Consumer Demand Analysis

Consumer Demand Analysis
FIN 30210: Managerial Economics Consumer Demand Analysis

Here’s where we stand… Product Markets Production Decisions
Factor Markets Businesses take factor prices as given Factor Usage/Prices Determine Production Costs Demand determines markup over costs

Consumer Preferences Demand Curves/Functions
The more information a business has about the customer it faces, the better it’s decisions can be with regards to pricing Elasticities Elasticities provide the least amount of information, but they do tell you something about how the consumer you face responds to various events Demand Curves/Functions Demand curves are an incomplete picture of the consumer. You know what decisions were made by consumers, but not the why Consumer Preferences If you know consumer preferences, you have the complete picture. You know what decisions consumers will make and why they make them

Price Elasticity With high elasticity goods, small price changes are associated with large quantity changes With low elasticity goods, large price changes are associated with small quantity changes Examples: Kit Kat Chocolate Bar, Porsche 911, Sunoco Gas Examples: Textbooks, Cigarettes, Gasoline

Cross Price Elasticity
Income Elasticity Cross Price Elasticity Income elasticity will be a positive number for normal goods Cross price elasticity will be a positive number for substitutes Cross price elasticity will be a negative number for compliments

Could I increase revenues by altering my price?
Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. You don’t know the demand curve you face, but you know the elasticity $250 $50,000 Could I increase revenues by altering my price? 200

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Let’s begin with an expression for total revenues I can rewrite this in percentage change terms $250 $50,000 Now, substitute in elasticity 200 A little rearranging

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Plugging in my known elasticity $250 $50,000 This tells me that if I lower my price by 10%, my revenues will go up by 40% 200 $250 -10% $225 $67,500 So, why didn’t I get 40%? 200 300 10(-5)=50%

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. As price falls, demand generally becomes more inelastic When the elasticity is equal to minus one, the percentage change in revenues is zero…a maximum! $250 $225 $150 $100 200 300 600 800 $150 $90,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Start with overall percentage change in quantity is affected by price changes and income changes Suppose that a recession causes a 20% drop in income. How much would we have to lower our price if we wanted to keep sales constant? We want the quantity change to be zero Plug in what we know and solve $150 $90,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Suppose that a recession causes a 20% drop in income. How much would we have to lower our price if we wanted to keep sales constant? $150 $140 $84,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Now, suppose that you actually have the demand curve Median Income in thousands Suppose that median income is $40,000 $250 $50,000 We can calculate the elasticity at any point 200

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. We can use the demand curve to find the revenue maximizing price Plug in the demand curve for Q simplify We are maximizing, so take the derivative with respect to p and set equal to zero $150 $90,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Note: We can do this using quantities as well Plug in the demand curve for P simplify We are maximizing, so take the derivative with respect to Q and set equal to zero $150 $90,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Given the demand curve I could also find the price where the elasticity equals 1. Plug in the demand curve for Q, and the slope coefficient Set the elasticity equal to -1 and solve $150 $90,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Suppose that a recession causes a 20% drop in income. How much would we have to lower our price if we wanted to keep sales constant? Income was originally $40k, a 20% drop would be $32k Simplify and set quantity equal to 600 $140 Solve for price $84,000 600

Suppose that you work for Delta and that you are setting the price for the shuttle from JFK to Boston. Demand with income equal to $32k Suppose that a recession causes a 20% drop in income. How much would we have to lower our price if we wanted to maximize revenues? Take the derivative and set is equal to zero $145 Solve for price $84,100 580

Demand Curves vs. Elasticities
If I do not know the demand curve, I need two points to calculate an elasticity $250 $225 200 240 One minor problem…

I get a different answer if I change the direction that I am moving. $250 $225 200 240 We can fix this…

Arc Elasticity calculates the percentage changes by taking the change divided by the midpoint Midpoint p = $237.50 Q = 220 $250 $225 200 240

If I have the demand curve, I can calculate the point elasticities analytically Income Elasticity Price Elasticity Suppose that my demand curve is not linear… Derivative of demand with respect to price Derivative of demand with respect to income

Now about this one…

There is an easier way to do this… Take the natural log of both sides A little mathematical trick… This just says that the difference in logs is a percentage change

Here’s another one… Take the natural log of both sides Log linear demand curves have constant elasticities!

