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

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Demandlearning objectives

Students should be able to• Describe and apply demand

function and demand curve• Distinguish between change in

quantity demanded and change in demand

• Calculate and interpret demand elasticity

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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

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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.)

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Variable values

Suppose the variables have the following values:

P = $30Ps = $50

Pr = $40

I = $50,000

How many tickets will PTC sell?

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The demand curve

Substitute variable values (except for P) into the equation and simplify:

P = 60 - 0.15Q

This is the equation for the demand curve.

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Graphing the demand curve

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Demand elasticity

The price elasticity of demand is given by

[Note: the convention used here is to express the elasticity as a negative quantity so that, when calculated, the result is a positive number]

P

Q

%

%

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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

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Calculating elasticityarc price elasticity

)(

)(

2)(

2)(

21

21

21

21

PPPQQQ

PPP

QQQ

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Arc price elasticityexample

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Calculating elasticitypoint price elasticity

Information requirements

• Demand curve equation:Q=a+bP, b=Q/P, b<0

• Current price and quantity P Q

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Calculating elasticitypoint price elasticity

Q

Pb

Q

P

P

Q

PPQ

Q

P

Q

%

%

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Point price elasticityexample

If the demand equation is Q=400-6.67P, P=35*, and Q=167, then elasticity is

*This price is midway between the two prices in the arc elasticity calculation.

4.1)167/35)(67.6(

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Range of price elasticities

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Determinants of price elasticity

• Availability of substitutes– few substitutes for milk– many 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?

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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=TR/Q=60-.30Q)

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

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Elasticity, prices, and total revenue

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Demand, total revenue, & marginal revenuelinear demand curve

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Other demand influences

• Complements versus substitutes– Cross price elasticity of demand

21

21

yy

y

xx

x

xy

PP

PQQQ

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Other demand influences

• Income– Normal goods– Inferior goods

• Income elasticity

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Product life cycle

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Omitted variables problem

1998 1999 2000

Income (I) $3,000 $4,000 $3,500

Advertising (A) 2 3 2.5

Price (P) 10 10 10

Sales (S) 236 284 260

True demand S=120-2P+8A+0.04I

Estimated demand S=140+48A

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Estimating demandthe identification problem

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

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