MORE ON DEMAND
Construction of the Demand Curve
The downward sloped demand curve
•
Law of Diminishing Marginal Utility
•
Income & Substitution Effects
UTILITY GENERATED BY CONSUMPTION OF
TACOS
(one unit of utility = a "util")
Unit Consumed Total
(one taco)
Utility
(utils)
0
0
Marginal
Utility
(utils)
10
1st
10
8
2nd
18
6
3rd
24
4
4th
28
2
5th
30
0
6th
30
-2
7th
28
Assume for a moment that a util is "worth" $1 to
a consumer (and the consumer has no budget
constraint). How much would the consumer pay
for the first unit? For the second?
Unit
consumed
Value
in $
1st
2nd
3rd
4th
5th
6th
7th
$10
$8
$6
$4
$2
0
$-2
Put differently, how many units would the
consumer buy at a price of $6/unit? At a price of
$4?
The more rapidly marginal utility falls, the less
elastic the demand curve.
WHY?
Constructing the demand curve using income
and substitutiton effects.
"A" $1/Meal
Meal
MU
MU/$
1st
10
10
2nd
8
8
3rd
7
7
4th
6
6
5th
5
5
6th
4
4
7th
3
3
"B" $2/Meal
Meal
MU
MU/$
1st
24
12
2nd
20
10
3rd
18
9
4th
16
8
5th
12
6
6th
6
3
7th
4
2
To maximize utility consume up to the point
where MU/$ is equal for all commodities, and
the budget is exhausted.
If your budget = $10, how much of "A" and how
much of "B" should you buy?
Sequence of Purchases (each choice involves
maximizing marginal utility per dollar spent)
Choice
#
1
2
3
4
Potential
choices
1st unit "A"
1st unit "B"
1st unit "A"
2nd unit "B"
2nd unit "A"
3rd unit "B"
2nd unit "A"
4th unit "B"
MU/$
10
12
10
10
8
9
8
8
Decision
$ left
1st unit "B"
$10-2=8
1st unit "A"
2nd unit "B"
$8-(2+1)=5
3rd unit "B"
$5-2=3
2nd unit "A"
4th unit "B"
$3-(2+1)=0
Maximum utility achieved with consumption of 2
units of "A" and 4 units of "B"
Total utility is 10+8 (from consumption of "A")
+24+20+18+16 (from consumption of "B") = 96
utils.
Always consume such that:
MU X MUY
=
PX
PY
Why? Because if the equality did not hold you
could take $1 away from the good with the lower
MU/$ and spend it on the good with the higher
MU/$. The loss in utility would be less than the
gain.
Example:
Bob buys 4 units of "A" and 3 units of "B". The
budget of $10 is exhausted. But for the last
units purchased
MUA 6
=
=6
PA
$1
MUB 18
=
=9
PB
$2
If Bob gave up the 4th unit of "A" he loses 6 utils
but if he spends it on "B" (assume he could buy
just 1$ worth of "B") he would gain 8 utils (i.e.,
the MU/$ for the 4th unit of "B"). In fact he
would give up the 4th and the 3rd unit of "A" and
lose 13 utils (6+7) and spend the $2 on "B"
thereby gaining 16 utils, for a net gain of 3 utils.
Now assume the price of "B" drops from $2 to
$1.
"A" $1/Meal
Meal
MU
MU/$
1st
10
10
2nd
8
8
3rd
7
7
4th
6
6
5th
5
5
6th
4
4
7th
3
3
"B" $1/Meal
Meal
MU
MU/$
1st
24
24
2nd
20
20
3rd
18
18
4th
16
16
5th
12
12
6th
6
6
7th
4
4
Choice
#
1
2
3
4
5
6
7
8
9
Potential
choices
1st unit "A"
1st unit "B"
1st unit "A"
2nd unit "B"
1st unit "A"
3rd unit "B"
1st unit "A"
4th unit "B"
1st unit "A"
5th unit "B"
1st unit "A"
6th unit "B"
2nd unit "A"
6th unit "B"
3rd unit "A"
6th unit "B"
4th unit "A"
6th unit "B"
MU/$
10
24
10
20
10
18
10
16
10
12
10
6
8
6
7
6
6
6
Decision
$ left
1st unit "B"
$10-1=9
2nd unit "B"
$9-1=8
3rd unit "B"
$8-1=7
4th unit "B"
$7-1=6
5th unit "B"
$6-1=5
1st unit "A"
$5-1=4
2nd unit "A"
$4-1=3
3rd unit "A"
$3-1=2
4th unit "A"
6th unit "B"
$2-2=0
Note, when the price of "B" falls from $2 to $1,
demand for "B" increases from 4 units to 6 units.
This represents 2 points on the demand curve
We could continue to change the price of "B"
and generate more "points" on the demand
curve.
Note, in this example when the price of "B" falls
the consumer ends up buying more "B" and "A".
If "A" and "B" are substitutes, how can this be?
(remember, the quantity demanded of a good is
supposed to be directly related to the price of
substitutes)
Answer. Two things are happening. The price
of the substitute "B" is falling, but income is in
effect rising.
At the old prices (PA = $1; PB = $2) the utility
maximizing combination of 2 "A" and 4 "B" cost
$10. At the new price (PA = $1; PB = $1) that
combination would cost only $6. In effect, the
consumer now has $4 dollars to spend.
The concept of “consumer surplus”
$
Y
65
Bob’s consumer surplus
50
P (the market price)
Demand=MB
0
Q*
Q
Bob pays 50$, but the jeans are worth 65$ to
him (he obtains a "surplus" of 15$)
The total value of jeans consumed is the area
0YPQ*.
The total amount paid is 50$ x Q*.
The difference (the triangle, 50YP) is called the
consumer surplus.
This a “new” meaning of surplus. It is the
difference between the value of something and
its economic cost.