Lecture 2(a) Basics of Demand

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Lecture 2(a) Basics of Demand
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Why Study Demand

• Obvious Reason To help with forecasting
  revenues
• What will happen to sales tax revenues collected
  from the sale of cigarettes if the price goes up
  as a consequence of the Federal Governments
  lawsuit?
• Less Obvious Reason To help understand pricing
  strategies
• Why do some firms make it difficult to buy
  unbundled--e.g., MS wants to sell Office or
  Explorer as a package?

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What Is Involved in Building a Complete Theoryof
Demand?

• A complete theory is based on and begins with a
  theory of individual demand
• And then considers how individual behavior
  aggregate to market behavior.

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The Theory of Individual Demand is Organized by
Conducting the Following Thought Experiment
What Determines How Much of _____ Do You Want to
Buy?

• Taste
• Price of the Good
• Income
• Price of Other Stuff

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Taste

• While may be the most important factor, but it is
  also the factor that is most difficult to model
  and forecast.
• Therefore, the conventional approach in
  microeconomics is to simply accept the consumers
  tastes as given (often pretentiously invoking the
  Latin expression non degustibus disputandemwhich
  I think means, there is no arguing about tastes
  and which I have no idea how to spell.)
• Interestingly, though, a small but brave group of
  economists have tried to formulate an economic
  theory of taste formation. In this class,
  though, well mostly accept the consumer as he or
  she is.

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The Relationship Between Price and Quantity

• When price goes up, it seems very unlikely that a
  consumer will choose to buy more (although can
  you think of exceptions?) and there are good
  reasons to think that higher prices will cause
  consumption to fall .
• (Note this prediction assumes that only price
  changes.)

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This Seems Obvious, but It is Worth Thinking
About Exactly Why People Buy Less When Prices Go
Up

• Most consumers are likely to be faced with income
  constraints and so as the price of something goes
  up, they have less to spend on some goods. This
  is easy to understand, but well give a simple
  example in class.
• Most consumers have preferences over most goods
  that are consistent with diminishing marginal
  utility.

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The relationship between prices of other goods
and demand(How Would My Demand for X Change if
the Price of Y Went Up?)

• Suppose X is a ticket to the opera in Verona,
  Italy and Y is an airplane ticket to italy.
• Suppose X is a ticket to the opera in Verona and
  Y is a ticket to the first round of the Italian
  Idol audition.
• Obviously the relationship depends on the type of
  goods
• X is a Substitute for Y, if an increase in the
  price of Y leads to an increase in the demand for
  X
• X is a Complement for Y, if an increase in the
  price of Y leads to an decrease in the demand for
  X

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The relationship between income and demand

• If I were Bill Gates, how would my life be
  different?
• Id buy more rides on private jets than I do now.
• But Id buy fewer coach tickets than now.
• The relationship between income and demand is
  ambiguous. Thus, we have the following
  definitions
• Normal good Any good such that as income goes
  up, demand goes up (e.g., Mercedes).
• Inferior good Income goes up, demand goes down
  (e.g., 1993 Mercury)

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Another way to make the same points

• What matters to most consumers is relative
  values, such as the price of one good relative to
  the price of another good and relative to the
  income of the consumer

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A Useful Way to Describe Demand Demand Function

• It can be helpful in some circumstances to
  express demand relationships mathematically. The
  most common way this is done is to write out a
  demand function relating the quantity demanded to
  the other relevant variables.
• Recall the Equibase problem where we might have
  assumed that the quantity of track programs
  demand (q) will depend on track attendance (A)
  the price of the program (P) and the price of a
  Daily Racing Form (Pd). Expressed in general
  notation, we would have written
• Q f(A,P,Pd)
• Of course these general expressions might not be
  that helpful, in which case you might decide to
  write down a more specific form of the function,
  such as in the Equibase problem where we assumed
• Q A(Pd-P) and A500, Pd5
• We dont have the time to talk about how one
  might find a specific functional form for a
  specific problem, except to point out that there
  are ways. In particular a number of specific
  statistical and econometric techniques have been
  derived to estimate demand functions.
• Sometimes it is useful to write the demand
  relationship with Price on the left hand side of
  the equation. Of course this is just a different
  way of different way of saying the same thing,
  but to help distinguish them we will refer to the
  first expression (Q on the left hand side by
  itself) as the demand function and the second
  expression as the inverse demand functions.
• When we draw a graph of such relationships it is
  conventional to put the price on the vertical
  axis and quantity on the horizontal axis.
• Some economists (and most textbooks) make a
  fetish out of the distinction between a shift in
  the entire curve (usually caused by a change in
  one of the many factors that influence demand and
  referred to as a change in demand) and movement
  along the demand curve (caused by a change in
  price and referred to as a change in quantity
  demanded.)

