Managerial Economics BEPP 6120 PDF

One minute warning 60 50 40 30 20 10 9 8 7 6 5 4 3 2 1 1  Reminders & Announcements All Office Hours and Recitations are now underway. – Times and rooms/Zoom links posted on Canvas. My Office...

One minute warning 60 50 40 30 20 10 9 8 7 6 5 4 3 2 1 1  Reminders & Announcements All Office Hours and Recitations are now underway. – Times and rooms/Zoom links posted on Canvas. My Office Hours: Wednesday 2:50pm-3:50pm (Dinan 332) First set of Practice Questions are due this week. – Covers Lectures 1 & 2, due Friday night at 11:59pm. 2 MANAGERIAL ECONOMICS BEPP 6120 Differentiated Products: Choice and Demand  Oligopoly Undifferentiated products Consumers place the same value on each firm’s product. One market price in equilibrium. Differentiated products Consumers place different values on the firms’ products. Different firms can have different prices. 4  OUTLINE Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems  Reservation values revisited What mattered was the consumer’s reservation value, 𝑣, and the price, 𝑝. In BEPP 6110, we motivated Reservation price demand by thinking about a If 𝑣 > 𝑝, the consumer buys. consumer who either will or If 𝑣 < 𝑝, the consumer doesn’t buy. won’t purchase one unit. If 𝑣 = 𝑝, the consumer is indifferent between buying and not buying. We need a new model to deal with more complicated situations where the consumer is deciding not just whether to buy, but what to buy. This model will have two parts. 6  Relevant options In BEPP 6110, our main model had Now, let’s consider a consumer that two options: faces more options: Buy one unit at some price 𝑝. Buy one unit from Firm A at price 𝑝". Don’t buy any at all. Buy one unit from Firm B at price 𝑝#. Don’t buy at all. Say a consumer is considering whether to buy a basic cell plan from either Verizon or AT&T. The options are then Buy from Verizon at price 𝑝!. Buy from AT&T at price 𝑝". Don’t buy a cell plan at all. Once we have the options, we need to know how the consumer decides which to choose. 7  Valuations Each consumer has a valuation, 𝑣$ , for each purchase option, 𝑖. She chooses the option that maximizes consumer surplus (i.e., 𝑣! − 𝑝! ). CS of the non-purchase option (i.e., “Don’t Buy”) is zero. If more than one choice maximizes CS, the consumer is indifferent between all CS-maximizing options. Consider a version of the Verizon/AT&T example 𝑝! = $45, 𝑣! = $55, 𝐶𝑆! = 𝑣! − 𝑝! = $10, The consumer 𝑝" = $40, 𝑣" = $45. 𝐶𝑆" = 𝑣" − 𝑝" = $5. chooses Verizon. What if instead 𝑝" = $50 and 𝑝! = $60? 8  OUTLINE Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems  Valuation Space With the BEPP 6110 model, we made an Consumer 4 ordered bar chart of everyone’s reservation Valuation for Verizon (𝒗𝑽 ) value to get demand. Consumer 2 This becomes more complicated when consumers have valuations for multiple goods. Consumer 1 Now, we will “order” them by representing Consumer 3 each consumer as a point on a graph. Valuation for AT&T (𝒗𝑨 ) 10  The “Swarm” of Consumers With the BEPP 6110 model, we made an ordered bar chart of everyone’s reservation Valuation for Verizon (𝒗𝑽 ) value to get demand. This becomes more complicated when consumers have valuations for multiple goods. Now, we will “order” them by representing each consumer as a point on a graph. Valuation for AT&T (𝒗𝑨 ) 11  Different Market Types in Valuation Space What kind of market is this? Valuation for Verizon (𝒗𝑽 ) Valuation for AT&T (𝒗𝑨 ) 12  Different Market Types in Valuation Space What kind of market is this? Valuation for Verizon (𝒗𝑽 ) Valuation for AT&T (𝒗𝑨 ) 13  Different Market Types in Valuation Space What