Assignment 3 Network Security Planning - SAFE· Securing a lar.docx

Assignment 3: Network Security Planning - SAFE
· Securing a large internetwork remains a daunting challenge.
Cloud computing and social networks add to this complexity. In
two to three (2-3) pages, and using the CISCO SAFE reference
architecture, review the modules that afford an organization the
foremost protection in evolving technologies and media.
Write a two to three (2-3) page paper in which you:
1. Determine if the SAFE architecture has any limitations.
Use at least three (3) quality resources in this assignment.
Note: Wikipedia and similar Websites do not qualify as quality
resources.
Your assignment must follow these formatting requirements:
. Be typed, double spaced, using Times New Roman font (size
12), with one-inch margins on all sides; citations and references
must follow APA or school-specific format. Check with your
professor for any additional instructions.
. Include a cover page containing the title of the assignment, the
student's name, the professor's name, the course title, and the
date. The cover page and the reference page are not included in
the required assignment page length.
1/2
Managerial Economics Formulas1
Elasticity of Demand
,
%

%
%
%
%
%
x x x
p
x x x
x x x
I
D
xX Y
x y
Y y x
Q dQ P
E
P dP Q
Q dQ P
E

I dI I
dQQ P
E
P dP Q
Price, Marginal Revenue and Elasticity
1 1
1
1
1P
P

MR P P MR
E
E
Consumption Theory
X
XY
Y
X X X Y
Y Y X Y
X Y
MU
MRTS
MU
MU P MU MU
MU P P P
X P Y P I

Calculus Rules: Derivatives
dy
y a then
dx
1
,
b bdY
y ax then abx
dx
dy dy dz
y u x z x then
dx dx dx

then
dY dZ dU
y u x z x u z
dx dx dx
. .
,
du dz
z u
u x dy dx dxy then
z x dx z
At Maximum
2
2
0
Y
X

and at minimum
2
2
0
Y
X
Production Theory
( )
L L L
L K L L
L K K K
L K
TP d TP
AP MP P MP W

L dL
MP MP MP P
P P MP P
TC L P K P
1
Ibrahim Elsaify, Applications in Managerial Economics, 2011.
All Rights Reserved.
2/2
Economies of Scale
( , )
( , )
Q f L K
Q f L K
Q Q IRS

Economies of Scope
, ) , 0) , )
) ) , )
, 0
, )
( ( (0
( ( (
(
x y x y
x y x y
x y
Economies of Scope
Also S Economies of Scope

TC Q Q TC Q TC Q
TC Q TC Q TC Q Q
TC Q Q
Equilibrium Conditions:
Market Equilibrium:
Q Q
d s
Firm Equilibrium: MR = MC where
( ) ( )
d TR d TC
MR and MC
dQ dQ

Cost Functions
( ) ( )
AC AVC AFC
TC TVC TFC
TC TVC TFC
Q Q Q
d TC d TVC
MC
dQ dQ
Market Concentration
a. N-Firm Concentration Ratio (N-Firm CR)
1 2 3 4
4 1 2 3 4
: i
i
T T

S S S S S
C W W W W Where W
S S
b. Herfindahal-Herchman Index (HHI)
1
2 2 2 2
10, 000 0 10, 000
1 1 1 1 1
: .....
1
-
n
i
i
HHI W where HHI
HHI N
N N N N N
Number equal size firms in the market
HHI

With N equal size firms
c. Lerner Index and Markup Factor
Markup Factor
1
1
1
1
P
E

P MC P
L P MC Markup Factor
P L MC
d. Rothchild Index
Market Elasticity of Demand
Firm Elasticity of Demand
MK
F
RI
Applications in Managerial Economics_Class R
10/17/2014
Page 1 of 32

Applications in Managerial Economics1
Ibrahim Elsaify, Ph.D.
(Draft 2014)
1 I developed the applications help my MBA Managerial
Economics (ECO642) students at Goldey Beacom College.
This is a work-in-progress and will change to include new
applications or revisions of existing ones. It may also
contain typos and simple errors. I will appreciate any feedback
or corrections you have, as this will enhance the
document and it more useful for future groups.
10/17/2014
Page 2 of 32
Market Equilibrium, Elasticity and Government Intervention
Answered Applications
1. The U.S. Department of Agriculture is interested in analyzing
the domestic market for wheat. The USDA's
staff economists estimate the following equations for the

demand and supply curves:
20 - 2
- 1
d
w w
s
w w
Q P
Q P
Quantities are measured in millions of bushels; prices are
measured in dollars per bushel.
a. Calculate the free market equilibrium values of P, Q, CS, PS,
and SW.
b. Calculate price elasticity of demand and supply at
equilibrium, and categorize demand and supply.
c. At what price is the price elasticity of demand equals to zero,
infinity, and one?

d. At a price floor of $9 per bushel, calculate surplus, CS, PS,
and SW. Compare with free market outcomes,
and calculate DWL. If government purchased the surplus, how
would this change the outcome?
e. Suppose that the USDA's staff economists expand their
estimation of the demand curve to include the price
of corn ( ) cP and the income of consumers ( ) I as follows:
= 20 -
i. Is wheat a normal or an inferior good?
ii. What is the relationship between wheat and corn?
Answer
* *
a. At equilibrium: 20 - 2 - 1 3 21 7 7 1 6
3(6)
$9
2
6(6)
PS= =$18
2
SW=9+18=$27
*
7
b. 2 2.33 (Demand is elsatic)
* 6

*
7
1 1.2 (Sy
* 6
d
s
d s
Q Q P P P P Q
w w w w w w w
CS
dQ P
dp Q
dQ P
dp Q

pply is elsatic)
c. 0 at 0, at 10, 1 at 5
s d
d. Surplus=Q -Q
@p=9 @p=9
d
Q =20-2(9)=2
@p=9
s
Q =9-1=8
@p=9
Surplus=8-2=6
1(2)
CS= =$1
2
6+8

PS=2 =$14
2
SW=1+14=15
DWL=27-15=$12
If gov
ernment purchased the surplus, CS stays the same at $1.
However PS increases to:
8(8)
PS= =$32
2
SW=1+32=$33
d
e. An increas in P increases Q Corn and wheat are substiututes.
c w
An increas in I increases
d
Q Wheat is a normal good.
w

