OPENING CASE: AIRLINE TICKET PRICING, PRICE DISCRIMINATION
On a typical United Airlines flight from Chicago-LA, there were at least 27 different fares charged, from $87 to $1248 depending on which factors?
This pricing strategy is called "price discrimination," where firms charge different prices to different customers for the same product or service, depending on different customers' price sensitivity or price elasticity of demand. Who pays a higher price, customers with elastic demand (price sensitive) or inelastic demand (price insensitive)? Airlines use a pricing strategy called "yield management," based on demand analysis, to determine how many prices to charge, how often to change prices, etc., with the goal of Maximizing Profit. They would like to fly planes as full as possible, as often as possible, and charge the maximum price possible to maximize profits. "Charge whatever the market with bear."
Other examples of Price Discrimination:
a.
b.
c.
d.
e.
DETERMINANTS OF DEMAND
In the simplified model in chapter 2, we assumed that demand was a function of only one variable: ________ [Qd = f (P)]. We now allow for other factors to affect Demand, such as?
Case Study: An airline flies two flights daily between Houston and Orlando and faces a single competitor on this route. The airline determines that demand for coach-class tickets primarily depends on three variables: Its own price for tickets (P), its competitor's price for tickets (Pc), and the income level (Y) of the customers flying between Houston-Orlando. The general demand function or equation for the number of tickets sold per flight would be:
Qd = f (P, Pc, Y)
What are the expected signs of these 3 variables (positive or negative)??
Suppose that the forecasting department has estimated the following specific demand equation for ticket sales (Qd) based on past history of ticket sales:
Qd = 25 + 3Y + 1Pc - 2P
Assume that Income (Y) is measured by an Income Index, based on Personal Income and Business Profits in Texas and Florida, Index = 100 in the base year 1994. The interpretation of the coefficients in the estimated demand equation is:
1. For every 1 point increase in the Income Index (Y), there will be 3 additional tickets sold per flight, ceteris paribus.
2. For every $1 increase in competitor's price, there will be 1 additional ticket sold, ceteris paribus.
3. For every $2 increase in its own price, the airline will sell 2 fewer tickets, ceteris paribus.
For example, assume that Y = 105, Pc = $240 and P = $240.
Q = 25 + 3 (105) + 240 - 2 (240) = 100 tickets.
If all three variables change simultaneously, then the total change in Q would be:
ΔQd = 3 ΔY + ΔPc - 2 ΔP
Example: If income increased by 5 points, and both airlines cut prices by $15, we find that:
ΔQd = 3 * (5) + 1 * (-$15) - 2 * (-$15) = + 30 tickets.
DEMAND CURVE AND SHIFTING DEMAND
We have not confirmed that P = $240 and Q = 100 are the Profit Maximizing level of output and price. The planes can seat 180 customers, so they have been flying at an average of only 55.6% full (load factor), with 80 empty and unsold seats. (Think of the MC of one additional passenger vs. MR, and the potential effect on profit).
Assume that Y will be stable at 105 and the competitor's fare will remain at $240, and the airline wants to forecast the effects of varying its price. Using the values specified, we estimate demand (as a function of P) to be:
Q = 25 + 3 (105) + 1 (240) - 2P
Qd = 580 - 2P (ceteris paribus)
Solving for P, i.e. the Inverse Demand Equation:
P = 290 - .5Q
We now relax the ceteris paribus assumption, and allow one of the variable to change, specifically Y = 119 (an economic expansion raises regional income).
Q = 25 + 3 (119) + 1 (240) - 2P
Q = 622 - 2P
P = 311 - .5 Q
See Figure 3.1 on p. 84 for the two demand curves (old and new). Notice that the slope is the same for both demand equations (slope = __________), and only the intercept has changed from ______ to ______. The demand curve has increased (shifted out). At any given P, there will now be MORE seats sold. For example, if P = $240, Q will increase from 100 to 142 as a result of the increase in Income and the increase in Demand. In fact, at any given Price, the demand will increase by 42 seats, see the horizontal axis (622 - 580 = 42). Also, for any given Q, the airline can sell that same amount of seats at an increased fare of $21. If Q = 100, P = $240 for the old demand curve, and P = $261 for the new demand curve. The $21 increase is reflected in the difference between the intercepts ($311 - 290).
