Answer key – Problem Set 3
Chapter 7
Managerial Economics and Business Strategy, 7e Page 1
Chapter 7: Answers to Questions and Problems
1. The four-firm concentration ratio is,
4 $175, 000 $150, 000 $125, 000 $100, 000 0.55 $1, 000, 000 C " ! ! ! " . 2. a. The HHI is 2 2 2 $200, 000 $400, 000 $500, 000 10, 000 =3,719 $1,100, 000 $1,100, 000 $1,100, 000 HHI " %!#' ($ !#' $( !#' $( &" ) * ) * ) * % & + , .
b. The four-firm concentration ratio is 100 percent.
c. If the firms with sales of $200,000 and $400,000 were allowed to merge, the resulting HHIwould increase by 1,322 to 5,041. Since the pre-merger HHI exceeds that under the Guidelines (1,800) and the HHI increases by more than that permitted under the Guidelines (100), the merger is likely to be challenged. 3. The elasticity of demand for a representative firm in the industry is –1.5, since
. 5 . 1 6 . 0 9 . 0 9 . 0 6 . 0 " # - F " # "# F E E . 4.
a. $100. To see this, solve the Lerner index formula for P to obtain
1 1 $35 $100 1 1 0.65 P MC L # $ # $ "' ( "' ( " # # ) * ) * . b. Since 1 1 P MC L # $ "' ( #
) * , it follows that the markup factor is 1 2.86 1 0.65 # $" ' # ( ) * .
That is, the price charged by the firm is 2.86 times the marginal cost of producing the product.
c. The above calculations suggest price competition is not very rigorous and that the firm enjoys market power.
5. Managers should not specialize in learning to manage a particular type of market structure. Market structure generally evolves over time, and managers must adapt to these changes.
6. To the extent that the HHIs are based on too narrow a definition of the product (or geographic) market or the impact of foreign competition, the merger might be allowed. It might also be allowed if one of the firms is in financial trouble, or if significant economies of scale exist in the industry.
Page 4 Michael R. Baye
17. See Table 7-1.
Own Price Elasticity of Market Demand
Own Price Elasticity of Demand for Representative Firm's
Product Rothschild Index
Agriculture -1.8 -96.2 0.019
Construction -1.0 -5.2 0.192
Durable manufacturing -1.4 -3.5 0.400
Nondurable manufacturing -1.3 -3.4 0.382
Transportation -1.0 -1.9 0.526
Communication and utilities -1.2 -1.8 0.667
Wholesale trade -1.5 -1.6 0.938
Retail trade -1.2 -1.8 0.667
Finance -0.1 -5.5 0.018
Services -1.2 -26.4 0.045
Table 7-1
Based on the Rothschild indices in Table 7-1, wholesale trade most closely resembles a monopoly, while finance most closely resembles perfect competition.
18. The Lerner index is $3 $0.30 0.9 $3
P MC
L P
! !
" " " , which indicates the firm has considerable market power. This makes sense because the product that the firm sells is currently under patent protection, which essentially makes the firm a legal monopoly.
19. Based on the information contained in Table 7-3 of the text, the food and apparel industries are most competitive and therefore probably represent the best match for the expertise of these managers.
20. The market for color film in the U.S. is highly concentrated. The five-firm
concentration ratio is 100 percent and Kodak alone accounts for 67 percent of all rolls sold. Market demand for color film is relatively elastic at -1.75; indicating that a 10 percent increase in price leads to a 17.5 percent decline in quantity demand for color film. The Rothschild index indicates that market demand relative to the demand for Kodak color film is 0.875
2 75 . 1 " ! ! "
R , indicating that Kodak’s demand is, roughly, as sensitive to price changes as is the entire market demand. The Lerner index for
Kodak is 0.50 95 . 6 $ 475 . 3 $ 95 . 6 $ ! " "
L , indicating that Kodak’s markup factor is 2. For every $1 spent on color film, $0.50 is markup. Taken together, these things suggest that the color film industry in the U.S. closely resembles an oligopoly.
Chapter 8
Managerial Economics and Business Strategy, 7e
Page 1
Chapter 8: Answers to Questions and Problems
1.
a.
7 units.
b.
$28.
c.
