Ch 13 Worksheet — The Costs of Production

Workers	Scopes (Q)	FC ($)	VC ($)	TC ($)	ATC ($)
0	0	100	0	100	—
1	1	100	30	130	130.00
2	2	100	60	160	80.00
3	3	100	90	190	63.33
5	4	?	?	?	?
8	5	?	?	?	?
13	6	?	?	?	?
21	7	?	?	?	?
34	8	?	?	?	?

Question a

The Silph Company's fixed cost (FC) is $___. This value does not change regardless of how many workers are hired or how many scopes are produced.

Fixed Cost FC ($)

Hint Use the row where Q = 2 (2 workers, 2 scopes). VC = 2×$10 + 2×$20 = $60. The table tells you ATC = $80.00 at Q=2, so TC = ATC × Q = $80 × 2 = $160. FC = TC − VC.

Explanation At 2 workers and 2 scopes: VC = (2×$10) + (2×$20) = $20 + $40 = $60.
ATC = $80.00, so TC = $80 × 2 = $160.
FC = TC − VC = $160 − $60 = $100.
Fixed cost is $100 for every row — it never changes no matter how much output is produced. This is the defining feature of a fixed cost.

Question b

When Silph hires 5 workers and produces 4 scopes, what is the variable cost (VC) and total cost (TC)?

Variable Cost VC ($)

Total Cost TC ($)

Hint VC = (number of workers × $10) + (number of scopes × $20). Then TC = FC + VC. FC is always $100.

Explanation VC = (5 workers × $10) + (4 scopes × $20) = $50 + $80 = $130.
TC = FC + VC = $100 + $130 = $230.
Notice that variable costs increase as both the number of workers and the quantity produced grow. Fixed cost stays at $100 regardless.

Question c

What is the average total cost (ATC) when Silph produces 6 scopes with 13 workers? Round to two decimal places.

ATC ($/scope)

Hint First find VC: (13×$10) + (6×$20). Then TC = FC + VC = $100 + VC. Then ATC = TC ÷ Q.

Explanation VC = (13 workers × $10) + (6 scopes × $20) = $130 + $120 = $250.
TC = $100 + $250 = $350.
ATC = TC ÷ Q = $350 ÷ 6 = $58.33.
Notice that ATC has fallen from $63.33 at Q=3 down to $58.33 at Q=6, which means the firm is still on the downward-sloping portion of its ATC curve (spreading fixed costs over more output).

Question 1

The Silph Company's marginal cost of increasing output from 4 scopes to 5 scopes is:

$20 $30 $50 $70

Hint MC = ΔTC ÷ ΔQ. Going from Q=4 to Q=5, workers increase from 5 to 8 (3 extra workers). Calculate ΔVC: those 3 extra workers plus the 1 extra scope.

Explanation Going from 4 to 5 scopes, workers rise from 5 to 8 (3 additional workers).
ΔVC = (3 workers × $10) + (1 scope × $20) = $30 + $20 = $50.
Since FC does not change, ΔTC = ΔVC = $50.
MC = ΔTC ÷ ΔQ = $50 ÷ 1 = $50.
This illustrates why MC rises as output increases — it takes more and more workers to produce each additional scope (diminishing marginal product).

Question 2

Does the Silph Company experience diminishing marginal product of labor? The marginal product of labor (MPL)…

Is constant at first (workers 1–3), then falls — yes, Silph experiences diminishing returns after the 3rd worker Is constant throughout all output levels — no diminishing returns Falls immediately from the very first worker — diminishing returns from the start Rises throughout — the firm experiences increasing returns to labor at all levels

Hint MPL = ΔQ ÷ ΔWorkers. Calculate it for each row: workers 0→1, 1→2, 2→3, 3→5, 5→8, 8→13, … Is each extra scope requiring more or fewer workers?