We can also verify the new price by putting Q = 100 in the new demand equation: P = 311 - .5 (100) = $261 (vs. $240 before).
GENERAL DETERMINANTS OF DEMAND
1. INCOME: Air travel is a typical of most goods and services, where an INCREASE in INCOME leads to an INCREASE in DEMAND for that product. Since we are talking about "market demand" for air travel, etc., an "increase in income" means an increase in national or regional income, usually due to a general economic expansion, causing a general increase in wealth, income and therefore demand for most goods and services. A product is a NORMAL GOOD if an increase in income raises its sales, and therefore the Income variable's sign in most demand equations is __________ .
Most goods and services are normal, the exception is INFERIOR GOODS, where an increase in income lowers its sales, and the Income variable's sign would be ___________ in the demand equation.
Examples of inferior goods:
a. Greyhound or local bus rides
b.
2. RELATED GOODS: SUBSTITUTES AND COMPLEMENTS:
a. Substitute goods are direct or indirect rivals, i.e. direct or indirect competitive products, goods or services. In the airline industry, there are often 5 or 6 carriers that all directly compete with each other for passengers on the same route. Examples of indirect competition for airlines: ________________ _________________________________. There are different degrees of substitutes, goods can be perfect substitutes or very close substitutes, or can be imperfect substitutes.
Example: Pepsi might be a perfect or very close substitute for Coke for many people, and an imperfect substitute for milk. Point: The greater the availability of perfect or close substitutes, the more competitive the market, e.g. 6 airlines competing on a route vs. 1 airline (Flint-Minneapolis), and the more price sensitive consumers will be, i.e., the greater price elasticity of demand.
b. Complementary goods (services) are jointly consumed goods or goods purchased as a bundle, so that an increase in demand for Good A will increase demand for Good B (A and B are complements).
Examples:
a. Computer software and computer hardware (see p. 85-86)
b. CD players and CDs
c. Florida resort packages at Disney World and air travel to Florida
d.
The demand for vacations at Disney would depend on airfares to Florida. In the Demand equation for Disney vacations, the variable "airfares to Florida" would have what expected sign? ___________ In the demand equation for computers, the variable "price of computer software" would have what sign? ____________. In the demand equation for computer software, the variable “price of computers” would have what sign? _______ (See p. 86, point #3).
3. DEMOGRAPHICS (Population, Tastes, Preferences, etc.)
Population: As the population grows, the number of consumers in the market grows, which would affect demand for air travel between Houston and Florida.
Demographics: Soft drink sales depend on the number of consumers age 10-25, beer sales on the group 18-45, wine sales on the group 35-55, etc.
Tastes/Preferences: Tastes and preferences change over time for music, food, fashion, health consciousness, recreation, travel, drugs, etc.
PROFIT MAXIMIZATION EXAMPLE:
A chemical producer's cost function is: TC = $500,000 + 2.5Q, so that the MC = $2.50/liter. The annual demand equation is:
Qd = 1,200,000 + 160,000 Pc - 200,000 P
where Annual Sales depend only on the firm's price (P) and its only competitor's price (Pc), both of which are $5/liter. The firm now sells:
Q = 1,200,000 + 160,000 ($5) - 200,000 ($5) = 1,000,000 liters per year. We want to see if 1m liters is the Profit Max level of output (Q*). We first set Pc = $5 and solve for the Inverse Demand equation:
Q = 1,200,000 + 160,000 ($5) - 200,000 P
Q = 2,000,000 - 200,000 P
Divide each term by 200,000 to get P by itself:
Q = 2,000,000 - 200,000 P
200,000 200,000 200,000
.000005 Q = 10 - P
P = 10 - .000005 Q
Solve for TR = P x Q
TR = (10 - .000005 Q) Q
TR = 10 Q - .000005 Q2
Solve for MR:
MR = 10 - .000010 Q
Set MR = MC
10 - .00001Q = $2.50
7.5 = .00001 Q
Q* = 750,000
Put Q* in the Inverse Price equation to get P*:
P* = 10 - .000005 (750,000)
P* = $6.25 per liter
To MAX PROFITS, the firm should REDUCE output from 1,000,000 to 750,000 liters and RAISE price from $5 to $6.25.