$224, since $32 x 7 = $224.
d.
$98, since $14 x 7 = $98.
e.
$126 (the difference between total cost and variable cost).
f.
It is earning a loss of $28, since ($28 -$32) x 7 = - $28.
g.
- $126, since its loss will equal its fixed costs.
h.
Shut down.
2.
a.
Set P = MC to get $80 = 8 + 4Q. Solve for Q to get Q = 18 units.
b.
$80.
c.
Revenues are R = ($80)(18) = $1440, costs are C = 40 + 8(18) + 2(18)
2= $832, so
profits are $608.
d.
Entry will occur, the market price will fall, and the firm should plan to reduce its
output. In the long-run, economic profits will shrink to zero.
3.
a.
7 units.
b.
$130.
c.
$140, since ($130 – 110) x 7 = $140.
d.
This firm’s demand will decrease over time as new firms enter the market. In the
long-run, economic profits will shrink to zero.
4.
a.
MR = 200 – 4Q and MC = 6Q. Setting MR = MC yields 200 – 4Q = 6Q. Solving
yields Q = 20 units. The profit-maximizing price is obtained by plugging this into
the demand equation to get P = 200 - 2(20) = $160.
b.
Revenues are R = ($160)(20) = $3200 and costs are C = 2000 + 3(20)
2= $3200,
so the firm’s profits are zero.
c.
Elastic.
d.
TR is maximized when MR = 0. Setting MR = 0 yields 200 – 4Q = 0. Solving for
Q yields Q = 50 units. The price at this output is P = 200 – 2(50) = $100.
e.
Using the results from part d, the firm’s maximum revenues are R = ($100)(50) =
$5,000.
f.
Unit elastic.
Page 2
Michael R. Baye
5.
a.
A perfectly competitive firm’s supply curve is its marginal cost curve above the
minimum of its AVC curve. Here,
50 8
3
2i i i
MC
!
"
q
#
q
and
2 3 250
4
50 4
i i i i i i iq
q
q
AVC
q
q
q
"
#
!
!
"
#
. Since MC and AVC are equal at the
minimum point of AVC, set MC
i= AVC
ito get
50 8
"
q
i#
3
q
i2!
50 4
"
q
i#
q
i2,
or
q
i!
2
. Thus, AVC is minimized at an output of 2 units, and the corresponding
AVC is
AVC
i!
50 4 2
"
$ % $ %
#
2
2!
46
. Thus the firm’s supply curve is described
by the equation
50
8
3
2i
i
q
q
MC
!
"
#
if
P
&
$46
; otherwise, the firm produces
zero units.
b.
A monopolist produces where MR = MC and thus does not have a supply curve.
c.
A monopolistically competitive firm produces where MR = MC and thus does not
have a supply curve.
6.
a.
Q = 3 units; P = $70.
b.
Q = 4 units; P = $60.
c.
1
$
$70 $40 1
%$ %
$15.
2
DWL
!
"
!
7.
a.
The inverse linear demand function is P = 10 – .5Q.
b.
MR = 10 – Q and MC = –14 + 2Q. Setting MR = MC yields 10 – Q = –14 + 2Q.
Solving for Q yields Q = 8 units. The optimal price is P = 10 – .5(8) = $6.
c.
Revenues are R = ($6)(8) = $48. Costs are C = 104 – 14(8) + (8)
2= $56. Thus the
firm earns a loss of $8. However, the firm should continue operating since it is
covering variable costs.
d.
In the long run exit will occur and the demand for this firm’s product will increase
until it earns zero economic profits. Otherwise, the firm should exit the business
in the long run.
8.
a.
The optimal advertising to sales ratio is given by
,,
0.1
0.05
2
Q A Q PE
A
R
!
"
E
!
!
.
b.
,$ %$
%
,0.1
.05 $50, 000
$2, 500
$50, 000
2
Q A Q PE
A
A
A
R
!
"
E
!
!
!
!
!
.
Page 4
Michael R. Baye
14.
Profit maximization requires equating MR and MC. Since
1
1 2.5
$1.25
$0.75
2.5
E
MR
P
E
!
"
!
"
!
"
#
#
$
#
#
$
#
"
%
&
%
&
and MC = $0.25, MR > MC. This means
your firm can increase profits by reducing price in order to sell more pills.
