable costs matter because fixed costs are already paid regardless of output. A firm should produce as long as revenue covers variable costs; fixed costs only affect whether to stay in business long-run or exit.

This is a critical insight for profit maximization: a firm comparing revenue to cost at the margin compares price to MC, and MC is unaffected by fixed overhead. A factory that has already paid $1 million in rent should not let that sunk cost influence how many units to produce today — only the variable cost of production (materials, labor per unit) and the selling price should drive that decision. Fixed costs matter for entry/exit and investment decisions, but not for moment-to-moment output choices.