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

Managerial Economics and Organizational Architecture, Chapter 4

Demand

The willingness and ability to buy


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


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


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.)


Variable values

Suppose the variables have the following values:

P = $30

Ps = $50

Pr = $40I = $50,000

How many tickets will PTC sell?


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.


Graphing the demand curve


Demand elasticity

The elasticity of demand is given by

⎟⎠

⎞⎜⎝

⎛ΔΔ

−=P

Q

%

%η


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


Calculating elasticityarc price elasticity

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+Δ+Δ

−=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

+Δ

+Δ

−=

)(

)(

2)(

2)(

21

21

21

21

PPPQQQ

PPP

QQQ

η


Arc price elasticityexample


Calculating elasticitypoint price elasticity

Information requirements

Demand curve equation:Q=a-bP, b=ΔQ/ΔP

Current price and quantity P Q


Calculating elasticitypoint price elasticity

⎟⎟⎠

⎞⎜⎜⎝

⎛×−=⎟⎟

⎠

⎞⎜⎜⎝

⎛×

ΔΔ

−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

Δ

Δ

−=⎟⎠

⎞⎜⎝

⎛ΔΔ

−=

Q

Pb

Q

P

P

Q

PPQ

Q

P

Q

%

%η


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


Range of price elasticities


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?


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.)


Elasticity, prices, and total revenue


Demand, total revenue, & marginal revenue

linear demand curve


Other demand influences

Complements versus substitutes– Cross price elasticity of demand

21

21

yy

y

xx

x

xy

PP

PQQQ

+Δ+

Δ

=η


Other demand influences

Income– Normal goods– Inferior goods

Income elasticity


Product life cycle


Estimating demandthe identification problem

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