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Issues

• Market demand vs individual demand.
• At on level, this is just arithmetic. For
  example, if each of 60 students demand 3 beers at
  a price of 3, market demand will be 180.
• But can you think of some goods where, an
  individuals demand may be influenced by the
  number of others demanding the good?
• Market demand vs firm demand.
• This is something well think a lot more about
  when we get to the part of the course on
  competitive markets, but for now think about why
  this distinction should matter. Also, think
  about why the market demand is probably less
  sensitive to price than an individual firms
  demand.
• What exactly do we mean by a good? That is, a
  good can be distinguished by (among other
  things).
• Geography (beer at the ball park versus beer at
  home)
• Quality (diet beer versus heavy beer)
• Since demand measures a flow (that is, the amount
  demanded over some period of time), what is the
  relevant time.

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From Demand to Revenue

• It is obviously possible to derive total revenue
  from demand simply by multiplying Q by P.
• TRPQ.
• Since this is economics, we of course want
  marginal revenue
• Words MR is the change in TR when Q changes
• For discreet changes MRChange in TR/Change in Q
  (approximate)
• Calculus MR d TR/ dQ (precise)

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• This example is consistent with demand being
  given by
• Q 1300- P or P1300-Q
• Thus
• Total Revenue PQ (1300-Q)Q 1300 Q Q2
• and
• Marginal Revenue dTR/dQ 1300 2Q
• (Remember the numbers for MR derived in the table
  are only an approximation).

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Puzzle Why Does TR Increase and Then Decrease?

• Good News When price falls from to 500 from
  600, you get 100 new passengers. Each of these
  contributes an extra 500 in revenues.
• Bad News In order to get the new customers, you
  had to cut the price of tickets by 100 (from
  600 to 500) for 700 passengers who would have
  been willing to fly without the price reduction.
• Summary MR(Revenue from new sales at the
  new price-revenue lost from sales to old
  customers at old price)/(number of new
  customers.
• Obvious (but useful) insight MR will be bigger,
  the more new customers are attracted by the
  reduced price

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Measuring the Responsiveness of Demand to Price
Elasticity of Demand

• Consider how much vital information is presented
  by the following formula
• Elasticity ( change in Quantity
  Demanded)/(Change in Price)
• If, for example, you were contemplating a 10
  price cut, and you know the value for demand
  elasticity, you would immediately be able to
  predict how much sales would increase.

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Formulas for Demand Elasticity and Some
Observations

• Since demand elasticity is expressed in terms of
  percentage changes (BTW, see if you can figure
  out why it is important to work with percentages
  instead of absolute changes), one way to write
  the formula is
• (?Q/Q)/(?P/P) (?Q/?P)(P/Q)
• When measuring discreet changes in any variable,
  the calculation of change may depend on the
  context of the problem. (Quick, tell me the
  difference between a price of 5 and 4.)
• In order to eliminate any confusion, it is often
  useful to explicitly rely on calculus to express
  elasticity. If we can write the demand function
  as xD(p), then elasticity is
• D(p)p/x

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More Fun Facts About Elasticity

• The value of elasticity will change depending on
  where you are taking the measurement. That is,
  for different values of p and x, the value of
  elasticity may be different (I say may because
  there are such things as constant elasticity
  demand curves.)
• Elasticity is actually a negative number (since
  dp/dx is always negative). It is a common, but
  not universal, convention to report it as an
  absolute value. But if that convention is not
  honored then elastic demand would describe a
  situation where elasticity lt -1

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Relationship between MR and Elasticity

• If absolute value of elasticitygt1 (defined as
  elastic), then MRgt0. This means that when p
  goes down and q goes up, TR goes up.
• If absolute value of elasticitylt1 (defined as
  inelastic), then MRlt0 (I.e., when p goes down
  and q goes up, TR goes down).
• If absolute value of elasticity1 (defined as
  unit elasticity), then MR0 (I.e., when p goes
  down and q goes up, TR remains constant).
• We can see from our example that this is true and
  a bit of clever algebra done with the exact (that
  is, calculus) definition of MR will also confirm
  that it is true. But if you really understand
  the intuitive definition of elasticity, it is
  really almost common sense.
• In fact, there is an extremely useful formula
  that captures this entire relationship. Letting
  v(x) stand for elasticity

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Quantity Price TR MR ?Q ?P Elasticity
500 800 400,000
600 700 420,000 200 18 13 1.36
700 600 420,000 0 15 15 1.00
800 500 400,000 -200 13 18 0.73
900 400 360,000 -400 12 22 0.53
Elasticity gt 1 means TR goes up
Elasticity lt 1 means TR goes down