Now, let’s complicate this pricing problem
Now, let’s complicate this pricing problem. Suppose that you face two types of consumers. For any price, the elasticity for business travelers is lower Business Travelers Recreational Travelers $400 $200 $150 $150 $75,000 $15,000 500 100 Total Profits = $90,000

Now, let’s complicate this pricing problem
Now, let’s complicate this pricing problem. Suppose that you face two types of consumers. Recreational Travelers Business Travelers If we can identify the different customers and prevent resale, we could charge different fares $400 $200 $200 $80,000 $100 $20,000 400 200 Total Profits = $100,000

This is “the Truth”. Two types of individuals making purchasing decisions. Individual decisions added up across all individuals create an aggregate demand curve. $400 At a price above $200, recreational travelers don’t fly. The only demand is coming from business travelers. At a price below $200, we now have two types of demanders flying. We need too add up across the two groups for every price $300 (Business) + (Recreational) $200 (Total) $100 200 600 800

If you do a linear estimation, what you end up with something like this…not really what we want
$400 My estimated demand curve will end up being an “average” of the two customer types $200 (Actual) 400 (Estimated)

However, all is not lost…we could use a dummy variable
$400 $200 Recreational Business 400 YES! We can do this!

Here’s two different customers. …
Here’s two different customers.…..different intercepts AND different slopes Business Travelers Recreational Travelers $200 $600 $150 $150 $22,500 $67,500 450 150 Total Profits = $90,000

Now, if we charge different prices….
Business Recreational $200 $600 $300 $90,000 $100 $30,000 300 300 Total Profits = $120,000

Again, This is “the Truth”
Again, This is “the Truth”. Two types of individuals making purchasing decisions. Individual decisions added up across all individuals create an aggregate demand curve. $600 At a price above $200, recreational travelers don’t fly. The only demand is coming from business travelers. At a price above $200, recreational travelers don’t fly. The only demand is coming from business travelers. At a price below $200, we now have two types of demanders flying. We need too add up across the two groups for every price (Business) $300 + + (Recreational) (Total) $200 $100 300 500 600 800

Again, with a linear estimation, what you end up with something like this…missing the underlying structure $600 $200 (Actual) 600 (Estimated)

Here, adding a dummy variable doesn’t do the trick either…
$600 $200 600

However, we could add a dummy variable that interacts with price to get a different slope!
$600 $200 Now we got it! 600

Now, how about this pricing problem
HP - Pavilion Touch-Screen $499.99 Features Windows 10 operating system 13.3” multi-touch screen 6th Gen Intel Core i3-6100U mobile processor 6GB system memory 500GB Hard Drive Intel HD Graphics 520 2 USB 3.0 ports HD Webcam with two microphones Multimedia software package included Weighs 3.66 Pounds Overall Customer Rating: 4.5 (75 Reviews)

How many customer types does HP face?
Business Professionals Gamers Small Business Owners Students Hackers

The sum total of there decisions is given by a market demand curve
Individual consumers have preferences over a variety of goods…they have limited incomes and face market prices. Consumers make choices on what to buy There is simply too much heterogeneity and complexity here to use dummy variables!! We need to dig deeper!

VS Which would you choose?
Suppose you walk into Best Buy and are confronted with the following choice VS 70” – LED p – Ultra HD TV $2,299.99 70” – LED p – Ultra HD TV $1,999.99 Which would you choose?

OR The choice you make tells us something about your preferences….
70” – LED p – Ultra HD TV $2,299.99 70” – LED p – Ultra HD TV $1,999.99 If you selected this TV, we know that: If you selected this TV, we know that: You prefer this TV to the alternative OR You prefer this TV to the alternative You could not afford the alternative

A B C C > B C ? A Now, let’s expand your choices to three $2,299.99
70” – LED p – Ultra HD TV $2,299.99 70” – LED p – Ultra HD TV $1,599.99 70” – LED p – Ultra HD TV $1,999.99 A B C You select C…what do we know? Suppose that you select C at the current prices, we know that you prefer C to B, but we can’t make a definitive statement about your preferences for A C > B C ? A

A B C B > A B ? C Now, how about a different set of prices…
70” – LED p – Ultra HD TV $1,799.99 70” – LED p – Ultra HD TV $1,999.99 70” – LED p – Ultra HD TV $2,299.99 A B C This time I choose B B > A Now, we know that I prefer B to A B ? C

What will I do here? 70” – LED p – Ultra HD TV $1,999.99 70” – LED p – Ultra HD TV $1,999.99 70” – LED p – Ultra HD TV $1,999.99 A B C If I am a rational person, I will choose C…..but why?