TR is currently 1,000,000 x $5 = $5,000,000
TC is currently $500,000 + $2.5(1m) = $3,000,000
PROFIT $2,000,000
New TR: 750,000 x $6.25 = $4,687,500
New TC: $500,000 + $2.5(750,000) $2,375,000
PROFIT $2,312,500
Profits will increase by $312,500 per year by lowering output and raising price!!
ELASTICITY OF DEMAND
1. PRICE ELASTICITY is a measure of consumers' price sensitivity, or a measure of how responsive consumers are to price changes. From the Law of Demand, we KNOW FOR CERTAIN that an increase (decrease) in a good's price will ALWAYS result in a decrease (increase) in the quantity demanded. That is, we KNOW the direction of the change (P goes up, Qd goes down). Price Elasticity answers the question: When Price goes UP, HOW MUCH does Qd fall? A lot? If so demand is responsive or _______________. A little? If so, demand is relatively unresponsive or ___________.
Why is elasticity important to a firm?
1. Knowing price elasticity, a firm can accurately predict what impact price changes will have on unit sales (Q).
2. Price elasticity can help the firm determine an optimal pricing strategy to MAX PROFITS.
Examples: If GM offers a $1000 rebate on 2007 cars, what effect will that have on unit sales, TR and profits?
If Northwest Airlines (NWA) offers a summer airfare sale, how will that affect tickets sold, TR and profits?
What effect will a coupon promotion for Wheaties have on profits?
How many different ticket prices should NWA offer to maximize profits?
Understanding the price elasticity of demand for its products can guide the firm in these decisions. Pricing is one the most important and critical decisions a firm faces, and elasticity is the key to determining optimal pricing. In most industries, e.g. the airline industry, pricing is a continual and ongoing decision process.
Prices are measured in dollars and Quantity in physical units, so we convert P and Q to percentage changes to compute elasticity as follows:
EP = % D Q = D Q / Q0 = (Q1 - Q0 ) / Q0
% D in P D P / P0 (P1 - P0 ) / P0
where P0 and Q0 are the initial price and quantity and P1 and Q1 are the new price and quantity.
Example: Airline's demand equation is: Q = 580 - 2P. At a fare of $240, the airline sells 100 seats. At a fare of $235, 110 seats are sold. Therefore:
EP = % Δ Q = (110 - 100) / 100 = +10% = -4.8
% D P (235 - 240) / 240 -2.1%
Again we make the ceteris paribus and assume the only variable that changed was Price. In this case, price was reduced by -2.1% and the Qd increased by +10%, so the EP is -4.8. Since the %Qd > %P, we know that demand is very price sensitive or that consumers are very responsive to price changes for airline tickets. Another interpretation of EP = -4.8 is that for EVERY 1% CHANGE IN PRICE, Qd WILL CHANGE BY 4.8% (in the opposite direction).
The coefficient EP answers the question: For a 1% change in price, how much does Qd change? Note: EP is ALWAYS negative, so we can sometimes ignore the negative sign for convenience.
In cases like this, when %Qd > % P (4.8% > 1.0%) in absolute terms, | EP | > 1 and we say that demand is ELASTIC.
When %Qd = % P, | EP | = 1, and we say that demand is UNITARY ELASTIC.
When %Qd < % P, | EP | < 1 and we say that demand is INELASTIC (not responsive/sensitive to price changes).
The calculation above for EP is called the Point Elasticity, or the elasticity at a single point on the demand curve. We made a small change above to calculate the percentage changes. Another way to calculate the Point Elasticity at a single point on the demand curve:
EP = dQ / Q , which we can rearrange to:
dP / P
EP = (dQ) * ( P )
(dP) ( Q )
Remember that the airline's demand curve is Q = 580 - 2P. If we graphed this equation, -2 would be the slope of the line, which is also (DQ / DP), the first term in the equation above. Therefore:
EP = -2 ( P )
( Q )
Thus, -2 is a constant, and we then calculate EP at any point on the demand curve, knowing P and Q. For example, from above we know that when P = $240, Qd = 100 and when P = $235, Qd = 110. We can solve the point elasticity at those two points:
EP = - 2 (240 / 100) = - 4.8
EP = - 2 (235 / 110) = - 4.27
What about when P = $200? Qd = 580 - 2 * (200) Q; and Qd = 180.
