demand the willingness and ability to buy how does marginal analysis inform simple pricing...

DemandThe willingness and ability to buy

How does marginal analysis inform simple pricing decisions?How can the concept of elasticity inform managerial decisions?

How can managers learn about consumer demand?

Professor SpryUniversity of St. Thomas

•Economics 600

•6:00pm-9:00pm

Today’s agenda• Demand functions

• Linear Demand Functions and Curves– Players Theater Example

• Own-Price, Cross-Price, and Income Elasticities of Demand

• Applications of Demand Estimation– Forecasting prices of FCC Licenses– The Demand for Hoosier Lottery Tickets

Motivating Example: Red Lobster

• All you can eat crab dinner – – For that 2nd and 3rd and … helping,

• What is the marginal cost to customer?

• What is the marginal benefit to customer?

• What is the marginal benefit & cost to Red Lobster?

• What if steak? Fish & chips?

Demand Function for Indiana Lottery GamesThe relationship between the quantity demanded of a good or service and all influencing factors :

Qd = f(X1, X2,X3,X4… Xn)where Qd is quantity demanded per period and the Xis are the factors influencing demand

Example: Demand for Indiana Lottery Tickets• Q = quantity of Lottery Tickets purchased per period•X1 = Price per ticket (expected loss)•X2 = Price of other goods •X3 = Average income per period•X4= A binary variable for a state border•Other variables such as advertising, proximity to riverboat casinos, seasonal variables

Demand CurveDefinition: A demand curve shows the amount of a

good/service consumer(s) are willing and able to buy per period at various prices; all else constant

“Plug in” values of other variables, such as income, prices of substitutes, ect. into the demand function to obtain the demand curve as a function of the price of the good only

P=a-bQ or Q(P) =

P

bb

a 1

Modeling demand as a constrained choice problem

The consumer has:• Desire to maximize

satisfaction from a variety of purchases Tastes & preferences affected

by advertising and other factors

• A budget constraint for those purchases Affected by income, prices of

goods & services under consideration

The Logic of Consumer Choice and Demand

Change in a demand factor:• E.g. lower price of good => change in budget constraint =>

reduces opportunity cost of purchasing this good => purchase more units– Movement along a single demand curve

• E.g. increase income => expands budget constraint => buy more of many goods and services– Demand curve shifts

• E.g. persuasive advertising => shapes tastes & preferences => may sway consumer toward this product without requiring a price decrease– Demand curve shifts

Market Demand Function 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.•Suppose the variables have the following values:

Ps = $50

Pr = $40

I = $50,000

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

Q = 400 – 6.6P demand curve; or

P = 60 – 0.15Q “(inverse) demand curve”

Graphing the demand curve for PTCPTC demand curve: P = 60 – 0.15Q

Think of P as the “Y” variableThink of Q as the “X” variable60 is the vertical “Y” intercept-0.15 is the slope (change in Y/change in X)

How Many Tickets Should PTC Sell: Using Linear Demand Curve Facts

In general, if • P = a – bQ (linear)• TR = aQ – bQ2

• MR = a – 2bQ*

This is an application of the derivative formula.If f(x)=axb then f’(x)=abxb-1.

Don’t sell as much as possible, maximize your profits!!!!

If it is worth producing, produce until

Marginal Revenue = Marginal Cost!!

Marginal Analysis and Pricing

Q = 400 – 6.6P demand curve; or

P = 60 – 0.15Q “(inverse) demand curve”

000,6$200*30$

30$3060200*15.06015.060

2003.0

60

03.602*)15.0(60

15.060)15.060( 2

PQTR

QP

Q

MCQQMR

QQQQPQTR

Price elasticity of demand• Measures the sensitivity of quantity

demanded to changes in demand factors

• The price elasticity of demand is given by

(all else constant):

P

Q

%

%

Absolute Value

Does a given (often a 1%) change in the price of the good lead to a small reduction or a huge, titanic reduction in the QUANTIY DEMANDED??

http://images.google.com/imgres?imgurl=www.cd.chalmers.se/~mag/pictures/absolut.gif&imgrefurl=http://www.dtek.chalmers.se/~d1mag/&h=387&w=233&sz=30&tbnid=jjRF5cN9Z0cJ:&tbnh=117&tbnw=71&prev=/images%3Fq%3Dabsolut%26imgsz%3Dsmall%257Cmedium%257Clarge%257Cxlarge%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26safe%3Doff%26sa%3DN

Determinants of price elasticity• Availability of substitutes• Size of good in consumer budget• Time period for consumer adjustment

Discuss: a) Southwest Airlines estimates the short-run price elasticity of business air travel to be 2 and the long-run elasticity to be 5. Does this seem reasonable? Explain.

b) Would the market demand for business air travel be more or less elastic than Southwest’s? Why?