kind of market is this? Valuation for Verizon (𝒗𝑽 ) Valuation for AT&T (𝒗𝑨 ) 14  Different Market Types in Valuation Space What kind of market is this? Valuation for Verizon (𝒗𝑽 ) Valuation for AT&T (𝒗𝑨 ) 15  Different Market Types in Valuation Space What kind of market is this? Valuation for Verizon (𝒗𝑽 ) Valuation for AT&T (𝒗𝑨 ) 16  Starlight Candy Service GOOD ONE: Everyone gets GOOD TWO: Everyone gets a peppermint starlight. a licorice starlight. What do your valuations look like? 17  OUTLINE Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems  Where Do Consumers Buy Nothing? 𝑝" Who buys nothing? Valuation for Verizon (𝒗𝑽 ) Consumers who both… Prefer Nothing to AT&T 𝑣" − 𝑝" ≤ 0 𝑣" ≤ 𝑝" 𝑝# Prefer Nothing to Verizon 𝑣# − 𝑝# ≤ 0 𝑣# ≤ 𝑝# Valuation for AT&T (𝒗𝑨 ) 19  Where Do Consumers Buy From Verizon? 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Consumers who both… Prefer Verizon to Nothing 𝑣# − 𝑝# ≥ 0 𝑣# ≥ 𝑝# 𝑝# Prefer Verizon to AT&T 𝑣# − 𝑝# ≥ 𝑣" − 𝑝" 𝑣# ≥ 𝑣" + 𝑝# − 𝑝" The boundary …with of this region slope 1… is a line… Valuation for AT&T (𝒗𝑨 ) …that runs through where the price lines cross. 20  Where Do Consumers Buy From AT&T? 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? Consumers who both… Prefer AT&T to Nothing 𝑣" − 𝑝" ≥ 0 𝑝# 𝑣" ≥ 𝑝" Prefer AT&T to Verizon 𝑣# − 𝑝# ≤ 𝑣" − 𝑝" 𝑣# ≤ 𝑣" + 𝑝# − 𝑝" Valuation for AT&T (𝒗𝑨 ) 21  A Map of Consumer Purchasing Decisions 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Valuation for Verizon (𝒗𝑽 ) Who buys nothing? Who buys Verizon? 𝑝# Who buys AT&T? Valuation for AT&T (𝒗𝑨 ) 22  Starlight Candy Service GOOD ONE: Everyone gets GOOD TWO: Everyone gets a peppermint starlight. a licorice starlight. Who buys what at given prices? 23  OUTLINE Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems  Building Demand From Consumer Valuations 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? How do I get the quantity demanded for Verizon at 𝑝# these prices? Count up the consumer dots in the blue region! Verizon’s demand is just the summary of this procedure for any combination of prices. Valuation for AT&T (𝒗𝑨 ) Denote it by 𝑄! 𝑝" , 𝑝!. 25  Properties of Imperfect Substitutes Demand 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? 𝑄! 𝑝" , 𝑝! is… 𝑝# Valuation for AT&T (𝒗𝑨 ) 26  Properties of Imperfect Substitutes Demand 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? 𝑄! 𝑝" , 𝑝! is… 𝑝# …decreasing in its own price, and… …increasing in its substitute’s price. Valuation for AT&T (𝒗𝑨 ) 27  Properties of Imperfect Substitutes Demand 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? 𝑄! 𝑝" , 𝑝! is… 𝑝# …decreasing in its own price, and… …increasing in its substitute’s price. Obviously, the same goes for AT&T’s demand, which we denote by 𝑄" 𝑝" , 𝑝!. Valuation for AT&T (𝒗𝑨 ) 28  Starlight Candy Service GOOD ONE: Everyone gets GOOD TWO: Everyone gets a peppermint starlight. a licorice starlight. What does demand for the two goods look like? 29  OUTLINE Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems  Linearized Demand Systems In MGEC 611, one-good demand functions were always linear, that is, of the form 𝑄 𝑝 = 𝑘 − 𝑎 𝑝. In MGEC 612, two-good demand functions will also be linear, that is, of the form 𝑄! 𝑝" , 𝑝! = 𝑘! − 𝑎! 𝑝! + 𝑏 𝑝" , 𝑄" 𝑝" , 𝑝! = 𝑘" − 𝑎" 𝑝" + 𝑏 𝑝!. Let’s talk a bit about where these linear demands come from, both in the old MGEC 611 context and in the new MGEC 612 context. 31 General One-Good Demand Functions Valuations for iPhone 13 valuation Normally distributed: Number of consumers: 1500 𝜇 = $800, in its substitute’s …increasing 𝑁 = 75price. 𝜎 = $300. 