EP = - 2 (200 / 180) = -2.2
Also notice that in the inverse demand equation: P = 290 - .5Q. In this equation, the slope is -.5, which is ΔP/ΔQ, the inverse of the first term in the Point Elasticity equation. Or 1 / ( dP / dQ ) = dQ / dP. Since we typically use the inverse demand equation (P = 290 - .5Q), we can express Point Elasticity as:
EP = 1 * P
slope of inverse demand curve Q
POINT ELASTICITY RULES
1. For demand equation, where a is the intercept and b is the slope: Q = a - b P, then EP = -b x (P / Q)
2. For inverse demand equation: P = a - b Q, EP = 1 / -b x ( P / Q)
See page 96 for another example. General rule: Demand is more elastic at higher prices than at lower prices. Demand becomes more inelastic (elastic) as we move down (up) the demand curve.
One potential flaw with the Point Elasticity is that it is NOT symmetrical. For example, using the numbers from above, assume now that we start with a price of $235 and Q = 110 and then raise the price to $240, resulting in Q = 100. Solving for the point elasticity:
EP = (100 - 110) / 110 = 10 / 110 = -4.27
(240 - 235) / 235 5 / 235
so we get a different elasticity coefficient, even thought the dP and dQ were the same as before.
One way to impose symmetry is to calculate the Arc Elasticity of Demand as follows:
EP = ΔQ / Avg. of Q1 and Q2 = 10 / 105 = 4.5
D P / Avg. of P1 and P2 5 / 237.50
EP = 4.5 whether it was a $5 increase or decrease in P.
The Arc Elasticity between P = $235 and P = $240 will be constant at -4.5 and it won't matter whether it was a $5 increase (first example) or a $5 decrease (second example).
However, in most of the examples of optimal pricing and marginal analysis we will use EP = Point Elasticity.
Graphically, when demand is elastic (inelastic), the demand curve is flat (steep), see page 89.
FACTORS AFFECTING PRICE ELASTICITY
What factors determines elasticity, price responsiveness??
1. The degree to which a good is a necessity. The MORE a necessity a good is, the LESS elastic and the MORE inelastic the demand will be. Consumers are not price sensitive to goods, products, services which are a necessity.
Examples: insulin, heroin, cigarettes, dental and health services are necessities, and therefore demand would be __________ .
2. Availability of substitutes. The greater (lower) the number of close substitutes, the more (less) competition, the more (less) selection consumers have and the more (less) price sensitive, the more elastic (inelastic), the demand.
Examples: A corner with 4 gas stations, versus one gas station in the middle of Nevada where the closest gas station is 100 miles away. Popcorn in a movie theater. Airline route with 6 carriers versus route with one carrier. Textbooks.
3. Proportion of Income Spent on a Good. The greater (lower) the proportion of our income spent on a good, the more (less) price sensitive and the more elastic (inelastic) the demand.
Examples: Demand for salt, toothpicks, matches, envelopes, tends to be relatively ____________ . Demand for cars, homes, furniture, appliances, education, vacations tends to be more ___________ .
A large percentage (60-70%) of a typical firm’s costs is for labor, so the demand for labor might be relatively ____________.
4. Time of adjustment. Given time for adjustment, consumers can usually find more substitutes in the long run compared to the short run, so demand is more elastic in the LR compared to the SR (more inelastic). Point: Demand becomes more elastic over time.
Example: Price of gasoline goes to $5/gallon tomorrow and stays there. What adjustments can people make in the LR to reduce consumption of gas?
OTHER ELASTICITIES
We can calculate other elasticities besides just price elasticity, such as Income Elasticity and Cross-Price Elasticity.
Income (Y) Elasticity:
EY = % Qd = D Q / Q
% Y D Y / Y
Income elasticity measures the percentage change in Qd from a percentage change in Income, ceteris paribus. See p. 93 for estimates of Price Elasticity and Income Elasticity.
