1. UNIT I: Theory of the Consumer
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UNIT I: Theory of the Consumer
Introduction: What is Microeconomics?
Theory of the Consumer
Individual & Market Demand
6/25

2. Theory of the Consumer Preferences Indifference Curves
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Theory of the Consumer
Preferences
Indifference Curves
Utility Functions
Optimization
Income & Substitution Effects
How do consumers make optimal choices?
How do they respond to changes in prices and income?

3. 4/14/2017
Theory of the Consumer
We said last time that microeconomics is built on the assumption that a rational consumer will attempt to maximize (expected) utility. But what is utility?
Over time, economists have moved away from a notion of cardinal utility (an objective, measurable scale, e.g., height, weight) and toward ordinal utility, built up from a simple binary relation, preference.

4. 4/14/2017
Preferences
We start by assuming that a rational individual can always compare any 2 alternatives (“consumption bundles” or “market baskets”).
We call this basic relationship preference: For any pair of alternatives, A and B, either
A > B A is preferred to B
A < B B is preferred to A
A = B Indifference
e.g., 2 apples & 3 oranges.

5. Preferences “Well-behaved” preferences are
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Preferences
“Well-behaved” preferences are
(i) Connected: For all A & B, either A>B; B>A; A=B
(ii) Transitive: If A > B & B > C, then A > C
(iii) Monotonic: More is always preferred to less
(free-disposition)
(iv) Convex: Combinations are preferred to extremes

6. Preferences X A B A = ( 2 , 3 ) B = ( 3 , 2 ) A ? B 3 2 2 3 4/14/2017Y X
A = ( 2 , 3 )
B = ( 3 , 2 )
A ? B A B 3 2

7. Preferences X A B A = (Xa, Ya) B = (Xb, Yb) A ? B Ya Yb Xa Xb
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Preferences Y X
A = (Xa, Ya)
B = (Xb, Yb)
A ? B A B Ya Yb
Xa Xb

8. Preferences X A C B A = (Xa, Ya) B = (Xb, Yb) C = (Xb, Ya) A ? B
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Preferences Y X
A = (Xa, Ya)
B = (Xb, Yb)
C = (Xb, Ya)
A ? B
C > A
C > B
A C B Ya Yb
Xa Xb

9. Preferences X A C B A = (Xa, Ya) B = (Xb, Yb) C = (Xb, Ya) A = B
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Preferences Y X
A = (Xa, Ya)
B = (Xb, Yb)
C = (Xb, Ya)
A = B
C > A
C > B
A C B Ya Yb
Xa Xb

10. Preferences X A C B Convexity A = (Xa, Ya) B = (Xb, Yb) C = (Xb, Ya)
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Preferences Y X
Convexity
A = (Xa, Ya)
B = (Xb, Yb)
C = (Xb, Ya)
A = B
D > E
D > B
D > A
A C B Ya Yb D E
Xa Xb

11. Preferences X A C B A = (Xa, Ya) B = (Xb, Yb) C = (Xb, Ya) A = B = E
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Preferences Y X
Indifference curves
A = (Xa, Ya)
B = (Xb, Yb)
C = (Xb, Ya)
A = B = E
D > E
D > B
D > A
A C B Ya Yb D E
Xa Xb

12. Indifference Curves X U = XY Indifference Curve:
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Indifference Curves Y X
U = XY
Generally, ICs are:
Downward sloping
Convex to origin
Inc utility, further from origin
Cannot cross
Indifference Curve:
The locus of points at which a consumer is equally well-off, U. 3 2

13. Indifference Curves X U = XY Generally, ICs are: Downward sloping
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Indifference Curves Y X
U = XY
Generally, ICs are:
Downward sloping
Convex to origin
Inc utility, further from origin
Cannot cross 3 2
U = 9
U = 6
U = 4

14. Indifference Curves X A B C U = XY Generally, ICs are:
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Indifference Curves Y X
U = XY
Generally, ICs are:
Downward sloping
Convex to origin
Inc utility, further from origin
Cannot cross
A = B; A = C; B > C !! A B C 3 2

15. 4/14/2017
Indifference Curves
Perfect Substitutes Perfect Complements

16. Indifference Curves Recall: Remember our simple example: Oranges
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Indifference Curves
Remember our simple example:
Recall:
Oranges
Freddie likes
oranges twice as
much as apples 25
100
Apples

17. Indifference Curves What does his utility function look like?
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Indifference Curves
What does his utility function look like?
Y Utility = No. of Apples + 2(No. of Oranges)
U = X Y
MUx = 1
MUy = 2 X
Generally, any set of preferences can be described by many utility functions -2 +1 5 4
Freddie is willing to trade 2 apples for 1 orange
U = 12