10/17/2014
Page 3 of 32
2. The United States Government uses wheat as an effective tool
of foreign aid. Therefore, the
government is committed to maintain a strategic production
level that far exceeds the domestic
market demand. In the meantime, this policy insures support of
farmers. The USDA's staff
economists estimate the following equations for the demand and
supply curves of wheat:
42 - 3
- 2
d
w w
s
w w
Q P
Q P

a Calculate the free market equilibrium values of P, Q, CS, PS,
and SW.
b Calculate price elasticity of demand and supply at
c. At what quantity is the price elasticity of demand equals to
zero, one and infinity.
d. f a price floor of $12/unit is imposed, what will be the
imbalance in the market? Calculate CS, PS,
and SW and DWL.
e. If government purchased all additional supply at the price
floor of $12/unit, calculate PS, and cost to
the government.
Answer
1
* *
a. At equilibrium: 42 - 3 - 2 4 44 11 11 2 9
3(9)
$13.5
2
9(9)
PS= =$40.5
2

SW =13.5+40.5=$54
*
11
b. 3 3.67. Demand is elasitic
* 9
*
11
1
* 9
d
s
d s
Q Q P P P P Q
w w w w w w w
CS
dQ P
dp Q
dQ P
dp Q

2
1 2
1.22. Supply is elasitic
. 0 42, 0, 1 21
s d
d. Surplus=Q -Q
@p=12 @p=12
2(6)
CS= =$6
2
10+4
PS=6 =$42

2
SW =6+42=48
DWL=SW 54-48=$6
e. If government purc
10 6 4
-SW =
hased the surplus, CS stays the same at $6. However PS
increases to:
10(10)
PS= =$50
2

SW=6+50=$56
The Cost to the gove
10/17/2014
Page 4 of 32
3. The elected officials in a west coast university town are
concerned about the "exploitative" rents being
charged to college students. The town council is contemplating
the imposition of a $350 per month
rent ceiling on apartments in the city. An economist at the
university estimates the demand and
supply curves as:
5600 - 8
4 - 500
Q P
Q P
Where P = monthly rent, and Q = number of apartments

available for rent. For purposes of this analysis,
apartments can be treated as identical.
and SW.
c. At what quantity does the price elasticity of demand equal to
zero, infinity, and 1?
d. What quantity will eventually be available if the rent ceiling
is imposed? Calculate shortage, CS, PS, SW
and DWL.
Answer
* *
1
. : 5600 - 8 4 - 500 6100 12 1, 533.3
(700 508.33)
$146, 946.68
2
(508.33 -125)
1533.33 $293,885.69
2

146, 946.68 293,885.69 $440,8
6100
508.3
12
1533.33
d s
a At equilibrium Q Q P P P P Q
w w
CS
PS
SW
32.37
*
508.30

. 8 2.65 Demand is elastic
* 1, 533.3
*
508.30
4 1.325 Supply is elastic
* 1, 533.3
. 0 5, 600, 0, 1 2,800
.
@ 350
4(350) -500 900
d
s
dQ P
b
dp Q
dQ P
dp Q
c at Q at Q at Q
s
d Q
p

2
1 2
@ 350 @ 350
(587.50 - 350) 350
$264, 375
2

(350 -125)(900)
$101, 250
2
264, 3751 101, 250 365, 625
440,832.37 - 365, 625 $75, 207.37
[5600 8(350)] 900 1,900
900
-
d s
Q Q
p p
CS
PS
SW
DWL SW SW
Shortage

10/17/2014
Page 5 of 32
4. U.S. Department of Agriculture is interested in analyzing the
domestic market for wheat. The USDA's
staff economists estimate the following equations for the
demand and supply curves:
29 - 2
- 1
d
w w
s
w w
Q P

Q P
and SW.
equilibrium, and categorize demand and supply
c At what quantity does the price elasticity of demand equal to
zero, one, and infinity
d. Suppose that the USDA's staff economists expand their
estimation of the demand curve to include
the price of corn ( ) cP and the income of consumers ( ) I as
follows:
20 - 2 3 -
i. What is the relationship between wheat and corn?
ii. Is wheat a normal or an inferior good?
Answer
*
*
*
*

1
a. At equilibrium:
29 - 2 - 1
3 30 10
10 1 9
10
b. 2 2.22. Demand is elastic
9
9(14.5 10)
$20.25
2
9(10 1)
$40.5
2
$60.7520.25 40.5
d s
w w
w w
w w
w

d
Q Q
P P
P P
Q
dQ P
dp Q
CS
PS
SW

*
*
10
1 1.11. Supply is elastic
9
c. 0 at Q 29
at Q 0
1 at Q 14.5
d. An increas in increases Corn and wheat are substiututes.
An increas in decreases Wheat is a
d
c w
d
w

s dQ P
dp Q
P Q
I Q
n inferior good.

10/17/2014
Page 6 of 32
Unanswered Applications
5. The supply and demand curves for corn are as follows:
3750 - 725
920 690
d
s
Q P
Q P
Where Q = millions of bushels and P = price per bushel.
and SW.

b. The government has imposed a $2.50 per bushel support
price. How much corn will the government
be forced to purchase?
c. Calculate the change in consumer surplus that would occur
under the support program.
Answer
10/17/2014
Page 7 of 32
6. The severe heat wave of last summer affected global demand
and supply for wheat. The United States
government uses wheat as an effective tool of foreign aid.
Therefore, the U.S. Department of Agriculture
is interested in analyzing the domestic market for wheat to
insure support of farmers and plentiful supply
of wheat for domestic market and as a policy tool. The USDA's
staff economists estimate the following
equations for the demand and supply curves:
41 - 2
- 1
d

w w
s
w w
Q P
Q P
and SW.
c. At what quantity is the price elasticity of demand equals to
d. If a price floor of $16/unit is imposed, what will be the
imbalance in the market? Calculate CS, PS, and
SW and DWL.
Answer

