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Managerial Economics &
Chapter 3
Quantitative Demand Analysis
Could we do it??
• You are the owner of a bookstore, and earn revenues
primarily from selling coffee and books. For the
past two years you have consistently earned, on
average, revenues of \$500 per week from selling
coffee and \$1000 per week from selling books. If
the own price elasticity of demand for coffee is -1.0
and the cross price elasticity of demand between
books and coffee is -1.8, what would happen to your
revenues if you lowered the price of coffee (if coffee
is good X) by 10%?
Income Elasticity

%QX   Q M
d          d
EQX , M                         x
%M    M Qx

If EQX,M > 0, then X is a normal good.

If EQX,M < 0, then X is a inferior good.
Example 1: Pricing and
Cash Flows
• 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?
• 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.
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?
   Remember AT&T’s own price elasticity of demand for long
distance services is -8.64
• Calls would increase by 25.92 percent!
%QX
d
EQX , PX    8.64 
%PX
%QX
d
 8.64 
 3%
 3%   8.64  %QX
d

%QX  25.92%
d
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?
• AT&T’s demand would fall by 36.24 percent!

%QX
d
EQX , PY    9.06 
%PY
% Q X
d
9.06 
 4%
 4%  9.06  %QX
d

%QX  36.24%
d
We can use elasticities to find the
supply and demand functions
• Midcontinent Plastics makes 80 fiberglass truck
hoods per day for large truck manufacturers. Each
hood sells for \$500.00. Midcontinent sells all of its
product to the large truck manufacturers. If the own
price elasticity of demand for hoods is -0.4 and the
price elasticity of supply is 1.5.
• Compute the supply and demand for truck hoods.
Interpreting Demand Functions
• Mathematical representations of demand curves.
• Example:

QX  10  2 PX  3PY  2M
d

• X and Y are substitutes (coefficient of PY is
positive).
• X is an inferior good (coefficient of M is
negative).
Linear Demand Functions
• General Linear Demand Function:

QX  0   X PX  Y P   M M   H H
d
Y

Q PX
d                   Qx PY
d
Qx M
d

EQX , PX    x      EQX , PY             EQX ,M 
Px QX                Py QX             M QX
Own Price           Cross Price              Income
Elasticity          Elasticity               Elasticity
Example of Linear Demand
• Qd = 10 - 2P.
• Own-Price Elasticity
   (-2){P/Q}.
• If P=1 what does Q equal?
   Q=8 (since 10 - 2 = 8).
• Own price elasticity at P=1, Q=8
   (-2){1/8}= - 0.25.
Log-Linear Demand
x   y    M       H
Q  cPx Py M
d
x                         H
• Take Natural Log of both sides to get general Log-
Linear Demand Function:
ln QX   0   X ln PX  Y ln P   M ln M   H ln H
d
Y

Own Price Elasticity :  X
Cross Price Elasticity :  Y
IncomeElasticity :       M
Example of Log-Linear
Demand
• ln(Qd) = 10 - 2 ln(P).
• Own Price Elasticity: -2.

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 views: 10 posted: 8/7/2012 language: pages: 15