1000 500 0 10 20 30 40 50 60 70 consumer number 32 General One-Good Demand Functions Valuations for iPhone 13 valuation Normally distributed: Number of consumers: 1500 𝜇 = $800, in its substitute’s …increasing 𝑁 = 75price. 𝜎 = $300. 1000 500 0 10 20 30 40 50 60 70 consumer number 33 General One-Good Demand Functions Valuations for iPhone 13 valuation Normally distributed: Number of consumers: 1500 𝜇 = $800, in its substitute’s …increasing 𝑁 = 75price. 𝜎 = $300. 1000 500 0 10 20 30 40 50 60 70 consumer number 34 General One-Good Demand Functions Valuations for iPhone 13 valuation Normally distributed: Number of consumers: 1500 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 225 𝜎 = $300. 1000 500 0 50 100 150 200 consumer number 35 General One-Good Demand Functions Valuations for iPhone 13 valuation Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. consumer number 36 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 37 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 38 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 39 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 40 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 41 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. quantity 𝑄 𝑝 price 42 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. quantity 𝑄 𝑝 price 43 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. quantity 𝑄 𝑝 price 44 General One-Good Demand Functions Valuations for iPhone 13 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 15 000 𝑞! = 11,250 10 000 5000 500 1000 1500 𝑝! = $800 price 45 Linearizing One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 15 000 𝑞! = 11,250 10 000 5000 500 1000 1500 𝑝! = $800 price 46 Linearizing One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 15 000 𝑞! = 11,250 10 000 5000 500 1000 1500 𝑝! = $800 price 47 Linearizing One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ ( 𝑝 =𝑞 −𝑎 𝑝−𝑝 ( Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 15 000 𝑞! = 11,250 10 000 5000 500 1000 1500 𝑝! = $800 price 48 Linearizing One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 = 11,250 − 𝑎 𝑝 − 800 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 15 000 𝑞! = 11,250 10 000 5000 500 1000 1500 𝑝! = $800 price 49 Linearizing One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 = 11,250 − 𝑎 𝑝 − 800 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝑄 𝑝 𝜎 = $300. 20 000 So, the slope, 𝑎, is −31. 15 000 𝑞! = 11,250 10 000 …then, 31 fewer consumers will buy. If I increase the price by $1… (i.e., 31 consumers have valuations (i.e., set the “run” to 1…) 5000 between $800 and $801) (i.e., the “rise” is −31.) 500 1000 1500 𝑝! = $800 price 50 Linearized One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 = 11,250 − 31 𝑝 − 800 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 20 000 15 000 10 000 5000 500 1000 1500 price 51 Linearized One-Good Demand Functions Valuations for iPhone 13 𝑄ℓ 𝑝 = 36,050 − 31 𝑝 Normally distributed: Number of consumers: quantity 𝜇 = $800, in its substitute’s …increasing price. 𝑁 = 22,500 𝜎 = $300. 20 000 15 000 10 000 5000 500 1000 1500 price 52  Do firms really do this? We used to say this is a good model to have in your head, even if most firms discuss these things mostly at an intuitive level. But things are changing fast: PhD economists do this at Amazon, Uber, Instacart, Microsoft, etc... 53 53 Do firms really do this? 54  Linearizing Two-Good Demand Systems 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? As with one-good demand, let’s linearize about two reference prices, 𝑝!" and 𝑝#". 