Transcript Welcome to EC 209: Managerial Economics- Group A Week Three

Welcome to
EC 209: Managerial
Economics- Group A
By: Dr. Jacqueline Khorassani
Week Three
1
Class One
Monday, September 17
11:10-12:00
Fottrell (AM)
The textbook is now available at the bookshop
Don’t forget that the first aplia assignment is
due before September 25
It is the week 4 assignment
Remember that if you don’t ask questions, I
assume you know.
I did not get any questions on this week’s
study guide. So,I will briefly go over what
you must know.
2
What does the elasticity
measure?

It measures how responsive (sensitive)
is variable “G” to one percent change in
variable “S”
EG , S
% G

% S
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
3
How can elasticity be shown
(measured) using calculus?

Suppose G = f (S), then
EG ,S
dG S

dS G
Where dG/dS is the
partial derivative of
G with respect to S
4
What is the own price elasticity
of demand?

Measures how sensitive the quantity
demand is to one percent change in
price.
5
How is it measured?
EQ X , PX

% Q X

% PX
d
Is it negative or positive?
– Negative, according to the “law of
demand.”
6
Let’s practice
If quantity demanded for sneakers falls by
12% when price increases 4%, we know
that the absolute value of the own-price
elasticity of sneakers is
–
–
–
–

A) 0.3.
B) 0.8.
C) 3.0.
D) 3.3.
Answer: C
7
What is the difference between
elastic, inelastic and unitary
elastic demands?
Elastic:
Inelastic:
Unitary
elastic:
EQ X , PX  1
EQ X , PX  1
EQ X , PX  1
8
How does elasticity change along a
linear demand curve?

At any point on demand, the absolute
value of elasticity = lower portion of
demand /upper portion of demand
At point A:
P
EQX , PX  BA / AC
C
A
What is the elasticity
at point C?
Infinity
What is the elasticity at
point B?
B
Q
Zero
9
How does elasticity change along a
linear demand curve?



The lower half of demand is inelastic
The upper half of demand is elastic
Mid point of demand is unitary elastic
P
Elastic
C
Unitary elastic
//
A
Inelastic
//
B
Q
10
How is a perfectly elastic demand
curve different from a perfectly
inelastic demand curve?
Price
EQ X , PX
% Q X

% PX
d
Price
D
D
Quantity
%ΔP = 0
Perfectly Elastic ( EQ X ,PX  )
Quantity
%Δ Q = 0
Perfectly Inelastic ( EQX , PX  0)
11
How does the own price
elasticity of demand relate
total revenue?
P
100
TR
0
10
20
30
40
50
Q
Q
0
12
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
13
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
800
0
10
20
30
40
50
Q
0
10
In the elastic portion of demand, as
you lower the price, TR goes up
20
30
40
50
14
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
40
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
15
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
In the inelastic portion of demand, as you
lower the price, TR goes down.
30
40
50
16
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Elastic
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
Elastic
30
40
50
17
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
Inelastic
50
18
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
In the meddle of demand, TR is at its
max
0
10
Elastic
20
30
40
Inelastic
50
19
Q
Managerial Economics

Week Three, Class 2
– Tuesday, September 18
– 15:10-16:00
– Cairnes

Remember: If you don’t ask, I
assume you know.
20
About Aplia Assignments


25% of grade
Fees = $20
– Need to be paid in 5 days or they kick you out of
the program
– I have no control over this
– Course Key: R8WC-VRSZ-SCBQ

Assignment 1 is due before noon on
September 25
– 5 grades question sets
21
Let’s practice

Assume that the price elasticity of demand
is -2 for a certain firm's product. If the firm
raises price, the firm's managers can expect
total revenue to:
–
–
–
–

a) Decrease
b) Increase
c) Remain constant
d) Either increase or remain constant depending
upon the size of the price increase.
Answer: A
22
How does the own-price
elasticity related to marginal
revenue?
What is marginal Revenue, MR?
 Revenue resulting from selling one
more unit of output
 MR = ΔTR/ΔQ

23
How does the own-price
elasticity related to marginal
revenue?

MR = P(1 + E)/E
Suppose E < -1
which means |E| >1  (elastic), then MR is
positive
Suppose E = -1
which means |E|=1 then MR is zero
Suppose E > -1 
which means |E|<1 (inelastic), then MR is
negative
24
How does the own-price
elasticity related to marginal
revenue?