10/17/2014
Page 8 of 32
7. To prevent the spread of Avian Flu, a pharmaceutical
company has made a breakthrough in preventing the
virus from infecting the workers coming in direct contact with
potentially infected birds. The marketing
department of the company estimated the demand on the
product, which is a latex complete outerwear, to be:
75 -
2 - 60
d
s
Q P
Q P
Quantities are measured in thousands of gears and prices are
measured in dollars per gear.

and SW.
c At what quantity is the price elasticity of demand equals to
d If a price ceiling of $35/unit is imposed, what will be the
imbalance in the market? Calculate CS, PS, and
SW and DWL.
e Calculate the cost to subsidize suppliers to keep the price at
$35/unit and supply the market with all
required gears at that price.
Answer
10/17/2014
Page 9 of 32
Consumption Theory (Optional)
1. An individual consumes products and X Y and spends $250
per time period. The prices of the two goods
are $3 per unit for X and $2 per unit forY . The consumer in
this case has a utility function expressed as:

a. Express the budget equation mathematically.
b. Determine the values of X and Y that will maximize utility of
the consumer.
c. Calculate the total utility at its maximum.
d. Suppose that a tax of $1/unit is levied on good X. How will
this change the consumer’s optimum choice?
How much will be the tax proceeds?
e. Suppose that an equivalent lump sum tax is imposed instead
of the unit tax. What will be the utility
maximizing combination?
f. Which of the two taxes will the consumer prefer? Explain
your answer carefully.
Answer
yx
x y
* *
* * *
d. With $1 tax
a. 3 2 250
MUMU
b. At equilibrium:

P P
.5 .5 3
3 2 2
3
Substituting into budget line 3 2 250
2
41.67
6 250 41.67 3 62.5
2
c. .5 .5(41.67)(62.5) 1, 302
X Y
Y X X
Y
X
X
X X Y
U X Y

yx
x y
* *
per unit on , the new budget line will be:
4 2 250
MUMU .5 .5
At equilibrium: 2
P P 4 2
Substituting into budget line 4 2 2 250
8 250 31.25 2 31.25 62.5
Tax proceeds will b

X
X Y
Y X
Y X
X X
X X Y
yx
x y
e $31.25e. With a lump sum tax equals to $31.25
e. With a lump sum tax of $31.25, the new budget line will be:
3 2 250 31.25 218.75
MUMU .5 .5 3
At equilibrium:
P P 3 2 2
Subst

(same as b)
X Y
Y X X
Y
* *
* * *
* * *
3
ituting into budget line 3 2 218.75
2
3(36.46)
6 218.75 36.46 54.69
2
f. with per unit tax .5 .5(31.25)(62.5) 976.56
with lump sum tax .5 .5(36.46)(54.69) 997
Therefore
X
X

X X Y
U X Y
U X Y
, the consumer will prefer a lump sum tax.
10/17/2014
Page 10 of 32
2. Anthony Bradford is an undergraduate student at Siena
College in Albany, New York. Anthony has a
discretionary spending income of $300 a semester. Anthony’s
favorite activities are going to the local
theater at Cross Gates Mall ( X ) or hanging out with friends at
the local Starbucks (Y ). Going to local

theater costs Anthony $15 and hanging out with friends at
Starbucks costs him $10. Anthony’s utility function
can be modeled as:
a Determine the equilibrium values of X, Y, and total utility.
b Suppose that City of Albany imposed 20% tax on theater
tickets, at the same time local Starbucks offered a
10% discount to Siena College students. How will this change
Anthony’s optimum choice?
c Compare Anthony’s utility after the change to his original
utility.
Answer
yx
x y
* *
* * *
b. With 20% tax on , and 10% d
a. 15 10 300
MUMU
At equilibrium:
P P

3 3 3
15 10 2
3
2
10
30 300 10 3 15
2
3 3(10)(15) 450
X
X Y
Y X X
Y
X
X
X X Y
U X Y

yx
x y
* *
*
iscount on Y, the new budget line will be:
18 9 300
MUMU 3 3
At equilibrium: 2
P P 18 9

36 300 8.3 2 8.3 16.67
c. after change in p
X Y
Y X
Y X
X X
X X Y
U
* *
10/17/2014
Page 11 of 32

3. An individual consumes products and X Y and spends $300
per time period. The prices of the two goods
are $3 per unit for X and $2 per unit forY . The consumer in
this case has a utility function expressed as:
( , )
a. Express the budget equation mathematically.
b. Determine the values of X and Y that will maximize utility of
the consumer.
c. Calculate the total utility at its maximum.
d. Suppose that a tax of $1/unit is levied on good X. How will
this change the consumer’s optimum choice?
How much will be the tax proceeds?
e. Suppose that an equivalent lump sum tax is imposed instead
of the unit tax. What will be the utility-
combination?
f. Which of the two taxes will the consumer prefer? Explain
your answer carefully.
Answer
yx
x y
* *
* * *
d. With $1 tax per unit on

a. 3 2 300
MUMU
b. At equilibrium:
P P
.5 .5 3
3 2 2
3
2
50
6 300 50 3 75
2
c. .5 .5(50)(75) 1875
X
X Y
Y X X
Y
X
X
X X Y

U X Y
yx
x y
* *
, the new budget line will be:
4 2 300
MUMU .5 .5

At equilibrium: 2
P P 4 2
8 300 37.50 2 37.5 75
Tax proceeds will be $37.5
e. With a
X Y
Y X
Y X
X X
X X Y
yx
x y
lump sum tax equals to $37.50, the new budget line will be:
3 2 300 37.5 262.50

MUMU .5 .5 3
At equilibrium:
P P 3 2 2
3
Substituting into budget line 3 2 262.50
2
6
(same as b)
X Y
Y X X
Y
X
X
X

* *
* * *
* * *
3(43.75)
262.50 43.75 65.63
2
f. with per unit tax .5 .5(37.5)(75) 1, 406.25
with lump sum tax .5 .5(43.75)(65.63) 1, 435.55
Therefore, the consumer will prefer a lump sum tax.
X Y
U X Y
U X Y

