Solutions to Odd–Numbered Problems
Chapter 3
1. a. 800 caps
b. $10
c. $20
3. b. P = $4.00
5. a. QD = 61,000 – 200P
b, 0, 26,000, 31,000, 36,000
c. $80
7. Supply curve shifts to right and demand curve shifts to left. The combined shifts drastically reduced the world market price of sugar.
9. a. No, because point elasticity is – 0.625.
b. Yes, although the number of units sold would drop from 12,000 to 10,000, the combined impact of an inelastic demand and the increase in advertising would raise total revenue from $36,000 to $40,000. Moreover the incremental revenue is far greater than the $100 increase in advertising expenses.
11. a. P = 25 – 0.1Q
b. P = 9.29 – 0.007Q
c. P = 90 – 2Q
Chapter 4
1. 0.2/–0.1 = –2
3. a. 1,400
b. 2
c. 2,000
d. 2
e. –0.43
5. a. –0.88
b. –0.58
c. –0.88
7. a. 4,421
b. 2,865
9. Arc price elasticity = –1.36
Arc cross elasticity = –0.85
11.a. negative
b. positive
c. negative
d. probably zero
13. a. Elasticity for Brown’s shoes may be greater than elasticity for all shoes in general. If elasticity for Brown’s shoes is >/1/, then price decrease could lead to revenue increase.
b. Increase 9 percent.
15. a. –1.4
b. Complementary good; cross elasticity –0.7.
c. Yes, revenues for ice cream and syrup rise, and probably so does profit.
17. a. 1,800
b. $0, $100, $25
c. TR = 100Q – 0.05Q2; MR = 100 – 0.1Q
d. TR = $42,000; MR = $40
e. ε = -2.33
f. TR = $48,000; MR = $20; ε = -1.5
g. 1,000
19. Elasticity is –0.934
Revenue decreases from £159,750 to £155,400.
21. a. 3
b. E = -0.66; $18,400,000
c. Demand curve is inelastic. Increase in price could increase revenue.
Chapter 5
Demand Estimation
1. Price: average price of furniture or of specific furniture type
Price of related products: competitors’ prices, housing prices
Tastes: advertising expenditure, information about buyers’ age, income, education, etc
Income: per capital disposable income
Credit: an interest rate such as prime rate or rate on short–term U.S. Treasuries
Number of buyers: number of households
3.a. Ep = –1.18, Ex= 0.68, EI = 1.62, EA = 0.113, EM = 0.07
b. Very concerned; elasticity is high.
c. Possibily; product is price elastic.
d. About 55%; Significant at 5% level.
5. a. Japanese luxury cars are close substitutes for European luxury cars.
b. Superior product
c. Relatively inelastic; not surprising
Forecasting
1. 16%
3. a. 1,500
b. 300, 375, 468.75, 356.25
5. a. 176.667 + 20.5879t; 176.667 + 20.5879 (11) = $403. Past 10 years describe straight line; thus some
confidence that trend will continue.
b. 382 x 0.7 + 353 x 0.3 = 373. Upward trend makes exponential smoothing an inferior forecasting tool; it
underestimates.
7. a. Q = 17,350
b. Q = 17,200, Q = 17,400
c. Q = 17,500
d. Q decreases by 1,200
9. January, $55.4 million; April, $104.3 million, July, $87.5 million; October, $109.6 million
11. 597.5
Chapter 6
1. a. False b. True c. True d. False
3. a. 4 units b. 1–6, 6–11, 11 and above units of labor
c. 9 workers, reduce to 8, no change because still in Stage II
5. a. more to Mexico or possibly Taiwan
b. either Mexico or Taiwan (Taiwan has lower MP/P but also lower overhead)
7. a. & b.
Variable Factor / Quantity / AverageProduct / Marginal
Product
0 / 0.0
1 / 7.5 / 7.5 / 7.5
2 / 15.6 / 7.8 / 8.1
3 / 23.7 / 7.9 / 8.1
4 / 31.2 / 7.8 / 7.5
5 / 37.5 / 7.5 / 6.3
6 / 42.0 / 7.0 / 4.5
7 / 44.1 / 6.3 / 2.1
8 / 43.2 / 5.4 / –0.9
9 / 38.7 / 4.3 / –4.5
10 / 30.0 / 3.0 / –8.7
9. a. log Q = 1.889 + .414 log M
b. Fairly satisfactory, could improve if additional independent variables are included.
c. 2.91, 2.66, 2.51, 2.46, 2.37, 2.22, 2.16
11. a. budget line shifts to right
b. budget line becomes steeper (from X)
c. budget line becomes flatter (from Y)
d. budget line rotates and becomes steeper
e. isoquant shifts to right with bias toward Y
f. parallel shift of isoquant to the left
13. a. CRTS b. CRTS c. IRTS d. DRTS e. IRTS f. IRTS
g. If exponents sum to unity, CRTS. If they are less than unity, DRTS. If they are greater than unity, IRTS.