18. Indifference Curves What does his utility function look like?
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Indifference Curves
What does his utility function look like?
Y Utility = No. of Apples + 2(No. of Oranges)
U = X Y
MUx = 1
MUy = 2 X -2 +1 5 4
Freddie is willing to trade 2 apples for 1 orange
U = 12

19. 4/14/2017
Indifference Curves
Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to trade between 2 goods. The amount of Y he is willing to give up for 1 unit of X.
Y Utility = No. of Apples + 2(No. of Oranges)
U = X Y
MUx = 1
MUy = 2
MRS = - MUx/MUy
= - ½ X -2 +1 5 4
Freddie is willing to trade 2 apples for 1 orange

20. 4/14/2017
Indifference Curves
Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to trade between 2 goods. The amount of Y he is willing to give up for 1 unit of X.
Y Utility = No. of Apples + 2(No. of Oranges)
U = X Y
MUx = DU/DX
MUy = DU/DY
MRS = - MUx/MUy
= - ½ X DX DY
Generally, this rate will not be constant; it will depend upon the consumer’s endowment.

21. 4/14/2017
Indifference Curves
Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to trade between 2 goods. The amount of Y he is willing to give up for 1 unit of X.
Y Utility = No. of Apples + 2(No. of Oranges)
U = X Y
MUx = DU/DX
MUy = DU/DY
MRS = - MUx/MUy
= - ½ X
Generally, this rate will not be constant; it will depend upon the consumer’s endowment. DX DY

22. 4/14/2017
Indifference Curves
Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to trade between 2 goods. The amount of Y he is willing to give up for 1 unit of X.
Y Utility = No. of Apples + 2(No. of Oranges)
U Along an indifference curve, DU = 0
Therefore, MUxDX + MUyDY = 0
MUxDX = MUyDY
- (MUx/MUy)DX = DY
DY/DX = - MUx/MUy
= MRS
= slope X
Generally, this rate will not be constant; it will depend upon the consumer’s endowment. DX DY

23. Utility Functions Assume 1 Good:
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Utility Functions
Assume 1 Good:
Utility: The total amount of satisfaction one enjoys from a given level of consumption (X,Y) U
U = 2X X

24. Utility Functions Assume 1 Good:
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Utility Functions
Assume 1 Good:
Marginal Utility: The amount by which utility increases when consumption (of good X) increase by one unit
MUx = DU/DX U
U = 2X
MUx = DU/DX
= 2
MUx DU DX X

25. Utility Functions Assume 1 Good:
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Utility Functions
Assume 1 Good:
Diminishing Marginal Utility: Utility increases but at a decreasing rate U
U = 2X
MUx = DU/DX
= 2 U
U (X) DU DX DU DX X X

26. Utility Functions Now Assume 2 Goods: U = f(X,Y) U Y X U (Y) U (X)
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Utility Functions
Now Assume 2 Goods:
U = f(X,Y) U
U (Y)
U (X) Y X

27. Utility Functions U U = f(X,Y) Y X Indifference curves U3 U2 U1 U0
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Utility Functions U
U = f(X,Y) U3 U2 U1 U0 Y
U0 U U U3
Indifference curves X

28. Utility Functions U U = f(X,Y) Y X U3 U2 U1 U0 U0 U1 U2 U3 4/14/2017DX DY
MRSyx X

29. 4/14/2017
Optimization
We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better!
Y Utility = No. of Apples + 2(No. of Oranges) U X
Indifference Curves depict consumer’s “willingness to trade”
Increasing utility

30. 4/14/2017
Optimization
We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better!
Y Utility = No. of Apples + 2(No. of Oranges) U X
Indifference Curves depict consumer’s “willingness to trade”
Indifference Curves depict consumer’s “willingness to trade”
Slope = - MRS
Budget Constraint depicts “opportunities to trade”
Slope = - Px/Py

31. 4/14/2017
Optimization
We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better!
Y Utility = No. of Apples + 2(No. of Oranges) U X
Indifference Curves depict consumer’s “willingness to trade”
Slope = - MRS
Indifference Curves depict consumer’s “willingness to trade”
Budget Constraint depicts “opportunities to trade”
Slope = - Px/Py A
At point A, MRS > Px/Py, so consumer should trade Y for X.

32. 4/14/2017
Optimization
We assume that a rational consumer will attempt to maximize her utility. But utility increases with consumption of all goods, so utility functions have no maximum -- more is always better!
Y Utility = No. of Apples + 2(No. of Oranges) U X
Indifference Curves depict consumer’s “willingness to trade”
Slope = - MRS
Indifference Curves depict consumer’s “willingness to trade”
Budget Constraint depicts “opportunities to trade”
Slope = - Px/Py B
At point B, MRS < Px/Py, so consumer should trade X for Y.

