CHAPTER 7
COST
THEORY AND ESTIMATION
1. Fairweather Construction, Inc., has
the following short-run total cost schedule:
Q 0 1 2 3 4 5 6 7 8 9 10 11
TC 100 106 109 110
112 115 119
124 130 137 145 155
(i) What is the firm's average fixed
cost when Q
= 5?
(ii) What is the firm's average
variable cost when Q = 4?
(iii) What is the firm's average total
cost when Q
= 4?
(iv) What is the firm's marginal cost
when Q
= 10?
(v) At what level of output does the
firm begin to experience diminishing returns?
Solution:
(i) AFC = 100/5 = 20 when Q = 5.
(ii) AVC = 12/4 = 3 when Q = 4.
(iii) ATC = 112/4 = 28 when Q = 4.
(iv) MC = (145 − 137)/(10 − 9) = (45 − 37)/(10
− 9) = 8 when Q =
10.
(v) MC is at a minimum when Q = 3. Therefore, diminishing returns set
in when
Q >
3.
2. Fairview Construction, Inc., has the
following short-run total cost schedule:
Q 0 1 2 3 4 5 6 7 8 9 10 11
TC 50 58 62 64 65 67 71 78 88 102 121 146
(i) What is the firm's average fixed
cost when Q
= 5?
(ii) What is the firm's average
variable cost when Q = 7?
(iii) What is the firm's average total
cost when Q
= 8?
(iv) What is the firm's marginal cost
when Q
= 9?
(v) At what level of output does the
firm begin to experience diminishing returns?
Solution:
(i) AFC = 50/5 = 10 when Q = 5.
(ii) AVC = 28/7 = 4 when Q = 7.
(iii) ATC = 88/8 = 11 when Q = 8.
(iv) MC = (102 − 88)/(9 − 8) = (52 − 38)/(9 −
8) = 14 when Q = 9.
(v) MC is at a minimum when Q = 4. Therefore, diminishing returns set
in when
Q >
4.
3. Oceanview Construction, Inc., has
the following short-run total cost schedule:
Q 0
1 2 3 4 5 6 7 8 9 10 11
TC 75 85 91 94 95 98 104 114
129 151 181
221
(i) What is the firm's average fixed
cost when Q
= 5?
(ii) What is the firm's average
variable cost when Q = 4?
(iii) What is the firm's average total
cost when Q
= 10?
(iv) What is the firm's marginal cost
when Q
= 8?
(v) At what level of output does the
firm begin to experience diminishing returns?
Solution:
(i) AFC = 75/5 = 10 when Q = 5.
(ii) AVC = 20/4 = 5 when Q = 4.
(iii) ATC = 181/10 = 18.1 when Q = 10.
(iv) MC = (129 − 114)/(8 − 7) = (54 − 39)/(8 −
7) = 15 when Q = 8.
(v) MC is at a minimum when Q = 4. Therefore, diminishing returns set
in when
Q >
4.
4. Farview Construction, Inc., has the
following short-run total cost schedule:
Q 0 1 2 3 4 5 6 7 8 9 10 11
TC 30 38 43 46 48 52 59 70 87 112 147
197
(i) What is the firm's average fixed
cost when Q
= 10?
(ii) What is the firm's average
variable cost when Q = 4?
(iii) What is the firm's average total
cost when Q
= 7?
(iv) What is the firm's marginal cost
when Q
= 9?
(v) At what level of output does the
firm begin to experience diminishing returns?
Solution:
(i) AFC = 30/10 = 3 when Q = 10.
(ii) AVC = 18/4 = 4.5 when Q = 4.
(iii) ATC = 70/7 = 10 when Q = 7.
(iv) MC = (112 - 87)/(9 - 8) = (82 - 57)/(9 -
8) = 25 when Q = 9.
(v) MC is at a minimum when Q = 4. Therefore, diminishing returns set
in when
Q >
4.
5. Tetrangle Manufacturing has fixed
costs of $2,160 per day. The firm manufactures bicycle component upgrade kits.
The kits have a short-run average variable cost of $48 and are sold for $66
each.
(i) What is the breakeven level of daily
output for the firm?
(ii) What is the degree of operating
leverage when daily output is Q = 170?
Solution:
(i) The breakeven level of daily output
for the firm is 2160/(66 − 48) = 120.
(ii) The degree of operating leverage (DOL) when daily output is Q = 170 is:
DOL =
{(170)(66 − 48)}/{(170)(66 − 48) − 2160} = 3.4
6. Triangle Manufacturing has fixed
costs of $2,000 per week. The firm manufactures tricycle kits. The kits have a
short-run average variable cost of $25 and are sold for $35 each.
(i) What is the breakeven level of
weekly output for the firm?
(ii) What is the degree of operating
leverage when weekly output is Q = 250?
Solution:
(i) The breakeven level of daily output
for the firm is 2000/(35 − 25) = 200.
(ii) The degree of operating leverage (DOL) when daily output is Q = 250 is:
DOL =
{(250)(35 − 25)}/{(250)(35 − 25) − 2000} = 5
7. Bob and Bill are college students.
They are trying to decide what to do over the next summer. Bob's father has
suggested that they both come and work at his plastics manufacturing company
where each will earn $3,600 over the summer. Bill's father, who runs the local
farmer's market, suggests that they go to a local resort area and sell fresh fruit
and vegetables to tourists. Their markup on the produce would be 25 percent, so
each $1.00 of revenue would involve a variable cost of $0.80. In addition to
purchasing the produce, they would have to rent a location. The cost to rent a
small roadside stand
for the summer is $2,400.
(i) How many dollars worth of produce
will they have to sell in order to break even in an accounting sense?
(ii) How many dollars worth of produce
will they have to sell in order to break even in an economic sense?
Solution:
(i) 2400/(1.00 − 0.80) = $12,000
(ii) (2400 + 3600 + 3600)/(1.00 − 0.80)
= $48,000
8. Barb and Cheryl are college
students. They are trying to decide what to do over the next summer. Barb's
mother has suggested that they both come and work at her plastics manufacturing
company where each will earn $5,250 over the summer. Cheryl's mother, who runs
the local farmer's market, suggests that they go to a local resort area and
sell fresh fruit and vegetables to tourists. Their markup on the produce would
be one-third, so each $1.00 of revenue would involve a variable cost of $0.75.
In addition to purchasing the produce, they would have to rent a location. The
cost to rent a small roadside stand
for the summer is $2,500.
(i) How many dollars worth of produce
will they have to sell in order to break even in an accounting sense?
(ii) How many dollars worth of produce
will they have to sell in order to break even in an economic sense?
Solution:
(i) 2500/(1.00 − 0.75) = $10,000
(ii) (2500 + 5250 + 5250)/(1.00 − 0.75) = $52,000
No comments:
Post a Comment