15. a. 0.75 + 0.3 = 1.05. Increasing
b.
Labor / Capital100 / 50 / 132.9
150 / 75 / 203.5
300 / 150 / 421.3
c. 10.9 percent
d. 7.4 percent; decreasing marginal product, e. 2.9 percent f. constant returns to scale
Chapter 7
1.
Q / TC / TFC / TVC / AC / AFC / AVC / MC0 / 120 / 120 / 0 / X / X / X
1 / 265 / 120 / 145 / 265 / 120 / 145 / 145
2 / 384 / 120 / 264 / 192 / 60 / 132 / 119
3 / 483 / 120 / 363 / 161 / 40 / 121 / 99
4 / 568 / 120 / 448 / 142 / 30 / 112 / 85
5 / 645 / 120 / 525 / 129 / 24 / 105 / 77
6 / 720 / 120 / 600 / 120 / 20 / 100 / 75
7 / 799 / 120 / 679 / 114.1 / 17.1 / 97 / 79
8 / 888 / 120 / 768 / 111 / 15 / 96 / 89
9 / 993 / 120 / 873 / 110.3 / 13.3 / 97 / 105
10 / 1120 / 120 / 1000 / 112 / 12 / 100 / 127
3. If only relevant costs are included, it would be $188 or $9.40 per fish.
5. a. False, decisions are future oriented so managers should use the replacement, not the historical costs of raw materials.
b. True, this can be explained by the mathematical relationship between marginal and average.
c. True, declining long–run AC means economies of scale and increasing long– run AC means diseconomies of scale.
d. False, marginal cost can also be used in long–run analysis because even the “fixed” cost varies in the long run.
e. False, the rational firm will operate where profit is maximized. This may not coincide with the point of minimum
average cost because per unit revenue must also be taken into account.
7. a.LRAC = 160 – 20Q + 1.2Q2
LRMC = 160 – 40Q + 3.6Q2
b. Because of the particular functional form of the LRAC, we know this firm experiences economies of scale
at about 8 units of output (8.3 to be exact).
9. b. & c. Straight line: TC = 94.93 + 0.46
R2 = 0.91 t = 8.96
Quadratic: TC = 106.68 – 0.13Q + 0.005Q2
R2 = 0.99 tb = –1.41; tc = 6.70
Cubic: TC = 99.5 + 0.51Q – 0.009Q2 + 0.00008Q3
R2 = 0.999 tb = 6.30; tc = –5.07; td = 8.36
Cubic function gives best fit.
11. c. (1) Straight–line function; AVC and MC are constant. (2) TC increases at increasing rate; MC rises. (3) TC increases at decreasing rate; MC, AVC, and AC decrease.
13. a. & b.
Quantity / Total Cost / Average Total Cost / Average Variable Cost / Marginal Cost1 / $193.5 / $193.50 / $23.50 / $23.50
4 / 282.0 / 70.50 / 28.00 / 32.50
7 / 397.5 / 56.79 / 32.50 / 41.50
10 / 540.0 / 54.00 / 37.00 / 50.50
13 / 709.5 / 54.58 / 41.50 / 59.50
c. Marginal cost rises throughout.
Chapter 8
1. The graph indicates the firm is losing money but is earning enough revenue to cover all its variable cost and
contributes the rest to its fixed cost. In the long run, it would have to drop out of the market unless the market
price increased or the firm is able to reduce its costs.
3. a. Implies a quadratic total cost function (i.e., law of diminishing returns occurs at outset of production).
b. At Q = 1,500, MC = $157.50; At Q = 2,000, MC = $160.00; At Q = 3,500, MC = $167.50
c. MC = $150 + 0.005, Q = $175, Q* = 5,000
d. Supply curve is the portion of the firm’s marginal cost that lies above the shutdown point.
5. b. Yes c. Produce 14 units because loss would be less than total fixed cost.
7. a. $63 b. $50
9. Setting the derivative of the total cost function equal to the derivative of the total revenue function and solving
for Q yields the same result as setting the total profit function equal to 0 and solving for Q.
Appendix 8B
1. a. 2,000 b. $50,000 c. $15,000 d. 2,500
e. 2,500 = (37,500 + 15,000)/(P – 10); P = $31
3. AVC = $77; TFC = $120,000
a. 120,000/(100 – 77) = 5,217 b. $521,700
c.
Q / Profit2,000 / $–74,000
4,000 / –28,000
6,000 / 18,000
8,000 / 64,000
10,000 / 110,000
5. a. 20,000 b. (60,000 + 15,000) / (9 – 6) = 25,000
c. undefined (denominator = 0); 5 d. 3
7. a. 70,000 b. (1) 80,000 (2) 70,000 = 1,200,000 / (P – 5); P = $22.14
c. (1) (Q x 12) – 840,000 = (Q x 14) – 1,200,000 Q = 180,000 Profit = $1,320,000 (2) 1.64; 1.91
(3) No; equal profit reached at 180,000 units.