33. 4/14/2017
Optimization
The optimal consumption bundle places the consumer on the highest feasible indifference curve, given her preferences and the opportunities to trade (her income & the prices she faces).
Y Utility = No. of Apples + 2(No. of Oranges) U Y*
X* X
Indifference Curves depict consumer’s “willingness to trade”
Slope = - MRS
Budget Constraint depicts “opportunities to trade”
Slope = - Px/Py C
At point C, MRS = Px/Py, so consumer can’t improve thru trade.

34. Optimization Two Conditions for Optimization under Constraint:
1. PxX + PyY = I Spend entire budget
2. MRSyx = Px/Py Tangency
MRSyx = MUx/MUy = Px/Py
=> MUx/Px = MUy/Py
The marginal utility of the last dollar spent on each good should be the same.

35. 4/14/2017
Optimization
Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally?
C Utility = No. of Apples + 2(No. of Oranges)
I/Pc=10 U 4
I/Pf =50 F
PfF + PcC = I
2(30) + 10(4) = 100

36. 4/14/2017
Optimization
Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally?
C Utility = No. of Apples + 2(No. of Oranges)
I/Pc=10 U 4
I/Pf =50 F
Pf/Pc = 1/5
MRScf = 1/2

37. Optimization: An Example
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Optimization: An Example
Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function:
U = X2Y
If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle.
Pat should choose the combination of food and all other goods that places her on the highest feasible indifference curve, given her income and the prices she faces. This is the point where an indifference curve is tangent to the budget constraint (unless there is a comer solution).

38. Optimization: An Example
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Optimization: An Example
Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function:
U = X2Y
If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle.
Since Pat’s utility function is U = X2Y, MUx = 2XY and MUy = X2. MRS = (-)MUx/MUy = (-)2XY/X2 = (-)2Y/X. Setting this equal to the (-)price ratio (Px/Py), we find ½ = 2Y/X, X = 4Y. This is Pat’s optimal ratio of the goods, given prices.

39. Optimization: An Example
4/14/2017
Optimization: An Example
Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function:
U = X2Y
If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle.
To find Pat’s optimal bundle, we substitute the optimal ratio into the budget constraint: I = PxX + PyY, 1800 = (1)X + (2)Y,
1800 = (1)4Y + (2)Y = 6Y, so
Y* = 300, X* = 1200.

40. Optimization: An Example
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Optimization: An Example
Graphically: Y X
U = XY
Maximize: U = X2Y
Subject to: I = PxX + PyY
I = 1800; Px = $1; Py = $2
Y* = 300, X* = 1200.
900
Y*=300
X*=1200

41. Optimization: An Example
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Optimization: An Example
Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function:
U = X2Y
Now suppose the price of food rises to $2.
MRS = (-)2Y/X. Setting this equal to the new (-)price ratio (Px/Py), we find 1 = 2Y/X, X = 2Y. Substituting in Pat’s new budget constraint: I = PxX + PyY, 1800 = (2)X + (2)Y,
1800 = (2)2Y + (2)Y = 6Y, so
Y** = 300, X** = 600.

42. Optimization: An Example
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Optimization: An Example
Graphically: Y X
U = XY
U = X2Y
I = 1800; Px = $1; Py = $2
Y* = 300, X* = 1200.
900
Y*=300
X*=1200

43. Optimization: An Example
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Optimization: An Example
Graphically: Y X
U = XY
Now: U = X2Y
I = 1800; Px’ = $2; Py = $2
Y* = 300, X* = 600.
900
Y**=300
X**=

44. Income & Substitution Effects
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Income & Substitution Effects
Graphically:
Because the relative price of food has increased, Pat will consume less food (and more of all other goods). This the substitution effect. But because Pat is now relatively poorer (her purchasing power has decreased), she will consume less of both goods. This is the income effect. Y X
U = XY
900
Y**=300 S
X**= S

45. Income & Substitution Effects
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Income & Substitution Effects
Graphically:
But because Pat is now relatively poorer (her purchasing power has decreased), she will consume less of both goods. This is the income effect.
In this case, the 2 effects are equal and opposite for Y, additive for X. Y X
U = XY
900
Y**=300
X**=

46. Next Time How to consumers respond to changes in income and prices?
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Next Time
How to consumers respond to changes in income and prices?

47. Next Time 7/2 Individual and Market Demand
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Next Time
7/2 Individual and Market Demand
Pindyck & Rubenfeld, Chapters 2 (review) & 4
Besanko, Chapters 2 (review) & 5