# Demand The willingness and ability to buy How does marginal analysis inform simple pricing decisions? How can the concept of elasticity inform managerial.

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Demand The 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 Spry University 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 2 nd and 3 rd 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 Games The relationship between the quantity demanded of a good or service and all influencing factors : Q d = f(X 1, X 2,X 3,X 4 … X n ) where Q d is quantity demanded per period and the X i s are the factors influencing demand Example: Demand for Indiana Lottery Tickets Q = quantity of Lottery Tickets purchased per period X 1 = Price per ticket (expected loss) X 2 = Price of other goods X 3 = Average income per period X 4 = A binary variable for a state border Other variables such as advertising, proximity to riverboat casinos, seasonal variables

Demand Curve Definition: 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) =

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 + 1.66P s - 3.3P r + 0.00661I where P is PTC ticket price, P s is price of symphony tickets, P r is price of nearby restaurant meals, and I is average per capita income. Suppose the variables have the following values: P s = \$50 P r = \$40 I = \$50,000 Substituting variable values (except for P) into the equation and rounding: Q = 400 – 6.6Pdemand curve; or P = 60 – 0.15Q“(inverse) demand curve”

Graphing the demand curve for PTC PTC demand curve: P = 60 – 0.15Q Think of P as the “Y” variable Think of Q as the “X” variable 60 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 – bQ 2 MR = a – 2bQ* This is an application of the derivative formula. If f(x)=ax b then f’(x)=abx b-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 – 6.6Pdemand curve; or P = 60 – 0.15Q“(inverse) demand curve”

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): 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??

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)) Cardiovascular0.4 Anti-infective0.9 Psychotherapeutic0.3 Anti-ulcer0.7 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 Curve point price elasticity Information requirements Demand curve equation: Q=α-βP, β =  Q/  P Initial price and quantity Q P

Calculating elasticity Using a linear demand Curve The demand curve facing the Como Park Golf Course is Q d =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?

Calculating elasticity arc price elasticity Information requirements: Quantity demanded before and after the price change Q 1 Q 2 Price before and after the price change P 1 P 2

Calculating elasticity arc price elasticity

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

Total Spending and the Shape of the Demand Curve: Inelastic Demand D S1S1 P Q

D \$5 100 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand D \$5 100 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand D S2S2 \$5 100 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand D S2S2 \$5 \$2 100160 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand D S2S2 \$5 \$2 100160 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand D S2S2 \$5 \$2 100160 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Inelastic Demand A CB D S2S2 \$5 \$2 100160 S1S1 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 D P Q

S1S1 D \$5 100 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 D \$5 100 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 S2S2 D \$5 100 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 S2S2 D \$5 \$4 100240 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 S2S2 D \$5 \$4 100240 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 S2S2 D \$5 \$4 100240 P Q

Total Spending and the Shape of the Demand Curve: Elastic Demand S1S1 S2S2 D C A B \$5 \$4 100240 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?

Inferior good: <0 Normal good: >0 Luxury good: >1 Examples of income elasticities of demand Powerball0.9 Daily games 0.68 Instant games 0.4 Income Elasticity of Demand

Log-Log Demand Functions Constant Elasticity of Demand Assumption – Constant own-price elasticity of elasticity of demand and constant income elasticity of demand

Estimating Demand Multiple Regression Technique Information requirements –Hypothetical demand relationship Q = a + bP + cP subst + dI + eAdvert. –Data series for Q, P, P subst, I, Advert.

Estimating Demand Multiple 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 Telecom CEO 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 Pop The 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?

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

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