C > B B C C > A B > A B A
Chosen Let’s review past choices…. C > B 70” – LED p – Ultra HD TV $1,599.99 70” – LED p – Ultra HD TV $1,999.99 B C C > A Chosen B > A 70” – LED p – Ultra HD TV $1,999.99 70” – LED p – Ultra HD TV $1,799.99 B Rational people should have preferences that display transitivity! A

Transitivity insures that there is always a clear ranking from best to worst of all choices!
> B C is preferred to B > C is preferred to B A

C > A Let’s try another one Pizza $2.00 per slice Beer
Choice A Pizza $2.00 per slice Beer $4.00 per pint Choice B Selected Cost = $10 Choice C Cost = $16 C > A Observation #1 Cost = $14 Option C is preferred to option A

B > C Let’s try another one Pizza $5.00 per slice Selected Beer
Choice A Let’s try another one Pizza $5.00 per slice Beer $2.00 per pint Selected Choice B Cost = $17 Choice C Cost = $16 B > C Observation #2 Option B is preferred to option C Cost = $11

VS VS C > A B > C > A B > C
Again, transitivity gives us a clear preference ranking! Choice A Choice B Choice C VS VS C > A Observation #1: B > C > A Choice B is most preferred, followed by C, followed by A B > C Observation #2:

A utility function is simply a mathematical representation of consumer preferences
B > C > A “Happiness” Is a function of Pizza and Beer Consumed Choice A Choice B Choice C VS VS

Indifference curves are a way to visualize preferences
“Happiness” Is a function of Pizza and Beer Consumed “I am just as happy with 1 pizza and 7 beers as I am with 6 pizzas and 2 beers” Indifference curves represent different combinations of (in this case, pizza and beer, that provide the same amount of utility

Here are my choices…I know what my preference ranking is…we need a utility function that matches my preference ranking B > C > A C B A

Transitivity implies that indifference curves cant cross
Transitivity implies that indifference curves cant cross! This is an absolute must have!! A=B B<C A=C Without transitivity, you don’t get a clear preference ranking! C B Without a clear preference ranking, how are we supposed to make decisions! The real problem here is that there is that I don’t seem to know how to rank choice A A

Some additional properties of consumer preferences….
We assume diminishing marginal utility for all goods…that is, the more you have of any good, the less that good is worth to you at the margin!

Marginal rate of substitution measures the relative value of x. Because of diminishing marginal utility, we know that when x is big (relative to y), its value is low (relative to y)

Diminishing marginal utility means that moderation is always preferred to extremes!

Some properties of consumer preferences….
Without diminishing marginal utility moderation extremes are preferred over moderation!

Decreasing marginal utility vs
Decreasing marginal utility vs. increasing marginal utility and consumer behavior Imagine you are put in a room with a big cake. How much you are willing to pay for the slice of cake is your ‘marginal utility’ Slice Willingness to Pay 1 $1 2 $.90 3 $.80 4 $.70 5 $.60 6 $.50 7 $.40 8 $.30 9 $.20 10 $.10 You will most likely have decreasing marginal utility here

Decreasing marginal utility vs. increasing marginal utility and consumer behavior Imagine you are put in a room with 10 crying babies. How much you are willing to pay to have each baby removed from the room Baby Willingness to Pay 1 $.01 2 $.02 3 $.04 4 $.06 5 $.08 6 $.60 7 $1.20 8 $2.60 9 $5.20 10 $10.20 Here, we most likely have increasing marginal utility

Decreasing marginal utility vs. increasing marginal utility and consumer behavior Now, Imagine, you were given $40 and had to stay in each of these rooms for 10 days. What would your spending pattern look like? Baby Willingness to Pay 1 $.01 2 $.02 3 $.04 4 $.06 5 $.08 6 $.60 7 $1.20 8 $2.60 9 $5.20 10 $10.20 Slice Willingness to Pay 1 $1 2 $.90 3 $.80 4 $.70 5 $.60 6 $.50 7 $.40 8 $.30 9 $.20 10 $.10 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 $4 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 $20 $0 With decreasing marginal utility, you would likely “smooth out” your spending. With increasing marginal utility, you would likely “binge”.

Have you ever binged on Netflix?