CROSS-PRICE ELASTICITY
Measures the change in sales (D Qx) from a change in the price (D Py) of a related good (substitute or complement).
ECP = % Qx / % Py
where goods X and Y are either substitutes or complements. How much does the quantity demand for Good X change when the price of Good Y changes?
Substitutes: If X and Y are substitutes (rivals, competitors), and the Price of Y goes up by 10%, what will happen to Qd for X?
Complements: If X and Y are complements (computer software, hardware), and the Price of Y goes up, what will happen to Qd for X?
Therefore, when cross-price elasticity is POS, the related goods are _____________.
When cross-price elasticity is NEG, the related goods are _____________.
PRICE ELASTICITY AND PREDICTION
The elasticity measure (Ep) answers the question: For a 1% rise (fall) in Price, what % will Qd fall (rise)?
For example, for gasoline Ep = -.32, which means that for a 1% (10%) rise in price, Qd will fall by .32% (3.2%).
What if the %DP is NOT exactly 1%? Then we use the formula:
%Qd = Ep (%P)
For example, suppose that gasoline prices increase from $1 to $1.20, a +20% increase. How would gallons purchased (Qd) be affected?
%Qd = (-.32) (+20%) = -6.2%
Therefore, gasoline demand is fairly inelastic (unresponsive to price), since a +20% increase in price led to only a -6.2% reduction in gallons purchased.
Ep = -2.1 for luxury cars, so what would be the effect of a 5% price increase?
%Qd = (-2.1) (5%) = -10.5%
Therefore, luxury car demand is elastic (price sensitive), since a 5% price increase led to a -10.5% reduction in sales.
RULES RESTATED:
1. When %ΔQd > %DP, then Ep > 1 and demand is ELASTIC.
2. When %DQd < %DP, then Ep < 1 and demand is INELASTIC.
We can also analyze the effect of more than one variable changing at the same time:
For nonbusiness air travel, Ep = -.38 and Ey = 1.8. What if fares increase by 8% and income increases by 5%?
%Qd = (-.38) (+8%) + (1.8) (+5%) = -3.04% + 9% = +6.04%
DEMAND ANALYSIS AND OPTIMAL PRICING
Price elasticity (Ep) and Total Revenue (TR):
If we know Ep for a good (elastic or inelastic), we also know the predicted relationship between prices changes (ΔP) and changes in TR (ΔTR).
1. Demand is Elastic: %ΔQd > %ΔP. For example, P goes up by 10%, Qd goes down by 20% and Ep= -2.
TR = P x Qd
%ΔTR = %ΔP x %ΔQd
%ΔTR = (+10%) + (-20%)
TR FALLS (Logic: -20% > +10%, so the net effect is negative)
When demand is elastic, price increases (decreases) will lead to lower (higher) TR.
Price and TR go in opposite directions when demand is elastic.
Example:
TR = $10 x 100 = $1000
Price goes up by 10% and Qd goes down by 20%:
TR = $11 x 80 = $880 (TR FALLS WHEN PRICE RISES, IF DEMAND IS ELASTIC)
2. Demand is Inelastic: %ΔQd < %ΔP. For example, P goes up by 10%, Qd goes down by 5%,
Ep = -.5
TR = (+10%) + (-5%) =
TR RISES (+10% > -5%, so the net effect is positive)
Example (Price rises by 10%, Qd falls by 5%):
TR = $10 x 100 = $1000
TR = $11 x 95 = $1045 (TR RISES WHEN PRICE RISES, IF DEMAND IS INELASTIC)
When demand is inelastic, price increases (decreases) will lead to higher (lower) TR.
Price and TR go in the SAME direction when demand is inelastic.
SUMMARY:
TO increase SLS when demand is elastic, firm should ___________ P.
TO increase SLS when demand in inelastic, firm should ___________ P.
MAXIMIZING REVENUE
When a firm's MC or VC is 0 (or almost 0), then it faces a "pure selling problem," where Maximizing TR might be appropriate.
Logic: Profit Max occurs when MR = MC. If MC = 0, then the rule becomes set MR = 0, and find the level of output (Q) that maximizes SLS.
Examples of when MC might be close to 0, see page 97.