Between 0 to Q* demand is elastic and MR>0
At Q* demand is unitary elastic and MR = 0
Above Q* demand is inelastic and MR <0
P
Elastic
MR >0
Unitary elastic
MR = 0
Inelastic
MR <0
0
D
Q*
MR
Q
25
Which factors affect the
own price ?

You need to study this one on your own.
–
–
PP 79-82
Ask me questions
26
Let’s practice

The demand for Adidas brand shoes is
– A) more elastic than the demand for
shoes in general.
– B) less elastic than the demand for shoes
in general.
– C) equally elastic to the demand for
shoes in general.
– D) none of the above.

Answer: A
27
Let’s practice

Lemonade, a good with many close
substitutes, should have an own-price
elasticity that is:
– a)
– b)
– c)
– d)

unitary.
relatively elastic.
relatively inelastic.
perfectly inelastic.
Answer: B
28
What does the cross price
elasticity of demand
measure?
It measures how sensitive the quantity demand for
good X is to one percent change in the price of good Y
EQX , PY
%QX

%PY
d
If EQX,PY > 0,
then X and Y are substitutes.
If EQX,PY < 0,
then X and Y are complements.
29
Suppose that a firm sells two related good and the
price of one good changes; how can the cross
price elasticity help us predict the changes in the
total revenue?
 


R  R X 1  EQX , PX  RY EQY , PX  %PX
ΔR = change in total revenue,
Rx = good X’s revenue,
RY = good Y’s revenue
30
What is the income
elasticity?
Measure the percentage change in quantity
demand for good X as the income of consumer
changes by one percent.
EQX , M
%QX

%M
d
If EQX,M > 0,
then X is a normal good.
If EQX,M < 0,
then X is a inferior good.
31
Uses of Elasticity
Example 1: Pricing and Cash Flows
(revenue)



According to an FTC Report by Michael
Ward, AT&T’s own price elasticity of
demand for long distance services is
-8.64.
AT&T needs to boost revenues in order
to meet it’s marketing goals.
To accomplish this goal, should AT&T
raise or lower it’s price?
32
Answer: Lower price!
 Since
demand is elastic, a
reduction in price will increase
quantity demanded by a greater
percentage than the price
decline, resulting in more
revenues for AT&T.
33
Example 2: Quantifying
the Change
 If
AT&T lowered price by 3
percent, what would happen
to the volume of long
distance telephone calls
routed through AT&T?
34
Answer
• Calls would increase by 25.92 percent!
EQX , PX
% QX
 8.64 
% PX
d
% QX
 8.64 
 3%
d
 3%   8.64   %QX
d
%QX  25.92%
d
35
Example 3: Impact of a
change in a competitor’s price


According to an FTC Report by Michael
Ward, AT&T’s cross price elasticity of
demand for long distance services is
9.06.
If competitors reduced their prices by
4 percent, what would happen to the
demand for AT&T services?
36
Answer
• AT&T’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
d
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
37
Interpreting Demand
Functions


Mathematical representations of demand
curves.
Example:
QX  10  2 PX  3PY  2 M
d

Where M is income
38
QX  10  2 PX  3PY  2 M
d

What can you say about the relationship
between good X and good Y?
– X and Y are substitutes (coefficient of PY is
positive).

Is X a normal or an inferior good?
– X is an inferior good (coefficient of M is
negative).