10/17/2014
Page 12 of 32
4. Adam Wilkins is an undergraduate student at John Carroll
University, which is located at University
Heights, a suburb on the east side of Cleveland, Ohio. Adam has
a discretionary spending income of $300
a semester. Adam favorite activities are going to the local
theater at University Circle ( X ) or hanging out
with friends at the local Starbucks (Y ). Going to local theater
costs Adam $15 and hanging out with friends
at Starbucks costs $10. Adam’s utility function can be modeled
as:
a. Determine the equilibrium values of X, Y, and total utility.
b. Suppose that City of Cleveland imposed 20% tax on ticket
theater, at the same time local Starbucks offered
a 10% discount to JCU students. How will this change Adam’s
optimum choice?
c. Compare Adam’s utility after the change to his original
utility
Answer

10/17/2014
Page 13 of 32
Production Theory
1. The production function of a process that uses two inputs,
labor ( )L and capital ( )K , is:
Where Q represents output per day (tons), labor costs $200 per
unit and capital costs $1,000 per unit. The goal
of the firm is to produce 10,000 tons daily.
a. Determine returns to scale of the production process, and its
elasticity with respect to labor and capital.
b. Determine the least-cost combination of L and K, and
calculate total cost.
c. Carefully analyze the effects on labor productivity and AC if
cost of capital declined to $800 a unit.
Answer
a. This plant exhibits increasing returns to scale since
increasing both inputs 10% increases output 21%. Also,
the sum of powers is greater than 1.
1
1
s
L

s
K
b. The equilibrium condition for profit maximization is:
L K
2
* *
L K
MP MP 4K 4L
= = L=5K
200 1000
Substituting 5K for L in Q=4LK, where Q=10,000:
10,000= 4K(5K)=20K * = 500 22.36
5 5(22.36) 111.80
Total Cost=L.P +K.P =111.80(200)+22.36(1000)=$44,720

L KP P
K
L K
L K
2
* *
L K
c. At equilibrium:
MP MP 4K 4L
= = L=4K
200 800
Substituting 4K for L in Q=4LK, where Q=10,000:
10,000= 4K(4K)=16K * = 625 25
4 4(25) 100
Total Cost=L.P +K.P =100(200)+25(800)=$40,000
Labor Pro

L KP P
K
L K
[email protected] 1,000
[email protected] 800
@ 1,000
@ 8
ductivity:
10,000
AP 89.45
111.8
10,000
AP 100
100
Therfore, a decrease in the price of capital increaes labor
productivity.
Average cost:
44,720

AC $4.4789
10,000
AC
K
K
K
K
P
P
P
P
Q
L
Q
L
TC
Q

00
40,000
$4.0
10,000
Therfore, a decrease in the price of capital decreases cost per
unit. This is consistent
with the increase in labor productivity.
TC
Q
10/17/2014
Page 14 of 32

labor ( )L and capital ( )K , is:
unit and capital costs $1,000 per unit.
b. If the goal of the firm is to produce 10,000 tons daily,
determine the least-cost combination of L and K, and
c. If cost were limited to $5,000, calculate the equilibrium
combination of L and K, and the level of production.
d. Carefully analyze the effects on labor productivity and
average cost in b and c above. Analyze your answer
carefully.
Answer
a. This plant exhibits increasing returns to scale since the sum
of powers is greater than 1.
2
2
s
L
s
K

2 2
2 2
2 2 4
* *
8 8
5
200 1000
5 4 , 10,000 :
10,000 4 (5 ) 100 * 10 3.16
5 5(3.16) 15.81
. . 15.81(200) 3.16(1000) $6,322.27
.
L K

L K
L K
MP MP LK L K
L K
P P
Substituting K for L in Q L K where Q
K K K K
L K
Total Cost L P K P
c A
*
2 2
@ 5000
L

$5,000 :
5000 200 * 1,000 *
5 5000 200(5 ) 1,000
2.5
* 5(2.5) 12.5
4(2.5) (12.5) 3,906.25
d. Labor Productivity and Average Cost:
10,000
AP 632.51
15.81
6,322.
TC
t C
L K
Substituting L K K K
K
L
Q Units
Q

L
AC
[email protected]=$5,000
27
$0.63
10,000
3,906.25
AP 312.5
12.5
5,000

$1.28
3,906.25
Therfore, limiting the cost to $5,000 decreased productivity and
increased average cost. This is due to IRS.
Q
L
AC
10/17/2014
Page 15 of 32
labor (L) and capital (K), is:
Q = 10LK
unit and capital costs $800 per unit. The goal

of the firm is to produce 16,000 tons daily.
b. Determine the optimum combination of L and K, and
c. Carefully analyze the effects on labor productivity and
average cost if cost of capital increased to $1,000
per unit.
Answer
a. This plant exhibits increasing returns to scale since sum of
powers is greater than 1.
1
1
s
L
s
K

2
* *
10 10
4
200 800
4 10 , 16,000 :
16,000 10 (4 ) 40 * 400 20
4 4(20) 80
. . 80(200) 20(800) $32,000
. :
L K
L K
L K
L
L
MP MP K L
L K
P P

Substituting K for L in Q LK where Q
K K K K
L K
Total Cost L P K P
c At equilibrium
MP
P
2
* *
10 10
5
200 1000
4 10 , 16,000 :
16,000 10 (5 ) 50 * 320 17.89
5 5(17.89) 89.44

. . 89.44(200) 17.89(1000) $35,778
Pr
K
K
L K
MP K L
L K
P
Substituting K for L in Q LK where Q
K K K K
L K
Total Cost L P K P
Labor oducti
@ 800
@ 1000

@ 800
@ 1,000
:
cos :
16,000
200
80
16,000
178.89
89.44
, .
32,000
$2
16,000
35,
K
K
K
K
L P
L P

P
P
vity
Average t
Q
AP
L
Q
AP
L
Therfore an increase in the price of capital decreaes labor
productivity
TC
AC
Q
TC
AC
Q

776
$2.24
16,000
An increase in the price of capital increases cost per unit. This
is consistent with a decrease in labor productivity.
10/17/2014
Page 16 of 32
labor (L) and capital (K), is:
Q = 5LK
unit and capital costs $1,000 per unit. The goal of
the firm is to produce 10,000 tons daily.