Explanation MPL at each step:
0→1 worker: ΔQ=1, ΔL=1 → MPL = 1.0
1→2 workers: ΔQ=1, ΔL=1 → MPL = 1.0
2→3 workers: ΔQ=1, ΔL=1 → MPL = 1.0
3→5 workers: ΔQ=1, ΔL=2 → MPL = 0.5
5→8 workers: ΔQ=1, ΔL=3 → MPL ≈ 0.33
8→13 workers: ΔQ=1, ΔL=5 → MPL = 0.2

The first three workers each add one scope (MPL = 1). After that, each additional scope requires more and more workers — diminishing marginal product sets in after the 3rd worker. This is why the MC curve eventually slopes upward.

Output (rides)	FC ($)	VC ($)	TC ($)	MC ($)	ATC ($)
0	50	0	50	—	—
1	A = ?	100	150	100	F = ?
2	50	180	230	80	115
3	50	240	290	60	96.67
4	50	320	370	80	92.50
5	50	450	500	130	100

Question 3

Refer to Table 1. What is the value of A — the fixed cost at output = 1?

$25 $50 $100 $200

Hint Fixed cost is, by definition, constant across all output levels. If FC = $50 at Q=0 and FC = $50 at Q=2, what must FC be at Q=1?

Explanation Fixed costs do not change with output — that is the entire definition of a fixed cost. The table shows FC = $50 at Q=0 and FC = $50 at Q=2. Therefore A = $50. The helicopter, insurance, and hangar lease cost the same whether Flying Elvis gives 1 ride or 5 rides per day.

Question 4

Refer to Table 1. What is the value of F — the average total cost (ATC) at output = 1?

$50 $100 $150 $200

Hint ATC = TC ÷ Q. At Q=1, TC = $150. What is $150 ÷ 1?

Explanation ATC = TC ÷ Q = $150 ÷ 1 = $150.
When only one unit is produced, ATC equals TC — there is no averaging to do. Notice how the ATC falls from $150 at Q=1 down to $92.50 at Q=4, then rises back to $100 at Q=5. This U-shape reflects the spreading of fixed costs at low output and diminishing returns at high output.

Question 5

When a factory is operating in the short run,

it cannot alter variable costs — those are fixed for the period total cost and variable cost are usually the same amount average fixed cost rises as output increases it cannot adjust the quantity of at least one fixed input

Hint The definition of the short run in economics: it's not about calendar time, but about what the firm cannot change. What distinguishes the short run from the long run?

Explanation The short run is defined as the period in which at least one input is fixed (typically capital — the factory size, the number of machines). The firm can still vary variable inputs like labor. Option A is wrong: variable costs can still change. Option B is wrong: TC = FC + VC, and FC > 0. Option C is wrong: AFC = FC/Q falls as Q rises (spreading the fixed cost over more units). Option D is the correct definition.

Question 6

If the marginal cost of producing the 10th unit is $2.50 and the average total cost of the 10th unit is $3.00, then ATC is rising at that output level.

Hint Think of the MC-ATC relationship like a grade average: if your next exam score (MC) is below your current average (ATC), does your average go up or down?

Explanation False. When MC < ATC, the "next unit" costs less than the average — so it pulls the average down. ATC is falling, not rising. ATC rises only when MC > ATC. ATC is at its minimum where MC = ATC. Here MC ($2.50) < ATC ($3.00), so ATC must be falling.

Question 7

Economists include both explicit and implicit costs when calculating economic cost, while accountants include only implicit costs.

Hint Explicit costs involve an actual cash payment. Implicit costs are opportunity costs with no cash outlay. Which type do accountants track? Which type do economists add on top?

Explanation False. The statement gets accountants exactly backwards. Accountants track only explicit costs — actual out-of-pocket payments like wages, rent, and materials. Economists include both explicit costs and implicit costs (opportunity costs like the owner's foregone salary or the return on capital invested elsewhere). This is why economic profit is always less than or equal to accounting profit.

Question 8

A firm with long-run total costs of $100, $200, $300, $400, $500 for quantities 1 through 5 is experiencing constant returns to scale.