15.
Notice that MR = 1,000 – 10Q, MC
1= 10Q
1and MC
2= 4Q
2. In order to maximize
profits (or minimize its losses), the firm equates MR = MC
1and MR =MC
2. Since Q
= Q
1+ Q
2, this gives us
$
%
$
%
1 2 1 1 2 21000 10
10
1000 10
4
Q
Q
Q
Q
Q
Q
"
!
#
"
!
#
.
Solving yields
1200
22.22
9
Q
#
&
units and
2500
55.56
9
Q
#
&
units. The optimal price
is the amount consumers will pay for the
1 2200
500
700
77.78
9
9
9
Q
!
Q
#
!
#
&
units,
and is determined by the inverse demand curve:
700
$5, 500
1, 000 5
$611.11
9
9
P
#
"
!
#
"
$
#
&
%
&
. At this price and output, revenues are R =
($611.11)(77.78) = $47,532.14, while costs are
$
%
$
2%
$
$
%
2%
1 2
10, 050 5 22.22
5, 000 2 55.56
$23,692.47
C
!
C
#
!
!
!
#
. The firm thus
earns profits of $23,839.67.
16.
College Computers is a monopolistically competitive firm and faces a downward
sloping demand for its product. Thus, you should equate MR = MC to maximize
profits. Here, MR = 1000 – 2Q and MC = 2Q. Setting 1000 – 2Q = 2Q implies that
your optimal output is 250 units per week. Your optimal price is P = 1000 – 250 =
$750. Your weekly revenues are R = ($750)(250) = $187,500 and your weekly costs
are C = 2000 + (250)
2= $64,500. Your weekly profits are thus $123,000. You should
expect other firms to enter the market; your profits will decline over time and you
will lose market share to other firms.
17.
Your average variable cost of producing the 10,000 units is $600 (depreciation is a
fixed cost). Since the price you have been offered ($650) exceeds your average
variable cost ($600), you should accept the offer; doing so adds $50 per unit (for a
total of $500,000) to your firm’s bottom line.
Chapter 9
Managerial Economics and Business Strategy, 7e
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Chapter 9: Answers to Questions and Problems
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Part 2.
Problem 1.
‐ See page 241‐243 of the textbook.
1 Part II
1.1 Problem 2
Marginal revenuesM R= 100−2Q
Marginal cost San JoseM CSJ = 4qsj
Marginal cost Santa CruzM CSC = 6qsc
We know that a sufficient condition to produce in both plants is M R = M CSJ=M CSC
working out the algebra, we getqsj= 3/2qsc and 100−2qsj−2qsc = 6qsc 100−3qsc−2qsc = 6qsc
100/11 = qsc
Therefore,qsj= 150/11
For completeness we need to check if joint profits is higher than profits producing using one plant.
πBOT H = 100−500/11−100−2∗(150/11)2−3(100/11)2
Notice thatq1SJ= 100/6andqSC1 = 100/8
πSJ= 100−200/6−75−2∗(100/6)2
πSC = 100−200/8−25−3∗(100/8)2
comparing profits, we can check that it is optimal to produce ONLY in Santa Cruz!
1.2 Problem 3 - from the game in class
let’s work out a general case and then use the variables given in the problem set,
assume a linear inverse demand P =A−b(!iN=1qi) = A−bQ and a liner
cost functionCi=cqi
where qi represents the quantity produced by firm i,N is the total number
of firms in the market andQthe total quantity produced in the market. the profits for the firmj is given by
πj=P qj−cqj the FOC is A−b( N " i=1 qi)−bqj−c= 0
then adding the FOC for each firm in the market
N·A−N·b·Q−bQ−N c= 0
1
then solving forQ
Q=N(A−c) b(N+ 1)
Now, let’s check the parameters given in the problem set. We know that
A= 100,N = 4,c= 4,b= 1
therefore, the total quantity in the market isQ= 4∗96
5 then each firm
pro-ducesqi= 96/5≈19
Note: Notice that game in class, groups are choosing quantities simulta-neously. Therefore, the appropiate model to study the game played is the COURNOT model. Cournot was one of the pioneers in micro-theory.
2