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

QQ

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%?