Holding price of Y and income constant, as
price of X goes up by 1, quantity
2
demanded for X goes ______
down by ______.
39
Managerial EconomicsGroup A

Week Three- Class 3
– Thursday, September 20
– 15:10-16:00
– Tyndall

Aplia Assignment 1
– due before noon on Tuesday, September
25
– 25% of grade
40
I received a question on how to calculate
own elasticity when we have the demand
function and only one price and one
quantity


Remember
Suppose G = f (S), then
EG ,S
dG S

dS G
Where dG/dS is the
partial derivative of
G with respect to S
41
A General Linear Demand
Functions
QX  0   X PX  Y PY   M M   H H
d
EQX , PX
EQX , M
PX
X
QX
Own Price
Elasticity =
(dQdx/dPx)*Px/Qx
EQ X , PY
PY
 Y
QX
Cross Price
Elasticity=
(dQdX/dPy)*Py/Qx
M
 M
QX
Income
Elasticity=
(dQdX/dM)*M/Qx
42
Example: What is own elasticity
if P = 1







P = 5 – 1/2 Qd
What is this?
Inverse demand function
Need to change it to a demand function
½ Qd = 5 – P
Qd = 10 - 2P.
Own-Price Elasticity = dQd/dP * P/Q
= (-2)* P/Q

If P=1, then Q is
– 8 (since 10 - 2 = 8).

Own price elasticity at P=1, Q=8:
(-2)(1)/8= - 0.25.
43
General Log-Linear
Demand Function
ln QX  0   X ln PX  Y ln PY   M ln M   H ln H
d
Own Price Elasticity :  X
Cross Price Elasticity :  Y
Income Elasticity :
M
44
Example of Log-Linear
Demand
 ln(Qd)
= 10 - 2 ln(P).
 Own Price Elasticity: -2.
45
Graphical Representation of
Linear and Log-Linear
Demand
P
P
Elasticity
varies along
this demand
curve
Elasticity is
constant
along this
demand
curve
D
Linear
D
Q
Log Linear
Q
46
Regression Analysis

Will not be covered at this time.
– PP: 95 -109
47
Let’s practice

Given a log-linear demand curve, we
know that
– A) demand is elastic at high prices.
– B) demand is inelastic at low prices.
– C) demand is unitary elastic at low
prices.
– D) the elasticity is constant at all prices.

Answer: D
48
Chapter 4

What are the properties of consumer
preferences and what do they mean?
1. Completeness
2. More is Better
3. Diminishing Marginal Rate of
Substitution?
4. Transitivity?
49
Property 1: Completeness

Given the choice between 2 bundles of
goods (A & B)
– consumer must have an opinion, meaning
that she should
prefers bundle A to bundle B: A  B;
 or, prefers bundle B to bundle A: A  B;
 or, be indifferent between the two: A  B.

50
Property 2: More is better

Bundles that have at least as much of
every good and more of some good
are preferred to other bundles.
– Example
Bundle A: 2 apples and 3 oranges
 Bundle B: 2 apples and 5 oranges
 Which one will you prefer?
B  A

– B is preferred to A
51
Property 3:Diminishing Marginal
Rate of Substitution?

Marginal Rate of Substitution (MRS)
– The rate at which a consumer is willing to
substitute one good for another and maintain
the same satisfaction level.
– Example:

You are indifferent between
– 10 apples + 4 oranges
– Or 7 apples +5 oranges

MRS of oranges for apples= number of apples
you are willing to give up to get 1 more orange
3
and stay as satisfied as before = _________.
52
Property 3: Diminishing
Marginal Rate of Substitution?

The more oranges you have, the fewer
apples you are willing to give up for an
additional orange.
– For the 5th orange, you gave up 3 apples
– For the 6th orange, you will give up
2
__________apples
53
Property 4: Transitivity

For the three bundles A, B, and C, the
transitivity property implies that
– if C  B and
– B  A,
– then C  A.


If you prefer apples to oranges and
oranges to bananas, then
You must prefer apples to bananas
54
What is an indifference curve and how
does it reflect the properties of consumer
preferences?
Indifference Curve
– A curve that defines the
combinations of 2 goods (X
and Y) that give a consumer
the same level of
satisfaction.
 Consumer
is indifferent
between these combinations
55