Post on 08-Jan-2016
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Chapter 2 homework
Numbers 7, 10, and 13
Managerial Economics & Business Strategy
Chapter 3Quantitative Demand Analysis
Anyone heard of ELASTICITY??
• How responsive is variable “G” to a change in variable “S”
If EG,S > 0, then S and G are directly related.If EG,S < 0, then S and G are inversely related.
S
GE SG
%
%,
If EG,S = 0, then S and G are unrelated.
The Elasticity Concept Using Calculus
• An alternative way to measure the elasticity of a function G = f(S) is
G
S
dS
dGE SG ,
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.
Own Price Elasticity of Demand
• Negative according to the “law of demand.”
Elastic:
Inelastic:
Unitary:
x
x
x
dx
X
dX
PQ Q
P
P
Q
P
QE
XX
%
%,
1, XX PQE
1, XX PQE
1, XX PQE
Perfectly Elastic & Inelastic Demand
)( ElasticPerfectly , XX PQE
D
Price
Quantity
D
Price
Quantity
)0, XX PQE( Inelastic Perfectly
What does this mean??
• EQx,PX = 3 A 1% increase in price will lead to a 3% decline in quantity
demanded. Would a firm find this to be a problem?
• EQx,PX = .3 A 1% increase in price will lead to a 0.3% decline in quantity
demanded. Would a firm find this to be a problem?
Why would a firm worry about elasticity?
• Impacts units sold Total Revenue Price * Quantity
• Elastic Increase (a decrease) in price leads to a decrease (an increase) in total
revenue.
• Inelastic Increase (a decrease) in price leads to an increase (a decrease) in total
revenue.
• Unitary Total revenue is unchanged Total revenue is maximized at the point where demand is unitary elastic.
Elasticity, Total Revenue and Linear Demand
P TR100
80
800
60 1200
40
20
Inelastic
Elastic
Elastic Inelastic
0 10 20 30 40 500 10 20 30 40 50
Unit elastic
Unit elastic
What should the airlines do to increase cash flow??
• Increase the price of tickets to raise money
• Decrease the price of tickets to raise quantity sold
• Elasticity = 1.8
• Elastic!!! Reduce price to increase TR
Factors Affecting Own Price Elasticity
Available Substitutes• The more substitutes available for the good, the more elastic
the demand. Time
• Demand tends to be more inelastic in the short term than in the long term.
• Find substitutes. Expenditure Share
• Cost more??? Think about it more More elastic
Cross Price Elasticity of Demand
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
x
y
y
dx
Y
dX
PQ Q
P
P
Q
P
QE
YX
%
%,
Predicting Revenue Changes from Two Products
Suppose that a firm sells goods that are related (pizza and beer). If the price of beer (good X) changes, then total revenue will change by:
XPQYPQX PERERRXYXX
%1 ,,
What???• Suppose a firm’s revenues are derived from the
sales of two products, X and Y. The firm’s revenue would be R = Rx + Ry,
• Rx = PxQx denotes revenues from the sale of product X
• Ry = PyQy denotes revenues from the sale of product Y. The impact of a given percentage change in the price of product X
on the total revenue of the firm are given by the following formula:
xPQyPQx PERERRxyxx
%*1 ,,
Can 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%?