Example: Sports team with 36,000 seat stadium on page 98. Solve for MR, set = 0 to find Q*:
PRICE DISCRIMINATION
We have so far assumed that firms charge a single price (P*) to all customers. A common alternative pricing strategy is Price Discrimination, where the firm charges different prices to different buyers for the exact same product, good or service, even when the cost of serving different customers is the same (e.g. airline seats).
3 conditions for Price Discrimination:
1. Firms must identify two (or more) market segments with different elasticities of demand, e.g. Group A with elastic demand and Group B with inelastic demand. Group A is charged a _________ price and Group B is charged a ____________ price. Firm charges each group the highest possible price, based on elasticity.
2. Firm must be able to separate/segment the two groups and prevent re-sale. For example, there was a chemical called methyl methacrylate produced by the Rohm and Hass Company that was used in both dentistry and industrial production. There were very few substitutes for this product in dentistry, but many for industrial uses. Who paid a higher price? Why kind of resale resulted? What could Rohm and Hass do to prevent resale??
3. Firm must be able to minimize resentment! Apartment lease example ($600/mo for 11 months = $550 for 12 months = $6600/year). Why advertise $600/month for a year lease with one-month free, instead of advertising at $550/month, when they both generate $6600 per year?
Examples of Price Discrimination:
Disneyworld in FL ($60 vs. $95 for one-day pass)
Airlines
Doctors, lawyers
Tuition (perfect price discrimination?)
Books
Coupons (about 25% of consumers use coupons. For cat food, elasticity = 1.13 for coupon users, .50 for non-coupon users)
Weekend discounts
Matinee Discounts
Lunch vs. Dinner
Full Price vs. Sale Price
Vehicles (perfect price discrimination?)
Telephone service
Third-degree Price Discrimination: Identifying two or more markets with different elasticities, charging two or more prices.
A firm faces different demand for its vehicles in two different markets, domestic and foreign. In the home (domestic) market, it faces little competition, in the foreign market, it faces stiff competition from local and other foreign manufacturers. Demand at home will be more inelastic and foreign demand will be elastic, and the firm should probably charge a __________ price domestically and a __________ price in the foreign market.
Demand for domestic market: PH = 30,000 - 50 QH
Demand for foreign market: PF = 25,000 - 70 QF
Production takes place at a single domestic factory, and MCH = $10,000. Shipping to the foreign market costs $1000, so MCF = $11,000.
TRH =
MRH =
set MR = MC for home market, solve for P* and Q*
TRF =
MRF =
set MR = MC for home market, solve of P* and Q*
Conclusion: Firm should charge $20,000 in the domestic market and $18,000 in the foreign market, even though the MC is higher in the foreign market.
FORMS OF PRICE DISCRIMINATION
Perfect Price Discrimination: If the firm can identify 3 groups (A, B, C) and charge 3 different prices, they will make even more profit. With 4 groups, 5 groups, etc., and 4 prices, 5 prices, etc., they will make even more money. To MAX Profits, the ideal is Perfect Price Discrimination (or first-degree), where every customer pays a unique price, based on the maximum price they are willing and able to afford. Perfect price discrimination is the limiting (extreme) case of price discrimination.
Logic: Suppose first that everybody pays the same single market price, P = $10, which is determined by the market demand curve. Assume that VC or MC are low, almost 0. The market demand curve is the summary of thousands of consumers, many of who are willing to pay more than $10 and many willing to pay less. If I can engage in perfect price discrimination, I can charge some existing customers more than $10, some people $10, and I can bring some new customers into the market by charging a P < $10. I can then generate more revenue and more profit.
Tuition Example: Assume that: a) demand for UM-Flint (is P = 6,000 - Q, and b) there is significant excess capacity (classes are not full), and c) MC = 0. Under these conditions, UM-Flint should MAX TR:
TR =
MR =
set MR = 0, solve for Q*:
TR =
Now assume that UM-Flint can engage in perfect price discrimination, and charge every student a unique price based on their willingness and ability to pay. What advantage does UM-F have? UM-Flint could set tuition at $6000 and then engage in perfect price discrimination and accommodate every student on the demand curve, by offering scholarships in various amounts to every student. In effect, they would be charging tuition of between $1-$6,000, setting a unique price for each student with financial aid. The scholarship would equal the difference between $6000 and the maximum each student is willing and able to pay.
