Transcript Lecture Slide 01

Topic 1(a): Review of Consumer Theory (demand)
Review of Demand.
•
Three areas to cover on the demand side:
i. Interpreting an individual consumer’s demand curve
ii. Measuring consumer well-being using the demand curve
iii. Deriving aggregate demand from individual demand
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Topic 1(a): Review of Consumer Theory
i.
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Interpreting an individual’s demand curve
Recall that a demand curve maps out a relationship between price
and quantity.
Demand curves usually slope downwards:
Price (P)
known as the “law” of demand.
Demand
Curve (D)
Remember, on the horizontal axis we are
measuring units of the good consumed (Q),
while on the vertical axis we are
measuring the price per unit (P),
in some form of currency (dollars,
Quantity (Q) cents etc).
How to interpret this demand curve?
Two interpretations, each of which will be useful, depending on
the context.
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Topic 1(a): Review of Consumer Theory
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The first interpretation of the demand curve is probably the most
familiar to you:
P
D
Interpretation 1: the D curve tells is how many units
of a good a consumer wishes to buy in total, at a
given price per unit for the good.
For instance, the D curve tells us that if
the price per unit is P1, then the
consumer would like to buy Q1 units.
etc.
P1
P2
Q1
Q2
Q
We can think of this interpretation as reading the D curve horizontally:
that is, if we plug in values for P,
we get out values for Q.
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Topic 1(a): Review of Consumer Theory
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The second interpretation of the demand curve may be less
familiar to you:
Interpretation 2: the height of the D curve at any
given point tells is how the consumer values
additional units of the good.
P
D
P1
P2
Q1
Q2
Q
For instance, the D curve tells us that if
the consumer is currently has Q1 units
of the good, then a small increase in
quantity would be worth P1 per unit to
the consumer. etc.
We can think of this interpretation as reading the D curve vertically:
that is, if we plug in values for Q,
we get out values for P.
We will elaborate on this interpretation by use of an example. 4
Topic 1(a): Review of Consumer Theory
Example: Suppose that demand is given by Q = 5 - (1/2)P.
From the D function, if P=$10, Q=0 will be demanded.
P($)
But if P = $8, Q = 1 will be demanded.
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 consumer’s maximum willingness to pay for the
first unit is greater than $8, but less than $10.
8
D
1
5
Q
Area of the rectangle ($10) thus gives an
upper bound on consumer’s willingness to
pay for the first unit.
So we know that the maximum willingness to pay for the first
unit is something greater than $8, but less than $10. Can we
do better than this?
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Topic 1(a): Review of Consumer Theory
Now consider smaller changes in P. Say P from $10 to $9 so
that Qfrom 0 to 0.5.
Consumer did not buy the first half unit when it cost $5, but
does when it costs $4.50.
P($)
 consumer’s maximum willingness to pay for this first
10
half unit is something less than $5.
9
8
D
0.5 1
Now suppose P from $9 to $8, so that total Q from
0.5 to 1.
Consumer did not buy the second half unit
when it cost $4.50, but does when it costs
Q $4.00.
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 consumer’s maximum willingness to pay for this second
half unit is something less than $4.50.
This tells us that the consumer’s maximum willingness to
pay for the first unit is greater than $8, but in fact something
less than $9.50 (as opposed to $10).
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Topic 1(a): Review of Consumer Theory
We could consider even smaller changes in prices and quantities .
P($)
In the limit, as we consider smaller and
smaller price changes, what we are doing
here is calculating the area under the
demand curve between Q=0 and Q=1.
10
9
8
D
0.5 1
5
Q
This area tells us the exact maximum willingness to pay by
this consumer for the first unit of the good.
In this case, the area of that trapezoid is equal to $9.
 The consumer is willing to pay at most $9 for the first unit.
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Topic 1(a): Review of Consumer Theory
By the same logic, the area under the demand curve as we
increase Q from 1 to 2 units tells us the maximum willingness to
pay for the second unit.
In this case, that area equals $7.
Indeed, the area under a D curve between any two
quantities tells us the maximum willingness to pay
for that additional quantity.
P($)
10
8
6
If we consider very small increases in
quantity, than the trapezoid representing the
willingness to pay has a very small base.
1
2
5
Q
In the limit, as we consider tiny tiny increases in Q, the base
of the trapezoid goes to zero, and the willingness to pay (per
unit) for these tiny tiny increases in Q is just equal to the
height of the demand curve.
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Topic 1(a): Review of Consumer Theory
This is the logic behind the second interpretation of the demand
curve, that the height at any point tells us how consumers value
small Q.
As we have seen, this is equivalent to telling us
P($)
how much the consumer is willing to pay for
10
small Q.
We can also think about this as telling us how
much additional benefit a consumer would get
from a small Q.
8
6
2
Q
When we are thinking about the D curve in
this way, we will refer to it variously as the:
1. Marginal Value (MV) curve
2. Marginal Willingness to Pay (MWP) curve
3. Marginal Benefit (MB) curve
Note that
these terms
are equivalent!
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Topic 1(a): Review of Consumer Theory
ii.
Measuring consumer well-being using the demand curve.
1st interpretation of D curve: tells us Q demanded at a given P.
2nd interpretation of D curve: area under the D curve measures
consumer’s willingness to pay for Q1 units.
P($)
But, how much did consumer actually have to pay for Q1?
A
Expenditure (price times quantity) given by area P1Q1.
P1
 consumer willing to pay more than she has to pay.
Q1
Q
Difference between willingness to pay and
expenditure measures consumer well-being.
Definition: consumer surplus (CS) = what a consumer is willing to
pay minus what they have to pay = NB from consuming that Q.
In the diagram above, the CS from buying Q1 units at P1 per unit is
equal to the triangle A.
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Topic 1(a): Review of Consumer Theory
iii.
Deriving aggregate demand from individual demand
Suppose two individuals - A and B - each with D curves drawn below.
P
P
DA
DB
Aggregate D
3
1
2
4
QA
QB
3
5
5
9
At $3, A demands 2 and B demands 3.
Aggregate demand at $3 therefore equals 2+ 3 = 5.
At $1, A demands 4, B demands 5, and agg. D = 4+5=9.
We are horizontally aggregating individual demands to get
aggregate demand.
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