b. Determine the least-cost combination of L and K, and
c. Carefully analyze the effects on labor productivity and
average cost of capital costs declined to $800 per unit.
Answer
10/17/2014
Page 17 of 32
5. The design unit at Silicon Graphs, which is specialized in
printing electronic circuits, estimates its production
function as:
Where Q represents number of units produced per day, ( )L is
labor which costs $200 per unit and ( )K is
capital which costs $400 per unit.

b. If the goal of the firm is to produce 16,000,000 units a day,
determine the least-cost combination of L and
K, and calculate total cost.
c. If cost were limited to $75,000 calculate the equilibrium
combination of L and K, and the level of
production.
d. Carefully analyze the effects on labor productivity in b and c
above.
Answer
10/17/2014
Page 18 of 32
Cost Structure
1. A firm's total cost function is given by the equation:
2TC = 125 + 10 Q + 5Q
a. Determine the level of output that minimizes AC.

b. Prove that MC=AC when AC is at its minimum.
c. How much is TC, FC and VC when MC=AC?
Answer
2
TC = 125 + 10 Q + 5Q
TC 125
a. AC= 10 5
Q
125 2 *5 0 5 125 5
2
125*b. AC = 10 5(5) [email protected] 5
5
10 10
* 10 10(5) [email protected] 5
MC=AC at its minimum (desired).
2*c. TC =125 10(5) 5(5) [email protected] 5
FC
Q
Q
dAC
Q Q

dQ Q
dTC
MC Q
dQ
dTC
MC
dQ
=125
2
VC =10(5) 5(5) 175
*@Q 5

10/17/2014
Page 19 of 32
2. A firm’s total cost function is given by the following
equation:
2TC = 256+20Q +4Q
b. Prove that AC =MC when AC reaches its minimum.
Answer
256 20 +4
. 4
*
4 0 8
2
*. [email protected] 8

20 8
* [email protected] 8
min ( ).
*. @ 8
2
256
20
256
2256 20(8) 4(8) 256 416 672
TC Q Q
TC
a AC Q
Q
dAC
Q
dQ
b AC Q
dTC
MC Q
dQ

MC Q
MC AC at its imum desired
c TC Q
Q
Q
FC FC VCVC

10/17/2014
Page 20 of 32
3. Stylish Accessories is a professional designer and
manufacturer of men’s wallets. Its total cost function is
estimated to be:
2 3TC = 100Q -20Q + 2Q
b. Prove that AC =MC when AC reaches its minimum.
d. If the firm can sell all what it wants at a price of $100/wallet,
calculate the level of sales that
maximizes the firm profit, and calculate that profit.
e. Calculate the minimum price acceptable to firm to start
production.
Answer
2
2
2

2 3
100Q-20 2
2
. 100 20 2
*
20 4 0 5
*. 100-20(5) 2(5) [email protected] 5
100 40 6
100 40(5) 6(5) 50*
@ 5
*. @ 5
2 3100(5)-20(5) 2(5)
TC Q Q
TC
a AC Q Q
Q
dAC
Q Q
dQ
b AC Q
dTC

MC Q Q
dQ
MC
Q
c TC Q
VC
2 3
250
0
250

. 100
202 *
: 100 100 40 6
3
100(7) 100(7) 20(7 ) 2(7
. .
2
100 - 20 2
7
) $294
0 20 4At a minimum:
FC
VC
d MR
At Equilibrium MR MC Q Q Q
TR TC
e Minimum acceptable price Min AVC
TVC
AVC Q Q
Q

dAVC
dQ
*
2
0 5
100 - 20(5) 2(5) $50

Q Q
Minmum AVC
10/17/2014
Page 21 of 32
4. A firm's total cost function is given by the equation:
000 0
a Write an expression for each of the following cost concepts:
ariable Cost

b Determine the quantity that minimizes average total cost.
c Demonstrate that the relationship between marginal cost and
average cost holds.
Answer
2
2
2
4,000
2
5 10
2
5 10
5 10
4,000 5 10 4,000
5 10
5 20
4000 *
10 0
. Relationship: M

4,000
. 400 20
. 4000 5 10
TFC
AFC
Q Q
Q Q
AVC Q
Q
Q Q
AC Q
Q Q
dTC
MC Q
dQ
dAC
Q
dQ Q
b
TFC

C=Min. AC
4,000
5 10(20) 405*
@ 20 20
5 20(20) 405*
@ 20
AC
Q
MC
Q
10/17/2014
Page 22 of 32

5. Fashion Frames is a professional designer and manufacturer
of photo frames. Its total cost function is
estimated to be:
2 3TC = 50Q -10Q + Q
a Determine the level of output that minimizes AC. (Round to
whole digit)
b Prove that AC =MC when AC reaches its minimum.
c How much is TC, FC and VC when MC=AC?
d If the firm can sell all what it wants at a price of $50/Frame,
calculate the level of sales that maximizes
the firm profit. Calculate that profit.
e Calculate the minimum price acceptable to firm to start
production.
Answer
10/17/2014
Page 23 of 32
Market Structure and Regulations
1. In a competitive market in long-run equilibrium, the market

supply and demand are:
30 0.50
100 - 1.5
P Q
P Q
where P is dollars per unit and Q is level of production and
sales in hundreds of units per day. A typical
firm in this market has a marginal cost of production expressed
as:
and SW.
b. Determine the level of sales by a typical firm and its PS.
c. If an output tax is imposed on ONE firm's output such that
the ONE firm has a new marginal cost
new level of production and PS?
d. If all firms in this industry were bought by a monopolist,
calculate monopolist equilibrium P, Q,
MUF, CS, PS, and SW
e. As a policy maker, what would you do to restore competitive

equilibrium outcome?
Answer
* *
a. At equilibrium: D=S 100 1.5Q=30+.5Q 2Q=70 Q 35 100
1.5(35) $47.5
52.5(35) 17.5(35)
$918.75 $306.25
2 2
918.75 306.25 $1,225
*. Firm's Equilibrium: MR=MC (MR is the market price P )
P
CS PS
SW CS PS
b
*2.5+15q=47.5 3
35
12
3

