Players Theater Company Should the theater cut prices? The theater has 500 seats; about 200 are filled in a typical performance The PTC has been charging $30/seat Issues: Price of meals at nearby restaurants Convenience of parking Price of other nearby theaters Quality of performances Should different seats sell for different prices?

Demand Function Q = f(X1, X2,…, Xn) Example: Q = 117 – 6.6 P + 1.66Ps – 3.3 Pr + .0066I Issues You might want to think about Q as the average number of seats sold at a performance during the season. In that case fractional numbers of seats are meaningful The linear demand function is convenient, but not required. There are many other items that we might want to put into the demand function including some of the items discussed on the previous slide.

Demand Curve Ticket Price in Dollars Income = $50,000 Price of Symphony tickets = $50 Price of meal at nearby restaurant = $40 60 30 Demand 200 400 Quantity of PTC Tickets

Demand Curve Ticket Price in Dollars Income = $50,000  $51,000 Price of Symphony tickets = $50 Price of meal at nearby restaurant = $40 61 60 30 200 400 406.6 Quantity of PTC Tickets

Elasticity of Demand Definition Calculating η = -(% change in Q) / (% change in P) Calculating

Ticket Price in Dollars Arc Elasticity Ticket Price in Dollars 60 40 30 133 200 400 Quantity of PTC Tickets

Estimates of Price Elasticities Sugar = 0.31 Potatoes = 0.31 Tires = 1.20 Electricity = 1.20 Haddock = 2.20 Movies = 3.70

Total Revenue, Marginal Revenue Total Revenue = P x Q Marginal Revenue = the change in total revenue associated with selling one more unit of the product

Ticket Price, Marginal Revenue In Dollars η > 1 η = 1 30 Demand Q Total Revenue in Dollars MR Total Revenue Q

Other Factors Influencing Demand Prices of related products Complements vs. Substitutes Defining a Market Cross Price Elasticity of Demand

Estimates of Cross Elasticities Electricity and Natural Gas = 0.20 Beef and Pork = 0.20 Natural Gas and fuel oil = 0.44 Margarine and Butter = 0.81

Other Factors Influencing Demand Income Normal vs. Inferior goods Income Elasticity of demand

Estimates of Income Elasticities Flour = -.36 Natural Gas = 0.44 Margarine = -0.20 Milk = 0.07 Dentist Services = 1.41 Restaurant Consumption = 1.48

Industry Quantity of output Advanced Issues Network Effects Product Attributes Product Life Cycles Industry Quantity of output Intro Growth Decline Network Effects: Some products are more valuable to customers the more other people there are that use them. This may cause firms to use low introductory prices in order to make more money later. Maturity Time

Demand Estimation Interviews Price Experimentation Statistical Analysis Omitted Variables Bias Multicollinearity Identification Problem

The Identification Problem Suppose that this is a history of recent price and quantity changes in our industry: Year Price Quantity 2004 25 4.5 million 2005 29 5.25 million 2006 22 7 million

The Identification Problem Price in dollars 2005 29 2004 25 2006 22 Industry output In millions 4.5 5.25 7

The Identification Problem Price in dollars D’ 2005 29 D 2004 25 S 22 Industry output In millions 4.5 5.25 7

The Identification Problem Price in dollars D’ 2005 29 D 25 2006 S 22 S’ Industry output In millions 4.5 5.25 7