Does Netflix take into account increasing marginal utility in their pricing?
DVD and Blue-ray Plans Plan DVD Price Blue-ray Price Discs Out at a Time 1-Disc $8 $10 One 2-Disc $12 $15 Two 3-Disc $16 $20 Three Limited $5 $6 Two Per Month Total Streaming Plans Plan Price # of Screens Resolution Basic $8 1 SD Standard $10 2 HD Premium $12 4 HD + Ultra HD

Can persistent poverty be the result of optimal behavior?
Marginal Utility Marginal Utility of Leisure Charles Karelis George Washington University Why do many very poor people not work? With very low levels of income, the marginal utility of that income should be very high! Marginal Utility of Income Optimal Hours Worked

Can persistent poverty be the result of optimal behavior?
Marginal Utility Marginal Utility of Leisure Charles Karelis George Washington University Marginal Utility of Income Charles Karelis argues that if the marginal utility of income is increasing at low levels of income, it might not be optimal to work! Optimal Hours Worked

Elasticity of substitution measures the curvature of preferences…it’s a measure of how easily x and y can be substituted for one another High Substitutability: Coke and Pepsi A high elasticity of substitution has a MRS (slope) that changes gradually

Elasticity of substitution measures the curvature of preferences…it’s a measure of how easily x and y can be substituted for one another Low Substitutability: Airline Travel and Bus Travel A low elasticity of substitution has a MRS (slope) that changes rapidly

Some special cases…. Perfect Substitutes: 5 one dollar bills vs. one 5 dollar bill Perfect Complements: Right Shoes and Left Shoes

An outline of consumer choice….
Our income and our preferences determine our choices We have preferences over a wide array of goods and services Our spending is limited by our available income

Consumers make decisions to maximize their well being that are also affordable given their income
Note: lambda measures the marginal impact of the constraint. Here, lambda is the marginal utility of income First, write down the lagrangian…. We have two maximization conditions and a constraint Optimality Affordability

If I gave up 1 unit of x, I could use the $4 to buy 2 units of Y
Example: Let’s suppose that the price of X is $4 and the price of Y is $2 and you have $200 to spend. If I gave up 1 unit of x, I could use the $4 to buy 2 units of Y Loss from giving up x Gain from additional y Could this choice be optimal? I’m consuming too much X!

If I gave up 2 units of y, I could use the $4 to buy 1 units of x
Example: Let’s suppose that the price of X is $4 and the price of Y is $2 and you have $200 to spend. If I gave up 2 units of y, I could use the $4 to buy 1 units of x Could this choice be optimal? Loss from giving up y Gain from additional x I’m consuming too much y!

Optimality suggests that I am allocating my income so that the utility per dollar spent is equal across all goods! The demand for x is a function of the price of x, the price of y and income

It’s generally assumed that demand curves slope down…but that is not necessarily the case!

Substitution Effect Income Effect
We can actually decompose a price change into two separate effects…. Substitution Effect As the price of x increases, we re-evaluate our decisions at the margin and substitute out of what has become relatively more expensive and into what has become relatively less expensive 2 Income Effect 1 3 As the price of x increases, the purchasing power of our income declines, which would generally cause us to buy less of everything

In economics, an inferior good is a good that decreases in demand when consumer income rises (or rises in demand when consumer income decreases), unlike normal goods, for which the opposite is observed. Normal goods are those for which consumers' demand increases when their income increases. Ramen Noodles Generic Brands Yugoslavian Cars Fake Meat Generic spam??? Really?? Payday Lending Services Bus Travel They do leave the light on, though

With Inferior goods, as your income falls (rises), you tend to buy more (less)

The goods taken should be inferior goods.
A Giffen good is typically an inferior product that does not have easily available substitutes, as a result of which the income effect dominates the substitution effect. Giffen goods are quite rare, to the extent that there is some debate about their actual existence The goods taken should be inferior goods. There should be no close substitute. The goods should cover substantial percentage of the income of the buyer, but not so much that the buyer can't buy any other normal good. Sir Robert Giffen 1837 –1910 Example: Lets suppose that you have $10/week to feed yourself Ramen Noodles Cost $0.30 apiece 21 Ramen Noodles X $0.30 = $6.30 1 Big Mac X $3.70 = $3.70 Ramen Noodles Cost $0.25 apiece 18 Ramen Noodles X $0.25 = $4.50 1 Big Mac X $3.70 = $3.70 1 Small Fries X $1.80 = $1.80 Price D $10.00 $10.00 .30 .25 Quantity 18 21