45(3)
Firm PS = $67.5
2
'. Firm's Equilibrium after the tax: MR=MC
*47.5=5+15q 2.83 less than quantity produced before tax.
(47.5 5)(2.83)
after the tax
q
Number of firms
c
q
Firm PS
2

d. Monopolist Equilibrium: MR=MC (MC is market Supply)
Monopolist faces market demand curve, therefore its MR curve
is donward sloping with twice the slop
MR=1
00-3Q
* *100 3Q=30+.5Q 70=3.5Q Q 20 100 1.5(20) $70m
70
1.75
40
(100 70)(20) (70 30) (70 40)
$300 20 $700
2 2
300 700 $1,000
1,225 1,000 $225
. We can restore com
Pm
P

MUF
MC
CS PSm m
SWm
DWL SW SWCompetition m
e
petition outcome by setting the price at its competitive level of
$47.5
10/17/2014
Page 24 of 32
2. In a competitive market with small, equal-size firms in long-

run equilibrium, the market supply and
demand are:
P = 30 + 0.5Q
P = 75 - Q
Where P is dollars per unit and Q is level of production and
sales in hundreds of units per day. A typical
firm in this market has a marginal cost of production expressed
as:
MC = 3.0 + 14q
Where q is the firm’s level of production.
and SW.
b. Determine a typical firm’s equilibrium quantity. How many
firms are in this market?
c. If all firms in this industry were bought by a monopolist,
calculate monopolist equilibrium P, Q,
MUF, CS, PS, and SW
d. As a policy maker, what can you do to regulate the
monopolist and restore competition outcome?
e. If an output tax is imposed on ONE firm's output such that
the ONE firm has a new marginal cost
level of production and PS be after
the tax is imposed? Compare with pretax levels.
Answer
* *

a. At equilibrium: D=S 75 Q=30+.5Q 45 1.5Q Q 30 75 30 $45
30(30)
$450
2
30(15)
$225
2
450 225 $675
*. Firm's Equilibrium: MR=MC (MR is the market price P )
30*3+14q=45 3 # Firms = 1
3
P
CS
PS
SW CS PS
b
q

. Monopolist Equilibrium: MR=MC (MC is market Supply)
MR=75-2Q
*75-2Q=30+.5Q 45=2.5Q Q 18m
Firms
c
Pm
* 75 18 $57
39 1.46
(75 57)(18)
$162
2
(57 39) (57 30)

18 $405
2
162 405 $567
675 567 $108
. We can restore competition outcome by setting the price at its
competitiv
P
MUF
MC
CSm
PSm
SWm
d

' *
*
e level of $45
. Firm's Equilibrium after the tax: MR=MC (MR is the market
price P )
45=5+14q 2.86 less than quantity produced before tax.
(45 5)(2.86)
after the tax $57.2
2
before th
e
q
Firm PS
Firm PS
(45 3)(3)

e tax $63
2
Therfore, the tax reduced the firm's PS by $5.8
10/17/2014
Page 25 of 32
3. A competitive market with the following demand and supply
curves:
2 - 60
75 -
S
d
Q P
Q P

where P is dollars per unit and Q is quantity produced and sold
in the market in hundreds of units.
A typical firm in this market has a marginal cost of production
expressed as:
Where q is the quantity produced by a typical firm.
a. Determine the market equilibrium P, Q, CS, PS, and SW.
b. Determine a typical firm equilibrium quantity and number of
firms. Calculate a typical firm PS.
c. If an output tax is imposed on one firm changing its MC to 10
firm equilibrium Q and PS? Comment on your result.
d. If all firms in this industry were bought by a monopolist,
calculate monopolist equilibrium P, Q, CS,
PS, and DWL.
e. As a policy maker, what would you do to restore competitive
equilibrium outcome?
Answer
*
a. At equilibrium: 2 - 60 75 - 3 135 $45
* 2(45) 60 30
30(30)
$450

2
15(30)
$225
2
450 225 $675
* *. Firm's Equilibrium: MR=MC (MR is the market price P )
45=3+14q 3
Number of Firms i
D S P P P P
Q
CS
PS
SW CS PS
b q

*Q 30
n the Industry= 10 firms
* 3
(45 3)(3)
Firm PS $63
2
' *. Firm's Equilibrium after the tax: MR=MC (MR is the
market price P )
*45=10+14q 2.5 less than quantity produced before tax.
Firm PS after the
q
c
q
(45 10)(2.5)
tax $43.75

2
Therfore, the tax reduced the firm's PS by $19.25
d. Monopolist Equilibrium: MR=MC (MC is market Supply).
MR=75-2Q
* *75-2Q=30+.5Q 45=2.5Q Q 18 75 18 $57m
(75 57)(18)
$16
2
Pm
CSm
2
(57 39) (57 30)
18 $405

2
162 405 $567
675 567 $108
. We can restore competition outcome by setting the price at its
competitive level of $45.
PSm
SWm
e
10/17/2014
Page 26 of 32
4. To encourage investment in Satellite Radio in its early stage
of development, a firm was given monopoly
power over the whole market for a specific period of time. The
demand and total cost function are

estimated to be:
2
P = 900 - 3Q
TC = 200 + 100Q+Q
Where P is dollars per unit and Q is level of production and
sales.
a. Determine the market equilibrium price, quantity, profit,
MUF, and social welfare under monopolist.
b. In a later stage, the market will be opened for competition. It
is expected that a large number of identical
small firms will be active in the market, and will act like
perfectly competitive firms. Determine price,
quantity, and social welfare under perfect competition. (Hint:
competitive supply is MC). Compare
results with monopolist.
c. If the number of firms in the competitive market is decreased
to eight identical firms, determine MC of
a representative firm, calculate each firm production and PS.
Answer
a. Monopolist Equilibrium: MR=MC

MR=900-6Q
* *900-6Q=100+2Q 800=8Q Q 100 900 3(100) $600m
* *
Pm
* 600(100) [200 100(100) 100(100)] $39,800
600
2
300
(900 600)(100)
$15,000
2
(600 100) (600 300)
100 $40,000
2
15,000 40,000 $55,000

