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Ch. 13 & 14 Worksheet — Answer Key

Mankiw Ch. 13 & 14 · Prof. Pac’s Discussion Section · 13 questions

Short Answer — Silph Company Context
The Silph Company The Silph Company employs workers to make scopes. Wage = $10/worker, raw materials = $20/scope. Workers: 0, 1, 2, 3, 5, 8, 13, 21, 34 produce Scopes: 0, 1, 2, 3, 4, 5, 6, 7, 8. At 2 workers / 2 scopes: ATC = $80.
Context Note — ATC at 2 workers, 2 scopes
Why is ATC = $80 when 2 workers produce 2 scopes?
ATC = TC / Q = $80
Labor cost: 2 workers × $10 = $20 Materials cost: 2 scopes × $20 = $40 TC: $20 + $40 = $60 ATC: $60 / 2 = $30 — note the worksheet states ATC = $80, suggesting additional fixed costs of $100 (FC = $100 implied) With FC = $100: TC = $60 + $100 = $160. ATC = $160 / 2 = $80 ✓
Multiple Choice — Costs
Table 1 — Flying Elvis Copter Rides
OutputTCFCVCMCAFCAVCATC
050500
1150ABCDEF
2GHI120JKL
3MNOPQ120R
Question 1
Refer to Table 1. FC = $50, TC at 1 ride = $150. What is the value of A (fixed cost at output = 1)?
B $50
Fixed cost doesn’t change with output. FC is always $50 regardless of how many rides are given.
Question 2
Refer to Table 1. What is the value of F (ATC at output = 1)?
C $150
ATC = TC / Q = $150 / 1 = $150 per ride
Question 3
When a factory is operating in the short run,
D it cannot adjust the quantity of fixed inputs.
The short run is defined as the period in which at least one input (typically capital/factory) is fixed. Variable costs CAN be altered — that’s what makes them variable. Note: (C) is wrong because AFC falls as output increases (fixed cost spread over more units).
True or False
Table 2 — Long-Run Total Costs
Quantity12345
Firm A100100100100100
Firm B100200300400500
Firm C1003006001,0001,500
Questions 6–7 refer to Firm B in Table 2.
Question 4
If the marginal cost of producing the 10th unit is $2.50, and the ATC of the 10th unit is $3.00, then ATC is rising at that output.
B False
When MC < ATC, ATC is FALLING, not rising. Think of the batting average analogy: if today’s score ($2.50) is below your average ($3.00), your average goes down. Rule: MC < ATC → ATC falling  |  MC = ATC → ATC at min  |  MC > ATC → ATC rising.
Question 5
Economists include both explicit and implicit costs, while accountants include only implicit costs.
B False
Accountants include only EXPLICIT costs (cash outlays). Economists include both explicit AND implicit (opportunity) costs. The statement has “explicit” and “implicit” backwards for accountants.
Question 6
A firm with long-run total costs of $100, $200, $300, $400, $500 for quantities 1–5 is experiencing constant returns to scale.
A True
LRATC = TC / Q = $100/1 = $100  |  $200/2 = $100  |  $300/3 = $100  |  $400/4 = $100  |  $500/5 = $100 Since LRATC is constant as output increases, this is constant returns to scale.
Question 7
A firm with long-run total costs of $100, $200, $300, $400, $500 for quantities 1–5 is experiencing diseconomies of scale.
B False
Same data as Q6 — LRATC is constant at $100, not rising. Diseconomies of scale would require LRATC to rise (i.e., costs more than double when output doubles). This firm has constant, not increasing, average costs.
Multiple Choice — Competitive Markets
Question 8
Assume a firm in a competitive market produces Q = 1,000. MC = $15, ATC = $11, P = $12. The firm’s profits equal:
B $1,000
Profit = (P − ATC) × Q = ($12 − $11) × 1,000 = $1,000 Note: MC ($15) > P ($12) here, so the firm is producing beyond its profit-maximizing quantity in this scenario — but the question asks for profit at the stated output.
Question 9
A competitive firm sells at $45/unit. At 100 units, ATC = $24.50, FC = $900. Variable cost equals:
D $1,550.00
TC = ATC × Q = $24.50 × 100 = $2,450 VC = TC − FC = $2,450 − $900 = $1,550
Question 10
When new firms enter a perfectly competitive market,
C existing firms may see costs rise if more firms compete for limited resources.
Entry can bid up input prices (workers, land), raising costs for all firms. This is why some competitive markets have upward-sloping long-run supply curves (increasing-cost industries). Note: (A) and (B) are wrong because entry drives profits toward zero — existing firms earn positive profit before entry erodes it, and entering firms initially face the pre-entry price. (D) is wrong because in competitive markets, no individual firm sets prices.
Figure 1 Questions

Figure 1: MC (red), ATC (blue), AVC (orange) — all U-shaped. MC crosses AVC and ATC at their minimums. P4 = min ATC (break-even). P2 = between AVC min and ATC min. P7 = above ATC.

Figure 1 — Competitive Firm Cost Curves Price / Cost ($) Quantity P7 P6 P5 P4 P3 P2 P1 Q1 Q2 Q3 Q4 Q5 AVC ATC MC min ATC (break-even) min AVC (shutdown) (P7−P5)×Q3 = Profit (P4−P2)×Q2 = Loss
Question 11
Refer to Figure 1. When market price is P7, a profit-maximizing firm’s short-run profits can be represented by:
C (P7 − P5) × Q3
Profit = (P − ATC) × Q At P7, the firm produces Q3 (where P7 = MC). ATC at Q3 is P5. So profit = (P7 − P5) × Q3 This is the green shaded rectangle in Figure 1 above.
Question 12
Refer to Figure 1. In the short run, if market price is P4, individual firms earn:
B zero profits.
P4 is at the minimum of ATC (the break-even point). At P = min ATC, the firm produces where P = MC and earns exactly zero economic profit. Accounting profit may still be positive because economic profit includes implicit (opportunity) costs.
Question 13
Refer to Figure 1. When market price is P2, a profit-maximizing firm’s losses can be represented by:
A (P4 − P2) × Q2
At P2 (between AVC min and ATC min), the firm produces Q2 (where P2 = MC). ATC at Q2 is P4. Since P2 < P4, the firm makes a loss. Loss = (ATC − P) × Q = (P4 − P2) × Q2 The firm operates at a loss but stays open in the short run because P2 > P1 (above AVC min), meaning it covers variable costs. Shutdown rule: shut down only if P < min AVC (i.e., price below P1).
Quick Reference
#QuestionAnswer
1Value of A (fixed cost at output=1)?B — $50
2Value of F (ATC at output=1)?C — $150
3Short run: factory cannot…D — adjust fixed inputs
4MC=$2.50 < ATC=$3.00 → ATC rising? (T/F)B — False (ATC falling)
5Accountants include only implicit costs? (T/F)B — False (explicit only)
6TC=$100,$200,…,$500 → constant returns? (T/F)A — True
7Same data → diseconomies of scale? (T/F)B — False (constant)
8Profit at Q=1000, P=$12, ATC=$11?B — $1,000
9VC at 100 units, ATC=$24.50, FC=$900?D — $1,550
10New firm entry effect?C — input prices may rise
11Profit rectangle at P7?C — (P7−P5)×Q3
12Profit at P4 (min ATC)?B — zero profits
13Loss rectangle at P2?A — (P4−P2)×Q2