9. a. 80,000
b. $100,000
c. 125,000
d. $9.50
e. $3.50
f. 125,000
Chapter 9
1. a. At 50–cent intervals starting from $12.50 and decreasing to $8.00, the arc elasticities are –1.96, –1.74,
–1.55, –1.38, –1.24, –1.11, –1, –0.9, and –0.8.
b. $8.75 would be too low for the students. Optimal price is between $12 and $11.50.
c. Students would suffer a loss if the opportunity cost of their venture were included in the total cost.
d. $8.75 may help increase the store’s revenue. It could even be offered to customers as a loss leader.
3. b. The first firm will have the following MR (starting from $10.00 and decreasing to $3.00 at one dollar
intervals): $8.75, $6.75, $4.75, $2.75, $0.75, –$1.25, and –$3.25. The second firms comparable data are
$4.33, $2.33, $.033, –$1.67, –$3.67, –$5.67, and –$7.67.
e. Range would be at where the MR line is vertical.
5. a. Although prices are lower, the costs of goods sold are proportionately even lower and so profit margins are
often higher for private–label goods than for brand name items.
b. Very often the manufacturers of the private products are the same ones that manufacture the brand names. By
selling them as private-label product, they save on the marketing expenses.
7. a. P = $22 b. Demand would fall, economic profit would approach zero.
c. P = $12
9. Assume you have decided $250,000 to be the maximum amount you could spend for the new product,
leaving the rest for the other products. You will probably end up spending this maximum amount (this is
the equivalent of a firm charging the lowest possible price).
Chapter 10
1. TC = 6 + 10Q; TR = 15X – 0.5Q2; Profit = –0.5Q2 + 5Q –6; Maximum profit = 6.5, at Q = 5 and P =
12.5
3. a. (1) Schedule: Q = 7–8, P = $340–360; Equation: Q = 7.5, P = $350
(2) Schedule: Q = 12–13, P = $240–260; Equation: Q = 12.5, P = $250
(3) Schedule: Q = 10, P = $300
b (1) Same as above. (2) Same as above. (3) Q = 9, P = $320
c. In the Baumol model, a change in TFC affects price and quantity.
5. $67.50
7. When TC = $15,000: profit = $21,000, peaches = 400 bushels, apples = 600 bushels. When TC = $25,000:
profit = $29,000, peaches = 600 bushels, apples = 900 bushels.
9. Authors would favor highest possible revenue; that would take place at a price lower than when profits are
maximized. Students would be on side of authors.
11. a. –4
b. 33.3%
Chapter 11
1. On horizontal and vertical axes: “high advertising spending” and “low advertising spending.” Within the matrix, the
numbers could represent the “contribution margin” (e.g., incremental profit minus incremental advertising
spending). The most difficult part of this exercise is to determine the relative magnitudes for the profit pay–off
matrix and as well as for “high” versus “low” amounts of advertising. These could be highly subjective but the
experienced manager might be able to provide a rough estimate of these values.
Chapter 12
1. Buyer must make monthly payments, thus decreasing balance in savings account, and interest earnings
will be lower.
3.Sell at end of year 4,
5.Operating cash flows (after taxes)
Year 1 $27,000
Years 2, 3, and 4, each 36,000
Year 5 24,000
PV of operating cash flows $114,927
PV of salvage (after taxes) 3,404
Additional working capital –15,000
PV of returned working capital 8,511
Original investment –150,000
NPV $–38,158
Do not make investment.
7. Net present value cost of furnishing car is $13,402. Net present value cost of paying mileage is $11,982.
Company should pay mileage.
9. Bonds +0.28 x 0.066 0.0185
Equity 0.72 x 0.14 0.1008
Weighted cost 0.1193 = 11.9%
11. a. NPV IRR
Project C 10,355 23.0%
Project D 9,237 25.0
b. Select C; NPV is higher.
13.a. $320 b. $30.98 c. 0.097
15.a. NPV = 295; σ = 115; CV = 0.3898
b. Relative risk is about equal, but B’s NPV is higher; thus, B could be selected.
17.CV of A = 0.25, CV of B = 0.33. A is preferred.
19. a.NPV = $870
b.NPV = $25,415
c.NPV = $–23,379
21. a. NPV = –$51,737; not acceptable
b. NPV = $21,671; acceptable
Value of option = $73,408.
Chapter 13
1. a. €1,692,740
b. $–147,049
c. Do not accept.
3. a. $1,400,000 b. $1,380,000 c. $1,390,000 d. gain
Review of Mathematical Concepts
1. a. Q = 75 – 0.5P b. P = 150 – 2Q
3. a. AVC = 300 – 25Q + 1.5Q2
AC = 1,500/Q + 300 – 25Q + 1.5Q2
MC = 300 – 50Q + 4.5Q2
AVC = 300 + 25Q
AC = 1,500/Q + 300 + 25Q
MC = 300 + 50Q AVC = 300
AC = Q + 300
MC = 300