. :
900 3Q=100+2Q 80
P
MUF
MC
CSm
PSm
SWm
b Competitive Market Equilibrium D S
(900 420)(160)
$38,400

2
(420 100)(160)
$25,600
2
38,400 25,600 $64,000
. If the number of firms deacreased to eight firms:
' :
MC=100+2Q 8 100
P
CSc
PSc
SW CS PSc
c
Firm s MC
Q q MC f

*Q 160*q = 20
8 8
PS 25600cFirm PS = $3200
8 8
600
. 2
300
q
units
P
d MUF
MC

10/17/2014
Page 27 of 32
Price Discrimination
1. American Tire and Rubber Company sells identical radial
tires under the firm's own brand name and to
discount stores for private labeling. Marginal cost is a constant
$10 per tire, regardless of the sub-market
in which the tire is sold. The firm has estimated the following
demand curves for each of the markets:
1 1
2 2
P = 70 - 0.0005 Q (brand name)
P = 20 - 0.0002 Q (private label).
Quantities are measured in thousands per month and price refers
to the wholesale price. Marginal cost is a
constant $10 per tire.
a. Find the equilibrium price, quantity, consumer surplus and
produce surplus in each market.
b. Calculate the elasticity of demand at equilibrium in each
market.
c. If the Company cannot price discriminate between the two
markets, calculate equilibrium quantity,

price, CS, and PS. Compare with your answer in (a).
Answer
1
1 1
* *
1 1 1
1
1
2 2
*
2 2
a. Equilibrium in first market: MR
70 .001
70 .001 10 60,000 70 .0005(60,0000) $40
(70 40)(60,000)
$900,000
2
(40 10)(60,000) $1,800,000
20 .0004

20 .0004 10 25,000
MC
MR Q
Q Q P
CS
PS
MR Q
Q Q
2
2

1 1 1
1 1
2 2 2
2 2
20 .0002(25,000) $15
(20 15)(25,000)
$62,500
2
(15 10)(25,000) $125,000
. Easticity of Demand
1 1 4
1 10 40 1 1.33
3
1 1 1.5
1 10 15 1 3
.5
. Witho
P
CS
PS
b

MR P E
E E
MR P E
E E
c
1
1 2
1
2 2
* *

ut price-discrimination: Q=Q
140,000 2000
100,000 5000
240,000 7000 34.29 .0001429 34.29 .0002858
equilibrium: MR=MC
34.29-.0002858Q=10 Q 84,975 34.29 .0001429(84,974) $22.
Q
Q P
Q P
Q P P Q MR Q
At
P
(34.29 22.14)(84,975)
$516,223.12

2
(22.15 10)(84,975) $1,031,596.5
Under price discrimination, the sum of CS in both markets is
$962,500, which is more than CS without price
discrimination. Simil
CS
PS
arlry, PS under price discrimination ($1,925,000) is more than
PS with a single price.
10/17/2014
Page 28 of 32
2. Thatcher Park of upstate New York has a low demand during
work days (Market 1), but on Saturday and
Sunday demand increases (Market 2). The demand functions
are estimated to be:

1 1
2 2
Market 1: P = 4 - 0.001Q
Market 2: P = 22.6 - 0.01Q
Q is the number of cars entering the park each day. The
marginal cost of running the park is the same on
weekdays and weekends:
MC = 1 + 0.004Q
In order to control crowds, the park's management uses peak-
load pricing which is a form of price
discrimination. This pricing policy controls crowds and makes
sure the park is self-supporting.
a. Find the equilibrium P, Q, and TR in each market.
b. Calculate CS, PS, and elasticity of demand at equilibrium in
each market.
c. If the park cannot price-discriminates, calculate P, Q and TR.
Compare with results in a.
Answer
1 1 1
* * *
1 1 1 1 1

2 2 2
2
a. Equilibrium in first market: MR 4 .002
3
4 .002 1 .004 500 Seat 4 .001(500) $3.5 3.5(500) $1, 750
.006
Equilibrium in second market: MR 22.6 .02
22.6 .02 1 .004
MC MR Q
Q Q Q P TR
MC MR Q
Q Q
* * *
2 2 2 2
1 1

1 1
1
21.6
900 Seat 22.6 .01(900) $13.6 13.6(900) $12, 240
.024
. CS, PS and Easticity of Demand at Equilibrium:
(4 3.5)(500) (3.5 1) (3.5 3)
$125 and (500) $750
2 2
1
1 3 3.5 1
Q P TR
b
CS PS
MR P
E

1
1
2 2
2 2 2
2 2
1 2
1
1 3.5
7
0.5
(22.6 13.6)(900) (13.6 1) (13.6 4.6)
$4, 050 and (900) $9, 720
2 2
1 1 13.6
1 4.6 13.6 1 1.51
9
. Without price-discrimination: Q=Q
4, 000 1000

E
E
CS PS
MR P E
E E
c Q
Q P
1
2 2
* *

2260 100
6260 1100 5.6 .0009 5.6 .0018
equilibrium: MR=MC 5.6 .0018 =1 .004 Q 809 Seats $4.87
793(4.89) $3,877.77
Yes. Thatcher Park benifits from price discrimination beacause
Q P
Q P P Q MR Q
At Q Q P
TR
TR is higher.