With Giffen Goods, as price falls (rises), you tend to buy less (more)

Marginal Rate of Substitution affects the height of the demand curve
X is not very valuable Consumers will only buy x at lower prices X is valuable Consumers will buy x at higher prices

Elasticity of Substitution affects the slope of the demand curve
X is not very substitutable Consumers don’t respond much to price changes X is very substitutable Consumers will respond to price changes

Some special cases… Linear Preferences Perfect Substitutes
Leontif Preferences Perfect Complements

Consider the Cobb-Douglas utility function
Charles Cobb Paul Douglas The tells us that for a fixed relative price, the ratio of x and y chosen is independent of income!

Charles Cobb Paul Douglas So, a 1% increase in the consumption of x relative to y alters they value of x relative to y by 1%

Charles Cobb Paul Douglas First, write down the lagrangian…. We have two minimization conditions and a constraint Set the lambdas equal to each other Solve for lambda

Some messy algebra Expenditure shares of x and y are constant!

Charles Cobb Paul Douglas Utility Function Demand Curves Estimated Demand Curves Price Elasticity of Demand Income Elasticity of Demand Cross Price Elasticity of Demand

It turns out, the Cobb-Douglas utility function is a special case of the more general CES utility function (introduced by Robert Solow) Robert Solow 1924 - Linear Cobb-Douglas Leontief

It turns out, the Cobb-Douglas utility function is a special case of the more general CES utility function (introduced by Robert Solow) Robert Solow 1924 - Utility Function Demand Curves Estimated Demand Curves A Price Index of x and y Price Elasticity of Demand Income Elasticity of Demand Cross Price Elasticity of Demand

CES utility function Demand Curves Robert Solow 1924 - Linear
Cobb-Douglas Leontief Demand Curves

How could we tackle this problem?
Recall the pricing problem faced by HP Features Windows 10 operating system 13.3” multi-touch screen 6th Gen Intel Core i3-6100U mobile processor 6GB system memory 500GB Hard Drive Intel HD Graphics 520 2 USB 3.0 ports HD Webcam with two microphones Multimedia software package included Weighs 3.66 Pounds How could we tackle this problem?

A B C HP might try something like this….
Laptop A Laptop B Laptop C “Everything Else” A B C Features Features Features Features Price Price Price Price Assume, say, three different laptops, with different features, and a composite good representing everything else – each with a price

HP then identifies several consumer types – each with different preferences for the computer features and the other good and different income levels. Maximize Maximize Maximize Subject to Subject to Subject to Each makes their choices to maximize utility subject to an income constraint. The results are decisions for purchases of laptops A, B, and C as well as “everything Else”

Note that we could take the decisions that are made and aggregate them to get market demand curves for A, B, and C Although, these demand curves aren’t really that useful!

More importantly, using this process and available consumer purchasing data, we can determine optimal prices/configurations Laptop A Laptop B Laptop C A B C Features Features Features Assumptions on consumer preferences Optimal Price Optimal Price Optimal Price

Example: Beer Pricing If Budweiser sold beer by the ounce, they might be able to estimate a demand curve for Beer (price per ounce) Demographic dummy variables We would expect this coefficient to be negative because of diminishing marginal utility We would expect this coefficient to be positive (beer is a normal good) Unfortunately, Budweiser doesn’t sell beer by the ounce…they have various packages (Total ounces)

Example: Beer Pricing With all the different packaging configurations, Budweiser has a pricing problem similar to that of HP

A consumer choice analysis would be needed
Consumer Types Income Education Age Gender Package Price Price per oz. Single $2.45 20.4 cents 6-Pack $12.75 17.7 cents 12-Pack $26.50 18.4 cents 24 Pack $40.95 14.2 cents 12 oz. can Attributes Package Price Price per oz. Single (24 oz.) $4.10 17.1 cents 6-Pack $11.95 16.6 cents 12-Pack $21.75 15.1 cents 24 Pack $34.95 11.2 cents Can Bottle Single 6 Pack 12 Pack 24 Pack Keg 12 oz. bottle Package Price Price per oz. 676 oz. $128.55 19.0 cents 1981 oz. $324.95 16.4 cents Price Keg

Consumer Demand Analysis

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