Result: UM-F now generates $18m in TR instead of $9m, they have doubled TR by engaging in Price Discrimination.
CASE STUDY: AIRLINE TICKET PRICING REVISTED
Market Demand for airline tickets: Qd = 580 - 2P. The current, single price is $240 and Q = 100 seats per plane, out of 180 maximum seats (56% capacity). TR = $24,000 per flight. Assume that MC = 0, so airline faces a "pure selling problem," and wants to MAX TR to MAX PROFITS. Solving for the inverse demand equation:
P = 290 - .5 Qd
TR =
MR =
Q* =
Q* exceeds the MAX number of seats (180), and even at Q=180, MR is still positive (MR = $110). Lacking extra seats (and without adding more flights), the best the airline can do is sell all seats, Q*=180 and P*= __________. With a price cut of $40, the airline can increase TR to $36,000 (180 x $200).
Suppose now that the airline wants to use price discrimination and charge business travelers a higher fare, and leisure travelers a lower fare, based on elasticity of demand.
Business: QB = 330 - PB or PB = 330 - QB and MRB = 330 - 2QB
Leisure: QT = 250 - PT or PT = 250 - QT and MRT = 250 - 2QT
To find the MAX TR, we set MRB = MRT. Why? Using Marginal Analysis, we know that the MR from the last (marginal) business traveler should equal the MR from the last (marginal) leisure traveler. Suppose the plane is full and the MRB > MRT, ($210 > $190) the airline can increase revenue by selling one less leisure ticket and one more business-class ticket. Anytime MR is greater for one segment, the airline should transfer seats from the high-MR segment to the low-MR segment, and increase TR. TR will be maximized only when MRB = MRT.
Setting MRB = MRT.
330 - 2 QB = 250 - 2 QT
QB = 40 + QT or QB - QT = 40
The firm should sell 40 more tickets to business travelers compared to leisure travelers. We also know that plane capacity is:
QB + QT = 180
Substituting 40 + QT in the above equation for QB and solving for QB, we know that:
QB = 110 and QT = 70
Using the demand equations, PB = $220 and PT = $180 and we also know that:
TR = $36,800 and MRB = MRT = $110.
By going from a single-price to a two-price strategy, they gain $800 in TR for every flight, with two flights per day that generates $584,000 additional TR and additional profits every year. If they go from two-price to three-price to four-price, etc., they could generate even more TR and profit.
INTERDEPENDENT DEMAND (see Appendix, page 131)
Most firms produce multiple products that have interdependent demand relationships, because they are related goods (substitutes or complements), i.e. there is either competition or complementarities.
Examples: GM offers dozens of cars, which are substitutes. They also offer financing through GMAC, which is a complement. Therefore, the demand for a Chevys is interdependent with the demand for Pontiacs and Oldsmobiles and Buicks. Demand for passenger cars is interdependent with demand for SUVs and trucks. Demand for GM cars is also interdependent with the demand for GMAC financing, and vice-versa. Low interest rates, more car sales. Attractive rebate program, more auto loans.
QB = f (PB and PA), where a firm produces both goods A and B. (Sign on PA is pos (neg) when A and B are _________/_________).
Suppose: PA = 280 - 2 QA and PB = 180 - QB - 2 QA
This implies that demand for A is independent of B, but that QB = 180 - PB - 2 QA , which implies that increased sales of A will negatively affect sales of B (the coefficient on QA in the equation for the demand for B is negative). MCA = $80 and MCB = $40. If we ignore B and just MAX profits for A:
MRA = 280 - 4Q = $80 (MC)
Q* = 50
P* = $180
However, if we take into account the interdependent demand, we want to maximize profits for both A and B. TR = TRA + TRB .... Ignoring the math, we end up with:
P*A = $220 and Q*A = 30
P*B = $80 and Q*B = 40
POINT: Taking product B into account, the firm should produce fewer units of A (30 and not 50), and charge a higher price ($220 and not $180). Illustrates the potential conflict between two products, two divisions, within a corporation.