10/17/2014
Page 29 of 32
3. Cleveland Orchestra leaves its Severance Hall in Cleveland
and operates from its summer home in Akron,
Ohio during the summer. The summer home is a magnificent
park with outdoor seating (Market 1) and a
covered pavilion (Market 2) and The demand functions are
estimated to be:
1 1
2 2
Market 1: P = 7 - 0.001Q
Market 2: P = 22.6 - 0.01Q
Q is the number of cars entering the park each day. The
marginal cost of running the park is the same on
weekdays and weekends:
MC = 1 + 0.004Q
In order to control crowds, the shrewdly-run Orchestra uses
peak-load pricing which is a form of price
discrimination. This pricing policy controls crowds and insures
Orchestra is self-supporting.
a. Find the equilibrium P, Q, and TR in each market.
b. Calculate CS, PS, and elasticity of demand at equilibrium in
each market.
c. If the Orchestra cannot price discriminate, calculate P, Q and

TR. Does Cleveland Orchestra
benefit from price-discrimination?
Answer
1 1 1
* * *
1 1 1 1 1
2 2
a. Equilibrium in first market: MR 7 .002
6
7 .002 1 .004 1, 000 Seat 7 .001(1, 000) $6 6(1000) $6, 000
.006
Equilibrium in second market: MR 22.6 .02
MC MR Q
Q Q Q P TR
MC MR Q
Cleveland Orchestra

* * *
2 2 2 2 2
1 1
1
21.6
22.6 .02 1 .004 900 Seat 22.6 .01(900) $13.6 13.6(900) $12, 240
.024
. CS, PS and Easticity of Demand at Equilibrium:
(7 6)(1, 000) (6 1) (6 5)
$500 and (1000) $3, 000
2 2
Q Q Q P TR
b
CS PS
MR P

1 1
2 2
2 2 2
2 2
1 2
1 1 6
1 5 6 1 6
1
(22.6 13.6)(900) (13.6 1) (13.6 4.6)
$4, 050 and (900) $9, 720
2 2
1 1 13.6
1 4.6 13.6 1 1.51
9
. Without price-discrimination: Q=Q
E
E E
CS PS
MR P E
E E
c Q

Q
11
2 2
* *
7, 000 1000
2260 100
9260 1100 8.42 .001 8.42 .002
equilibrium: MR=MC 8.42 .002 =1 .004 Q 1, 236 Seat $7.18
1, 236(7.18) $8,879

Yes. Cleveland Orchestra benifits from price discr
P
Q P
Q P P Q MR Q
At Q P
TR
imination beacause TR is higher.
10/17/2014
Page 30 of 32
4. The local zoo has hired you to assist them in setting
admission prices. The zoo's managers recognize that there

are two distinct demand curves for zoo admission. One demand
curve applies to those ages 12 to 64, while the
other is for children and senior citizens. The two demand and
marginal revenue curves are:
PA = 9.6 - 0.08QA MRA = 9.6 - 0.16QA
PCS = 4 - 0.05QCS MRCS = 4 - 0.10QCS
Where PA = adult price, PCS = children/senior citizens price,
QA= daily quantity of adults, and QCS = daily
quantity of children and senior citizens. Crowding is not a
problem at the zoo, so that the managers consider
marginal cost to be zero.
a. If the zoo decides to price discriminate, what should the price
and quantity be in each market? Calculate
total revenue in each sub-market.
b. What is the elasticity of demand at the quantities calculated
in (a) for each market.
c. If the zoo cannot price discriminate, what will be the
equilibrium price and quantity? Can price
discrimination increase total revenue?
1
* *
1 1 1 1 1
1

* *
2 2 2 2 2
2
1 1
1
a. Equilibrium in first market: MR
9.6 .16 0 0.16 9.6 60 9.6 .08(60) $4.8
60(4.8) 288
4 0.1 0 0.1 4 40 4 .05(40) $2
40(2) 80
. Easticity of Demand
1
1
MC
MR Q Q Q P
TR
MR Q Q Q P
TR
b
MR P
E

1
1
2 2 2
2 2
* *
*
1 4.8
0 4.8 1 1
4.8
1 1 2
1 0 2 1 1
2
. 120 12.5 80 20 200 32.5 6.15 .03
6.15 .06
: 6.15 .06 0 102.5 3.08

102.5(
A SC A SC
E
E
MR P E
E E
c Q Q Q P P Q P P Q
MR Q
At Equilibrium MR MC Q Q P
TR

10/17/2014
Page 31 of 32
Managerial Economics Formulas2
Elasticity of Demand
,
%
%
%
%
%
%
x x x
p
x x x
x x x
I

D
xX Y
x y
Y y x
Q dQ P
E
P dP Q
Q dQ P
E
I dI I
dQQ P
E
P dP Q

Price, Marginal Revenue and Elasticity
1 1
1
1
1P
P
MR P P MR
E
E
Consumption Theory
X
XY
Y

X X X Y
Y Y X Y
X Y
MU
MRTS
MU
MU P MU MU
MU P P P
X P Y P I
Calculus Rules: Derivatives
dy
y a then
dx
1 , b b

dY
y ax then abx
dx
dy du dz
y u x z x then
dx dx dx
dY dz du
y u x z x u z
dx dx dx
. .
,
du dz
z uu x dy dx dxy then

z x dx z
At Maximum
2
2
0
Y
X
and at minimum
2
2
0
Y
X

10/17/2014
Page 32 of 32
Economies of Scale
( , )
( , )
Q f L K
Q f L K
Q Q IRS
Economies of Scope
, ) , 0) , )
) ) , )
, 0

, )
( ( (0
( ( (
(
x y x y
x y x y
x y
Economies of Scope
Also S Economies of Scope
TC Q Q TC Q TC Q
TC Q TC Q TC Q Q
TC Q Q
Equilibrium Conditions:
Market Equilibrium:

Firm Equilibrium: MR = MC where
( ) ( )
d TR d TC
MR and MC
dQ dQ
Cost Functions
( ) ( )
AC AVC AFC
TC TVC TFC
TC TVC TFC
Q Q Q
d TC d TVC
MC
dQ dQ

Market Concentration
a. N-Firm Concentration Ratio (N-Firm CR)
1 2 3 4
4 1 2 3 4 :
i
i
T T
S S S S S
C W W W W Where W
S S
b. Herfindahal-Herchman Index (HHI)
1
2 2 2 2
10,000 0 10,000
1 1 1 1 1
: .....
1
-

n
i
i
HHI W where HHI
HHI N
N N N N N
Number equal size firms in the market
HHI
With N equal size firms
c. Lerner Index and Markup Factor
Markup Factor

1
1
1
1
P
E
P MC P
L P MC Markup Factor
P L MC
d. Rothchild Index
Market Elasticity of Demand
Firm Elasticity of Demand
MK
F

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