Estimated Price Elasticities• Prescription drugs (Baye, Maness, Wiggins in Applied Economics 29

(1997))

• Cardiovascular 0.4• Anti-infective 0.9• Psychotherapeutic 0.3• Anti-ulcer 0.7

• Recreation* 1.1 (short term) 3.5 (long term)• Clothing* 0.9 (short term) 2.9 (long term)• Alcohol & tobacco*0.3 (short term) 0.9 (long term)

*Baye, Jansen, Lee, in Applied Economics 24 (1992)

Calculating elasticity from a linear Demand Curvepoint price elasticity

Information requirements

• Demand curve equation:

Q=α-βP, β =Q/P• Initial price and quantity

• Q• P

Q

P

Q

P

P

Q

P

Q %

%

Calculating elasticityUsing a linear demand Curve

• The demand curve facing the Como Park Golf Course is Qd=100 – 2P

• The current price is $20.00 for a round of golf.• 60 golfers play Como per day. • What is the own-price elasticity of demand at Como at a

price of $20.00?

667.060

40

60

202

Q

P

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

2

)(

2

)(

21

21

PPP

QQQ

Example: Housing Sales• From March to April of 1998, the price of an average

single-family home decreased from $128,200 to $127,100. Interest rates and income were unchanged.

• Housing sales increase from 4,700,000 to 4,890,000.Source: WSJ, May 27, 1998

6.4

0086.0396.

650,127100,1

000,795,4000,190

2/200,128100,127200,128100,127

2/70.489.470.489.4

2/21

12P

2/21

12Q

demand of ElasticityDE

MMMM

PP

P

QQ

Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand

D

S1

P

Q


D

$5

100

S1

P

Q


D

S2

$5

100

S1

P

Q


D

S2

$5

$2

100 160

S1

P

Q


A

C BD

S2

$5

$2

100 160

S1

P

Q

Total Spending and the Shape of the Demand Curve: Elastic Demand

S1

D

P

Q


S1

D

$5

100

P

Q


S1S2

D

$5

100

P

Q


S1S2

D

$5

$4

100 240

P

Q


S1S2

D

C

A

B

$5

$4

100 240

P

Q

Cross-Price Elasticity

• Positive if substitutes; negative if complements• Cross-price elasticity of demand for new car

sales from a change in gas prices = - 0.214– (McCarthy, in Economic Inquiry 28 (July

1990), pp. 530-43)– Interpretation?

y

xxy P

Q

%

%

Inferior good: <0Normal good: >0Luxury good: >1

Examples of income elasticities of demand• Powerball 0.9• Daily games 0.68• Instant games 0.4

Income Elasticity of Demand

I

I

QI %

%

II

Log-Log Demand FunctionsConstant Elasticity of Demand

• Assumption– Constant own-price elasticity of elasticity of

demand and constant income elasticity of demand

IPQ

IPQ

lnlnlnln

Estimating DemandMultiple Regression Technique

Information requirements

– Hypothetical demand relationship

Q = a + bP + cPsubst + dI + eAdvert.

– Data

series for Q, P, Psubst , I, Advert.

Estimating DemandMultiple Regression Technique

• Use statistical program (e.g. Excel) to estimate parameters using multiple regression techniques– a, b, c, d, e

• Assess summary statistics to judge reliability

Caution: Demand Estimation Problems

• Omission of relevant variables– Important demand

variable

• Identification problem– Price changes may not be

exogenous– Supply shifts muddy the

water

• Critical issue because estimates of parameters can be seriously biased

Demand Estimation in TelecomCEO of a regional tel. Co. was interested in bidding on licenses for airwaves in

the region that the FCC was licensing off. Purpose was for wireless communications networks. He read a New York Times article that contained the following data: price paid per license in 10 different regions (Millions of dollars), number of licenses sold, quantity of licenses, and regional population (millions). Given the three logarithmic data series, he clicked the regression tool button and found the following relation:

Ln P = 2.23 – 1.2 ln Q + 1.25 ln PopThe estimated equation should give him info on how much he should expect to

bid to buy a license. You can show that with log-linear demand functions such as this one, the estimated coefficients equal elasticities. Since the population in the region is 7 percent higher than the average, this means

or the % change in P = 8.75%. Thus, the CEO would expect to pay 8.75 % higher in his region. The data

showed the average price to be $70.7 million for a license. So he should expect to pay $76.9 million.

What type of information would the CEO want to know whether to place a high degree of confidence in this estimate? Why?

7%

Pin %change 1.25

Looking Forward

• Assignment #1 Due Sept. 30, Oct. 4 or 5– Due at start of class!

• Read Managerial Economics Chapter 5 – Moneyball and the Oakland A’s

http://images.google.com/imgres?imgurl=www.sims.berkeley.edu/courses/is290-2/f98/oaklandkids/sites/coliseum/images/athletics.gif&imgrefurl=http://thetornidentity.com/mt/&h=185&w=185&sz=11&tbnid=JtKJxG_IlCUJ:&tbnh=96&tbnw=96&prev=/images%3Fq%3Doakland%2Ba%2527s%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26safe%3Doff%26sa%3DN

demand the willingness and ability to buy how does marginal analysis inform simple pricing...

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