Hint Compute the long-run ATC at each quantity: TC ÷ Q. Is the result rising, falling, or flat? That tells you whether the firm faces diseconomies, economies, or constant returns to scale.

Explanation True. Long-run ATC at each quantity:
Q=1: $100÷1 = $100
Q=2: $200÷2 = $100
Q=3: $300÷3 = $100
Q=4: $400÷4 = $100
Q=5: $500÷5 = $100

ATC is constant at $100 across all output levels — the definition of constant returns to scale. The long-run ATC curve is flat, and doubling inputs exactly doubles output.

Question 9

A firm with long-run total costs of $100, $200, $300, $400, $500 for quantities 1 through 5 is experiencing diseconomies of scale.

Hint This is the same cost data as Question 8. Diseconomies of scale means long-run ATC is rising. What did you find about ATC in Question 8?

Explanation False. As shown in Question 8, the long-run ATC is a constant $100 at every output level — this is constant returns to scale, not diseconomies. Diseconomies of scale would require ATC to rise as output increases (e.g., TC = $100, $210, $330, $460, $600 — rising ATC). Economies of scale would require ATC to fall. Here ATC is flat.

Question 10

A firm's total cost is $500 when it produces 10 units and $550 when it produces 11 units. The marginal cost of the 11th unit is:

$5 $50 $500 $550

Hint MC = ΔTC ÷ ΔQ. What is the change in total cost? What is the change in quantity?

Explanation MC = ΔTC ÷ ΔQ = ($550 − $500) ÷ (11 − 10) = $50 ÷ 1 = $50.
This is the straightforward application of the marginal cost formula. The 11th unit adds $50 to total cost. Note that MC has nothing to do with the total level of costs — only the change in cost matters.

Question 11

A baker quits a $60,000-per-year job to open a bakery that earns $80,000 in revenue with $25,000 in explicit costs. The baker's economic profit is:

$55,000 $20,000 −$5,000 $80,000

Hint Economic profit = Revenue − Explicit costs − Implicit costs. The implicit cost here is the salary the baker gave up. Accounting profit only subtracts explicit costs.

Explanation Accounting profit = Revenue − Explicit costs = $80,000 − $25,000 = $55,000.
But the baker also gave up a $60,000 salary — this is an implicit cost (opportunity cost).
Economic profit = $80,000 − $25,000 − $60,000 = −$5,000.
Despite earning positive accounting profit, the baker suffers an economic loss. Economically, staying at the old job would have been better. This is why economists consider implicit costs essential to any real business decision.

Question 12

The efficient scale of a firm is the quantity that minimizes:

marginal cost average variable cost average fixed cost average total cost

Hint "Efficient scale" is a specific term from Mankiw. A competitive firm produces at efficient scale in long-run equilibrium. What cost curve is at a minimum at that point?

Explanation The efficient scale is the quantity at which average total cost (ATC) is minimized. This is the bottom of the U-shaped ATC curve. AFC always falls (so it has no minimum in the usual sense). MC always crosses ATC from below at the ATC minimum. In a competitive market, firms are driven to produce at efficient scale in the long run, where price = minimum ATC.

Question 13

When marginal cost is below average total cost,

ATC is falling ATC is rising ATC is at its minimum point ATC equals MC

Hint Use the grade average analogy: if the grade on your next test (MC) is below your current course average (ATC), what happens to your average? Apply the same logic to costs.

Explanation When MC < ATC, producing one more unit costs less than the current average, so it pulls the average down — ATC is falling. When MC > ATC, the next unit costs more than average, pulling ATC up. ATC is at its minimum precisely where MC = ATC (the MC curve intersects ATC from below). This three-way relationship is one of the most tested concepts in Ch 13.

Practice Worksheet

Short Answer — The Silph Company Cost Table

Multiple Choice — Silph Co. & Cost Concepts

Multiple Choice — Flying Elvis Copter Rides (Table 1)

True or False

More Multiple Choice