𝑝# = 𝑝#2 We express the linearized, two-good demand system in terms of deviations from the reference prices: 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Here, 𝑞#" , 𝑎# , and 𝑏# characterize how Verizon’s quantity demanded changes with the prices. Valuation for AT&T (𝒗𝑨 ) Similarly 𝑞!" , 𝑎! , and 𝑏! describe AT&T’s demand. 55  Reference Quantities 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? Clearly, 𝑞#2 and 𝑞"2 are just the quantities 𝑝# = 𝑝#2 demanded at the reference prices. 𝑄! 𝑝#$ , 𝑝!$ 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. 𝑄# 𝑝#$ , 𝑝!$ Valuation for AT&T (𝒗𝑨 ) We call 𝑞#" and 𝑞!" the reference quantities. 56  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Valuation for AT&T (𝒗𝑨 ) 57  Own- and Cross-Price Responses $1 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝"2 𝑝" Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Valuation for AT&T (𝒗𝑨 ) 58  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Valuation for AT&T (𝒗𝑨 ) 59  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝#2 the graph... $1 𝑝# What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Valuation for AT&T (𝒗𝑨 ) 60  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. Valuation for AT&T (𝒗𝑨 ) 61  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. So… Valuation for AT&T (𝒗𝑨 ) 𝑏" = 𝑏! = 𝑏 62  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. So… Valuation for AT&T (𝒗𝑨 ) 𝑎! ≥ 𝑏 𝑎" ≥ 𝑏 63  Own- and Cross-Price Responses 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? It turns out that the 𝑎 and 𝑏 coefficients are also easily read from 𝑝# = 𝑝#2 the graph... What if AT&T raises its price $1 above 𝑝#$ ? What if Verizon drops its price $1 below 𝑝!$ ? 𝑄!ℓ 𝑝# , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝# − 𝑝#$ , 𝑄#ℓ 𝑝# , 𝑝! = 𝑞#$ − 𝑎# 𝑝# − 𝑝#$ + 𝑏# 𝑝! − 𝑝!$. So… (in English) Valuation for AT&T (𝒗𝑨 ) Cross-price responses are the same for the two goods. Own-price responses are larger than cross-price responses. How much larger depends on how many potential customers are on the fence between buying the good and buying nothing. 64  Marginal Consumers 𝑣# = 𝑣" + 𝑝# − 𝑝" 𝑝" = 𝑝"2 Who buys nothing? Who buys Verizon? Valuation for Verizon (𝒗𝑽 ) Who buys AT&T? h itc sw ALSO: When we think about small 𝑝# = 𝑝#2 changes in price (or valuation), what matters are consumers who change opt-out/opt-in purchasing behavior in response. (Verizon) opt-out/ opt-in We call such consumers (AT&T) marginal. Valuation for AT&T (𝒗𝑨 ) 65  Starlight Candy Service GOOD ONE: Everyone gets GOOD TWO: Everyone gets a peppermint starlight. a licorice starlight. What do the linearized demands for the two goods look like? 66  Simplifying the Demand System As in MGEC 6110, we will often dispense with information about the reference prices to simplify the demand system. 𝑄 ℓ 𝑝 = 𝑞 $ − 𝑎 𝑝 − 𝑝$ 𝑄ℓ 𝑝 = 11,250 − 31 𝑝 − 800 𝑄 ℓ 𝑝 = 𝑞 $ + 𝑎 𝑝$ − 𝑎 𝑝 𝑄ℓ 𝑝 = 36,050 − 31 𝑝 67 Simplifying the Demand System As in MGEC 6110, we will often dispense with information about the reference prices to simplify the demand system. 𝑄!ℓ 𝑝" , 𝑝! = 𝑞!$ − 𝑎! 𝑝! − 𝑝!$ + 𝑏! 𝑝" − 𝑝"$ , 𝑄"ℓ 𝑝" , 𝑝! = 𝑞"$ − 𝑎" 𝑝" − 𝑝"$ + 𝑏" 𝑝! − 𝑝!$. 𝑄!ℓ 𝑝" , 𝑝! = 𝑞!$ + 𝑎! 𝑝!$ − 𝑏 𝑝"$ − 𝑎! 𝑝! + 𝑏 𝑝" , 𝑄"ℓ 𝑝" , 𝑝! = 𝑞"$ + 𝑎" 𝑝"$ − 𝑏 𝑝!$ − 𝑎" 𝑝" + 𝑏 𝑝!. 𝑄!ℓ 𝑝" , 𝑝! = 𝑘! − 𝑎! 𝑝! + 𝑏 𝑝" , 𝑄"ℓ 𝑝" , 𝑝! = 𝑘" − 𝑎" 𝑝" + 𝑏 𝑝!. 68  Starlight Candy Service GOOD ONE: Everyone gets GOOD TWO: Everyone gets a peppermint starlight. a licorice starlight. What do the simplified linearized demands for the two goods look like? 69  Differentiated Products: Choice and Demand SUMMARY Choosing Between Two (really three!) Options Valuation Space Dividing Valuation Space by Purchasing Behavior General and Linearized Demand Systems