Transcript Chapter 2 Utility and Choice

CHAPTER 2
UTILITY AND CHOICE
Objective
•
Build a model to understand how a consumer makes
decisions under scarcity.
•
To understand his choice we need to know:
1.
2.
Preferences
Constraints
Utility
• Consumer makes a choice that results in the maximum
satisfaction or UTILITY.
• Two goods available: X1 and X2.
• Utility = U(X1, X2; other things)
• Utility depends on the amount of X1 and X2 consumed and other
things.
• Assume other things are held constant.
Three Assumptions About Preferences
We make the following assumptions about preference so
we can represent preferences by a utility function
• Completeness
• Given two options, A and B, a person can state which option they
prefer or whether they find both options equally attractive.
• Transitivity
• Preferences are internally consistent.
• If I prefer A to B, and prefer B to C, then I must prefer A to C.
• More is Better
• Economic “goods”
• What’s an economic “bad”?
More is Better Graphically
Combinations of X and Y in the green
area are preferred to (X*, Y*)
Quantity of Y
per week
(X*, Y*) is preferred to combinations of X
an Y in the red area.
Can’t say about the other points.
?
Y*
?
X*
Quantity of X
per week
Indifference Curves
• We want to find a way to compare points in the two ?
regions from the last picture.
• Two goods: soft drinks and hamburgers.
• Indifference curve
• A curve that shows all the combinations of two goods that give the
same level of utility
• If you get the same utility you must be indifferent.
Indifference Curve
Let’s say you are indifferent between A,
B, C and D.
Hamburgers
per week
Draw a curve through those points.
A
6
Every point gives the same level of utility.
B
4
C
3
D
2
U1
2
3
4
5
6
Soft drinks
per week
Indifference Curve
What can we say about combination E?
Hamburgers
per week
What about F?
A
6
B
E
4
C
3
D
2
U1
F
2
3
4
5
6
Soft drinks
per week
Indifference Curve
Why does the indifference curve have a negative slope?
Hamburgers
per week
Because, if you give up hamburgers, you need
to get more soft drinks to still get the same level
of utility.
A
6
B
E
4
C
3
D
2
U1
F
2
3
4
5
6
Soft drinks
per week
Indifference Curve Maps
An indifference curve map shows the utility a person gets from all possible
combinations of two goods.
Hamburgers
per week
As you move to the northwest, utility
increases: U3 > U2 > U1
U3
U2
U1
Soft drinks
per week
Marginal Rate of Substitution (MRS)
• The absolute value of the slope of the indifference curve
• The MRS measures the rate at which you are willing to
reduce the consumption of one good to get one more unit
of another good and still remain indifferent.
MRS
From A to B: the person is willing to give
up 2 burgers to get 1 more soda.
From B to C: the person is willing to give
up 1 burger to get 1 more soda.
Hamburgers
per week
From C to D: the person is willing to give
up ½ burger to get 1 more soda.
A
6
B
E
4
C
3
D
2
U1
F
2
3
4
5
6
Soft drinks
per week
Diminishing MRS
• As you consume more and more soda, the number of
burgers you are willing to give up to get one more soda gets
smaller and smaller.
• This is known as diminishing marginal rate of
substitution.
• People prefer balanced consumption to extremes.
• From convexity
• Move along the indifference curve
• Same utility level
• MRS decreases
Calculating MRS
• MRS=-MU1/MU2
• Calculate Mui, where i =1 or 2, from utility function
Convexity of Preferences
Suppose we create a basket that is ½
of A and ½ of D: point G.
Hamburgers
per week
You would prefer 4 burgers and 4
sodas to 6 of one good and 2 of the
other good.
A
6
G
4
D
2
U1
0
2
3
4
6
Soft drinks
per week
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Representing Preferences Graphically
• Upward sloping indifference curves
• A good and a bad
• Flat indifference curves
• Goods that yield no utility
• Useless goods
• Straight-line indifference curves
• Goods that are perfect substitutes
• MRS - constant along an indifference curve
• In a two-good world
• Indifference curve - straight line
17
(b)
(a)
Good 2 (x 2)
Good 2 (x 2)
+∆x2
a
10
9
5
4
0
Good 1 (x 1)
(a) Flat indifference curves. The good
measured on the horizontal axis is
yielding no utility for the consumer.
0
-∆x1
+∆x2
-∆x1
3
8 11
Good 1 (x 1)
(b) Straight-line indifference curves:
perfect substitutes. The same amount
of good 2 is always needed to
compensate the consumer for the
loss of one unit of good 1.
18
Representing Preferences Graphically
• Right-angle indifference curves
• Goods that are perfect complements
• Must be consumed in a fixed ratio to produce utility
• Bowed-out indifference curves
• Nonconvex preferences
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(d)
(c)
Good 2 (x 2)
11
10
0
Good 2 (x 2)
+∆x2
+∆x2
-∆x1
b +∆x
2
-∆x1
a
-∆x1
b
c
a
5 6
I1
Good 1 (x 1)
0
Good 1 (x 1)
(c) Right-angle indifference curves:
(d) Bowed-out indifference curves: nonperfect complements. Adding any
convex preferences and the MRS. As the
amount of only one good to bundle a consumer gets more of good 2, he values it
yields no additional utility.
more.
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Perfect substitutes
Pepsi
0
Coke
Mary’s marginal rate of substitution is constant at any bundle of
Pepsi and Coke.
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Budget line
Good 2
150
100
50
Good 1
0
50
100
150
Points on the budget line indicate all the bundles of goods that the
consumer can afford.
Budget Line and Government Policy
What is the effect of the following on the budget line?
• Quantity tax
• Value tax
• Lump sum tax
• Voucher
• rationing
23
Optimal Consumption Bundle
• Optimal consumption bundle
• Maximize consumer’s utility
• Within the economically feasible set
• Best bundle
• According to consumer’s preferences
• Characteristics of optimal bundles
• Indifference curve tangent to budget line
• Slope of indifference curve = MRS = -∆x2/∆x1
• Slope of budget line = price ratio = p1/p2
• MRS = p1/p2
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The optimal consumption bundle
Good 2 (x 2)
B
x
+1
-3
z
-4
e
k
+1
m
n
F
0
B’
Good 1 (x 1)
At the optimal point e, the indifference curve is tangent to the budget line