Managerial Economics and Organizational Architecture, Chapter 4 Demand The willingness and ability...

Managerial Economics and Organizational Architecture, Chapter 4

Demand

The willingness and ability to buy

Managerial Economics and Organizational Architecture, Chapter 4

Demandlearning objectives

Students should be able toDescribe and apply demand function and demand curveDistinguish between change in quantity demanded and change in demandCalculate and interpret demand elasticity

Managerial Economics and Organizational Architecture, Chapter 4

Demand Function

A mathematical representation of the relationship between the quantity demanded and all factors influencing demand:

Q = f(X1, X2,… Xn)

where Q is quantity demanded and the Xis are the factors influencing demand

Managerial Economics and Organizational Architecture, Chapter 4

Demand for PTC Tickets

Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I

where P is PTC ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income.

(Interpret each term of the above equation.)

Managerial Economics and Organizational Architecture, Chapter 4

Variable values

Suppose the variables have the following values:

P = $30

Ps = $50

Pr = $40I = $50,000

How many tickets will PTC sell?

Managerial Economics and Organizational Architecture, Chapter 4

The demand curve

Substituting variable values (except for P) into the equation and simplifying:

P = 60 - 0.15Q

which is the equation for the demand curve.

Managerial Economics and Organizational Architecture, Chapter 4

Graphing the demand curve

Managerial Economics and Organizational Architecture, Chapter 4

Demand elasticity

The elasticity of demand is given by

⎟⎠

⎞⎜⎝

⎛ΔΔ

−=P

Q

%

%η

Managerial Economics and Organizational Architecture, Chapter 4

Calculating elasticityarc price elasticity

Information requirements:

Quantity demanded before and after the price change Q1

Q2

Price before and after the price change P1

P2

Managerial Economics and Organizational Architecture, Chapter 4

Calculating elasticityarc price elasticity

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+Δ+Δ

−=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

+Δ

+Δ

−=

)(

)(

2)(

2)(

21

21

21

21

PPPQQQ

PPP

QQQ

η

Managerial Economics and Organizational Architecture, Chapter 4

Arc price elasticityexample

Managerial Economics and Organizational Architecture, Chapter 4

Calculating elasticitypoint price elasticity

Information requirements

Demand curve equation:Q=a-bP, b=ΔQ/ΔP

Current price and quantity P Q

Managerial Economics and Organizational Architecture, Chapter 4

Calculating elasticitypoint price elasticity

⎟⎟⎠

⎞⎜⎜⎝

⎛×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛×

ΔΔ

−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

Δ

Δ

−=⎟⎠

⎞⎜⎝

⎛ΔΔ

−=

Q

Pb

Q

P

P

Q

PPQ

Q

P

Q

%

%η

Managerial Economics and Organizational Architecture, Chapter 4

Point price elasticityexample

If the demand equation is Q=20-4P, P=14, and Q=27, then elasticity is

07.2)27/14)(4( −=−=η

Managerial Economics and Organizational Architecture, Chapter 4

Range of price elasticities

Managerial Economics and Organizational Architecture, Chapter 4

Determinants of price elasticity

Availability of substitutes– few substitutes for milk– lots of substitutes for milk at the supermarket

Size of good in consumer budget– consider salt versus a Lexus

Time period for consumer adjustment– given enough time, how do we adjust to higher

fuel prices?

Managerial Economics and Organizational Architecture, Chapter 4

Price changes and total revenue

PTC’s total revenue is TR=PQ The inverse demand curve is P=60-.15Q Substituting, TR=(60-.15Q)Q=60Q-.15Q2 From this we can derive marginal revenue

(MR=ΔTR/ΔQ=60-.30Q)

(Well, OK, we did use a little calculus for that last step. Trust us.)

Managerial Economics and Organizational Architecture, Chapter 4

Elasticity, prices, and total revenue

Managerial Economics and Organizational Architecture, Chapter 4

Demand, total revenue, & marginal revenue

linear demand curve

Managerial Economics and Organizational Architecture, Chapter 4

Other demand influences

Complements versus substitutes– Cross price elasticity of demand

21

21

yy

y

xx

x

xy

PP

PQQQ

+Δ+

Δ

=η

Managerial Economics and Organizational Architecture, Chapter 4

Other demand influences

Income– Normal goods– Inferior goods

Income elasticity

Managerial Economics and Organizational Architecture, Chapter 4

Product life cycle

Managerial Economics and Organizational Architecture, Chapter 4

Estimating demandthe identification problem