Outline Airline ticket pricing The demand function Determinants of demand Elasticity of demand Price elasticity, revenue, and marginal revenue
Airline ticket pricing Consider United Airlines Flight 815 from Chicago to LA on October 31, 1997 1 There were 27 different one-way fares, ranging from $1,248 for a first class ticket purchased the day of the flight to $87 for an advance purchase coach ticket. Some travelers cashed in frequent flier miles. Some qualified for senior citizen discounts. Some passengers traveled on restricted tickets that required Saturday stayovers. 1 So, How much did you pay for your ticket, New York Times, April 12, 1998
Yield management Yield management means pricing seats to maximize profits. Our task in this chapter is demonstrate how demand analysis can be useful useful in establishing a profit maximizing fare structurealbeit one that is bewildering to travelers
Assumptions 1.You are a manager for a regional airline offering non-stop service between Houston, TX and Orlando, FL. 2.Your airline makes one departure from each city per day (2 flights total). 3.One rival airline offers non-stop service on this route. 4.We ignore first class service and focus on the demand for coach-class travel.
The demand function Q = f(P, P O, Y) [3.1] [3.1] can be read as follows: The number of your airlines coach seats sold per flight (Q) is a function of the your airlines coach fare (P), its rivals fare (P O ), and income in the region (Y) Your forecasting unit has estimated the following demand function: Q = 25 + 3Y + P O – 2P [3.2]
Effect of changes in the explanatory variables 1.For each one point increase in the income index (Y), 3 additional seats will be sold, ceteris paribus. 2.For each $10 increase in the airlines fare, 20 fewer seats will be sold, ceteris paribus. 3.For each $10 increase in the competitors fare, 10 additional seats will be sold, ceteris paribus. Q is the dependent variable; P, P O, and Y are the independent or explanatory variables.
The demand curve Definition: Curve indicating the quantities demanded of a good or service (such as air service) at various prices (fares, etc.), ceteris paribus. Example: Let Y = 105 and P O = $240. Our demand function is given by: Q = 25 + 3(105) + 1(240) –2P = 580 – 2P [3.4] Our inverse demand function is given by: P = 290 – Q/2 [3.4a]
Ceteris paribus Price 290 240 142100622580 P = 290- Q/2 Quantity of Units Sold 219 Remember that as we move along the demand curve we hold all other things constant. In our case this means Y and P O
Shifts of the demand curve Price 290 240 142100622580 P = 290- Q/2 P = 311- Q/2 Quantity of Units Sold $311 What would happen if, ceteris paribus, Y increased to 119? Work it out and you will discover the new inverse demand function is given by P = 311 – Q/2
Normal and inferior goods A product (or service) is said to be a normal good if an increase in income raises its sales, ceteris paribusthat is, the coefficient of Y is positive. Air travel, cellular service, and luxury automobiles are examples of normal goods. Conversely, an inferior good has a negative income coefficient. Macaroni and hot dogs are examples of inferior goods.
Substitutes and complements If an increase in the price of good Y causes an increase in the demand for good X (shift to the right), then X and Y are substitutes. Examples of substitutes include: car and air travel; chicken and pork; doctors and midwives. If an increase in the price of good Y causes an decrease in the demand for good X (shift to the left ), then X and Y are complements. Examples: PCs and digital cameras; tents and sleeping bags; TVs and DVD players; shotguns-camo.
Elasticity Issue: How responsive is the demand for air service to changes in fares, ceteris paribus. The concept of price elasticity of demand is useful here.
Price elasticity of demand Let price elasticity of demand (E P ) be given by: E P = % change in Q % change in P [3.1]
Example Price 0 Output P = 290 – Q/2 240 235 100110 Question: What is E P in the range of demand curve between fares of $240 to $235? To find out: Meaning, a 1% increase in fares will result in a 4.8% decrease in passengers per flight (and vice-versa). A B
Point elasticity In our previous example we computed the elasticity for a certain segment of the demand curve (point A to B). For purposes of marginal analysis, we are interested in point elasticitymeaning, elasticity when the change in price in infinitesimally small.
Formula for point elasticity [3.11] Here we are calculating the responsiveness of sales to a change in price (fares) at a point on the demand curve that is, a defined price- quantity point.
Arc elasticity To compute arc elasticity, or average elasticity between two price-quantity points on the demand curve: Samuelson and Marks note the advantage of arc elasticitythat is, it matters not what the initial price is (say, $240 or $235), our calculation of E P does not change.
Perfectly inelastic demand Price 50 Quantity 100150200250 10 30 20 50 40 70 60 80 90 $100 E P = 0 0 Buyers are absolutely non- responsive to a change in price
Perfectly elastic demand E P =- infinity Price 50 Quantity 100150200250 1 3 2 5 4 7 6 8 9 $10 (b) Perfectly Elastic Demand 0 In this case, if the price rises a penny above $5, quantity- demanded falls to zero.
Income elasticity Issue: Is demand for a good or service sensitive to a change in consumer income, ceteris paribus? Income elasticity of demand (E Y ) is given by: Where Y is consumer income
Cyclical sales? If E Y > 1, then sales are cyclicalthat is, sensitive to economic (business cycle) fluctuations. Autos, furniture, and major appliances are examples of cyclical industries. If E Y < 0, then sales are counter-cyclical. An overall decrease in consumer income will result in an increase in sales for these products. Examples: Pawnbroker services, macaroni, bus travel
Cross price elasticity of demand 1.How sensitive is the demand for rental cars to airline fares? 2.How does the demand for apples respond to a change in the price of oranges? 3.Will a strong dollar hurt tourism in Florida? Cross price elasticity gives us a measure of the responsiveness of demand to the price of complements or substitutes
Formula for cross price elasticity Cross price elasticity of demand (E p o) is given by: Where Q is the quantity of the good (X) and P 0 is the price of of a related good or service( good Y) If E P 0 > 0, then X and Y are substitutesthat is, an increase in the price of good Y will result in an increase in the demand for good X If E P 0 < 0, then X and Y are complementsthat is, an increase in the price of good Y will result in a decrease in the demand for good X
Price Elasticity Changes Along a Linear Demand Curve $ 400 300 200 100 4001,200,1600 Quantity Demanded Price 800 Marginal revenue Demand is price elastic Demand is price inelastic B M A Elasticity = MR = 400-.5Q P = 400-.25Q 0 (a) Demand tends to be elastic at higher prices and inelastic at lower prices
Revenue rule Revenue rule: When demand is elastic, price and revenue move inversely. When demand is inelastic, price and revenue move together. As price falls along the elastic portion of the demand curve (price above $200), revenue will increase; whereas as price falls along the inelastic portion (below $200), revenue will decrease
$ 160,000 120,000 4001,200 Quantity Demanded Revenue 800 (b) Total revenue R = 4 0 0 Q-.2 5 Q 2 0 Notice the Marginal Revenue (MR) function dips below the horizontal axis at Q = 800.