Chapter 2 Utility and Choice
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Transcript of Chapter 2 Utility and Choice
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CHAPTER 2 UTILITY AND CHOICE
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Objective• Build a model to understand how a consumer makes
decisions under scarcity.
• To understand his choice we need to know:1. Preferences2. Constraints
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• 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.
Utility
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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”?
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Quantity of Y
per week
Y*
Quantity of Xper week
?
?
X*
More is Better GraphicallyCombinations of X and Y in the green area are preferred to (X*, Y*)
(X*, Y*) is preferred to combinations of X an Y in the red area.
Can’t say about the other points.
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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.
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Hamburgersper week
6 A
B
CD
U1
4
3
2
Soft drinksper week2 3 4 5 6
Indifference CurveLet’s say you are indifferent between A, B, C and D.
Draw a curve through those points.
Every point gives the same level of utility.
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Hamburgersper week
6 A
B
CD
U1
4
3
2
Soft drinksper week2 3 4 5 6
Indifference Curve
E
What can we say about combination E?
What about F?
F
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Hamburgersper week
6 A
B
CD
U1
4
3
2
Soft drinksper week2 3 4 5 6
Indifference Curve
E
F
Why does the indifference curve have a negative slope?
Because, if you give up hamburgers, you need to get more soft drinks to still get the same level of utility.
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Hamburgersper week
Soft drinksper week
Indifference Curve Maps
U1
U2
U3
An indifference curve map shows the utility a person gets from all possible combinations of two goods.
As you move to the northwest, utility increases: U3 > U2 > U1
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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.
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Hamburgersper week
6 A
B
CD
U1
4
3
2
Soft drinksper week2 3 4 5 6
MRS
E
F
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.
From C to D: the person is willing to give up ½ burger to get 1 more soda.
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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
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Calculating MRS• MRS=-MU1/MU2• Calculate Mui, where i =1 or 2, from utility function
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Hamburgersper week
6 A
G
DU1
4
2
Soft drinksper week2 3 4 60
Convexity of Preferences
You would prefer 4 burgers and 4 sodas to 6 of one good and 2 of the other good.
Suppose we create a basket that is ½ of A and ½ of D: point G.
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Representing Preferences Graphically
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• 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
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Good 1 (x 1)
0
Good 2 (x 2)
(a) Flat indifference curves. The good measured on the horizontal axis is yielding no utility for the consumer.
(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.
(a) (b)
a
Good 1 (x 1)
0 3 8 11
Good 2 (x 2)
9
54
10
+∆x2-∆x1
+∆x2
-∆x1
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Representing Preferences Graphically
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• 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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I1
19
Good 1 (x 1)0
Good 2 (x 2)
(c) Right-angle indifference curves: perfect complements. Adding any amount of only one good to bundle a yields no additional utility.
(d) Bowed-out indifference curves: non-convex preferences and the MRS. As the consumer gets more of good 2, he values it more.
(c) (d)Good 2 (x 2)
1011
-∆x1-∆x1
Good 1 (x 1)
0 5 6
bc
a-∆x1
b
a
+∆x2+∆x2
+∆x2
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Perfect substitutes
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Coke0
Pepsi
Mary’s marginal rate of substitution is constant at any bundle of Pepsi and Coke.
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Budget line
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Points on the budget line indicate all the bundles of goods that the consumer can afford.
Good 2
150
50
100
Good 11501000 50
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Budget Line and Government PolicyWhat is the effect of the following on the budget line?
• Quantity tax• Value tax• Lump sum tax• Voucher• rationing
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Optimal Consumption Bundle
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• 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
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At the optimal point e, the indifference curve is tangent to the budget line
Good 1 (x 1)0
Good 2 (x 2)
x
ez
B
B’
F
+1
+1
-4
-3
mn
k