Transcript Lecture 1(b) Models - Southern Methodist University

Lecture 2(a) Basics of
Demand
Why Study Demand
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Obvious Reason: To help with forecasting revenues
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What will happen to sales tax revenues collected from the sale of
cigarettes if the price goes up as a consequence of the Federal
Government’s lawsuit?
Less Obvious Reason: To help understand pricing
strategies
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Why do some firms make it difficult to buy “unbundled”--e.g.,
MS wants to sell Office or Explorer as a package?
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?
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Taste
Price of the Good
Income
Price of Other Stuff
Taste
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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 disputandem—which 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, we’ll mostly
accept the consumer as he or she is.
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 .
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(Note: this prediction assumes that only price
changes.)
This Seems Obvious, but It is Worth
Thinking About Exactly Why People
Buy Less When Prices Go Up
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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 we’ll give a
simple example in class.
Most consumers have preferences over most
goods that are consistent with diminishing marginal
utility.
The relationship between prices of other goods
and demand
(How Would My Demand for X Change if the
Price of Y Went Up?)
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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
The relationship between income
and demand
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If I were Bill Gates, how would my life be
different?
I’d buy more rides on private jets than I do now.
 But I’d buy fewer coach tickets than now.
The relationship between income and demand is
ambiguous. Thus, we have the following
definitions
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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)
Another way to make the same points
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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
Some Helpful Jargon About Demand
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Suppose we thought that the relationship between price and the quantity demanded of
a particular good could be represented by the following linear relationship (where P
represents the price and Q the quantity demanded).
Q=2(50-P)
This expression could be rearranged as
P=50-.5Q
These expressions are, of course, really just two different ways 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”.)
Issues
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Market demand vs individual demand.
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Market demand vs firm demand.
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This is something we’ll 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 firm’s demand.
What exactly do we mean by a good? That is, a good can be distinguished by
(among other things).
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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 individual’s demand may be
influenced by the number of others demanding the good?
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.
From Demand to Revenue
It is obviously possible to derive total revenue from
demand simply by multiplying Q by P.
TR=P*Q.
 Since this is economics, we of course want marginal
revenue
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Words: MR is the change in TR when Q changes
 For discreet changes: MR=Change in TR/Change in Q
(approximate)
 Calculus: MR = d TR/ dQ (precise)
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Example: Demand for Airline Seats
MR
TR
Price
Quantity
500
$
800
$
400,000
600
$
700
$
420,000
200
700
$
600
$
420,000
0
800
$
500
$
400,000
-200
900
$
400
$
360,000
-400
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This example is consistent with demand being given by
Q= 1300- P or P=1300-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).
Puzzle: Why Does TR Increase and
Then Decrease?
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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” pricerevenue 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
Measuring the Responsiveness of
Demand to Price: Elasticity of Demand
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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.
Formulas for Demand Elasticity and Some
Observations
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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
(ΔQ/Q)/(ΔP/P) = (ΔQ/ΔP)(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 x=D(p), then elasticity is
D’(p)p/x
More Fun Facts About Elasticity
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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 < -1
Relationship between MR and
Elasticity
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If absolute value of elasticity>1 (defined as “elastic”), then MR>0. This
means that when p goes down and q goes up, TR goes up.
If absolute value of elasticity<1 (defined as “inelastic”), then MR<0 (I.e.,
when p goes down and q goes up, TR goes down).
If absolute value of elasticity=1 (defined as “unit elasticity”), then MR=0
(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
Quantity
Price
TR
MR
% ΔQ
% ΔP
Elasticity
Elasticity > 1 means
TR goes up
500
$800
$ 400,000
600
$700
$ 420,000
200
18%
700
$600
$ 420,000
0
800
$500
$ 400,000
900
$400
$ 360,000
13%
1.36
15%
15%
1.00
-200
13%
18%
0.73
-400
12%
22%
0.53
Elasticity < 1 means
TR goes down