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
6/23

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

3. 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

4. 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) increases by one unit
MUx = DU/DX U
U = 2X
MUx = DU/DX
= 2
MUx DU DX X

5. Utility Functions Assume 1 Good:
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Utility Functions
Assume 1 Good:
We generally assume diminishing marginal utility U
U = 2X
MUx = DU/DX
= 2 U
U (X) DU DX DU DX X X

6. 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

7. 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

8. Utility Functions U U = f(X,Y) Y X U3 U2 U1 U0 U0 U1 U2 U3 4/17/2017DX DY X

9. 4/17/2017
Utility Functions
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

10. 4/17/2017
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
Increasing utility

11. 4/17/2017
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.

12. 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.

13. 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).

14. 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.

15. 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.
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.

16. 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

17. 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.

18. 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**=

19. 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

20. 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**=

21. Individual & Market Demand
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Individual & Market Demand
Income & Substitution Effects (from last time)
Normal, Inferior, and Giffen Goods
Consumer Demand
Price Elasticity of Demand
Next Time: The Theory of the Firm

22. Individual & Market Demand
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Individual & Market Demand
We have seen how consumers make optimal choices. A rational consumer will attempt to maximize utility subject to market conditions (relative prices) and income. That is, given I, Px, Py, she chooses X and Y to maximize U.
Now, we want to ask, how do changes in prices effect these consumption decisions? X = f(Px).
We will see that changes in prices affect quantities through two causal channels: Income and substitution effects.

23. Income & Substitution Effects
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Income & Substitution Effects
Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Y X
Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk.
Draw his new budget constraint.
1200
960
800

24. Income & Substitution Effects
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Income & Substitution Effects
Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Y X
Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk.
Will he work more than, less than, or equal to 50 hrs/wk?
What is the income effect?
His purchasing power is greater, so he will consume more leisure, work less.
1200
960
800

25. Income & Substitution Effects
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Income & Substitution Effects
Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Y X
Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk.
Will he work more than, less than, or equal to 50 hrs/wk?
What is the substitution effect?
At 50 hrs/wk., the new wage rate is the same as the old ($8/hr).
=> no substitution effect!
1200
960
800
Px/Py = 8

26. Income & Substitution Effects
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Income & Substitution Effects
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
Originally, the price of food is $1 and the price of all other goods is $2. Then the price of food rises to $2.
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. .

27. Income & Substitution Effects
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Income & Substitution Effects
Because the relative price of food has increased, Pat will consume less food (and more of all other goods). This the substitution effect. Y X
900
Y**=300 S
X**= S

28. Income & Substitution Effects
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Income & Substitution Effects
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**=

29. Income & Substitution Effects
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Income & Substitution Effects
The move from A to B is the substitution effect;
B to C is the income effect.
B is a point on the original indifference curve, tangent to the new budget constraint, indicating the bundle the consumer would choose at the new prices. Y X
900
Y**=300 B A I S C
X**= I S

30. Income & Substitution Effects
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Income & Substitution Effects
U = X2Y
We are looking for a point on the indifference curve that includes
Y = 300, X = 1200, for which MRS = 1 (the new price ratio):
At point B, MRS = 2Y/X = 1
=> X = 2Y.
Also, Ua = Ub = 432,000,000
4Y3 = 432,000,000
Y3 = 108,000,000
Yb = 476; Xb = 952 Y X
900
Y**=300 B A I S C
X**= I S

31. Income & Substitution Effects
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Income & Substitution Effects
U = X2Y
4Y3 = 432,000,000
Y3 = 108,000,000
Yb = 476; Xb = 952
So the substitution effect is a decrease in X of 248 and an increase in Y of 176.
The income effect is a
decrease in X of 352
and a decrease in Y
of 176. Y X
900
Y**=300 B A I S C
X**= I S

32. Income & Substitution Effects
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Income & Substitution Effects
How much would Pat be willing to pay to avoid this price increase? Y X
900
Y**=300
X**=

33. Income & Substitution Effects
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Income & Substitution Effects
To calculate this amount, start by finding the minimum income Pat needs to purchase a bundle on the new indifference curve. Y X
900
Y**=300
X**=

34. Income & Substitution Effects
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Income & Substitution Effects
The difference between the market price of this bundle and her income ( = 1800) is the amount she’d be willing to pay to avoid the price increase. We call this the equivalent variation measure of utility loss. Y X
900
Y**=300
X**=

35. Normal & Inferior Goods
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Normal & Inferior Goods
Normal Good
Income-Expansion Path Y
For most goods, the quantity consumed will increase as income increases.
We call these normal goods.
Y = f(X)
optimal ratio X

36. Normal & Inferior Goods
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Normal & Inferior Goods
Normal Good
Income-Expansion Path
Engels Curve Y
Income
X = f(I) X X

37. Normal & Inferior Goods
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Normal & Inferior Goods
Inferior Good
Income-Expansion Path Y
For some goods, consumption will decrease at higher levels of income (e.g., hamburger).
We call these inferior goods. X

38. Normal & Inferior Goods
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Normal & Inferior Goods
Inferior Good
Income-Expansion Path
Engels Curve Y
Income X X

39. Normal & Inferior Goods
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Normal & Inferior Goods
Normal Good Y Y
Px increases from $1 to $2.
The movement from A to B is the substitution effect. B B A A
Px = 1
Px = 2 X X S S

40. Normal & Inferior Goods
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Normal & Inferior Goods
For both normal and inferior goods, the substitution effect is negative: consumption will increase as price decreases.
Normal Good
Inferior Good Y Y
Px increases from $1 to $2. B B A A
Px = 1
Px = 2 X X S S

41. Normal & Inferior Goods
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Normal & Inferior Goods
For normal goods the income effect is positive, and for inferior goods it is negative.
Normal Good
Inferior Good Y Y B B A A C C X X I I

42. Normal & Inferior Goods
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Normal & Inferior Goods
For some inferior goods, the income effect is so large it outweighs the substitution effect (eg., ?).
Giffen Good Px 2 1 Y
… giving rise to a upward sloping demand curve. C B A A C
Px = 1
Px = 2 X X S I

43. Normal & Inferior Goods
Do any of these cases violate the assumptions of
well-behaved preferences that we look at last time?
No. Well-behaved preferences can give rise to all sorts of demand curves (depending on income and prices).

44. Consumer Demand X U = X2Y I = 1800; Py = 2
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Consumer Demand
U = X2Y
I = 1800; Py = 2 Y X
Px*** = $3 Y*** = 300, X*** = 400.
900
Y**=300

45. Consumer Demand : U = X2Y I = 1800; Py = 2 Demand Curve Y Px X = f(Px)
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Consumer Demand
U = X2Y
I = 1800; Py = 2 :
Demand Curve Y Px
Find the equation for the demand curve.
X = f(Px)
400 3
600 2
1200 1 3 2 1
Px = X X

46. Consumer Demand U = X2Y I = 1800; Py = 2 Demand Curve Y Px X = f(Px)
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Consumer Demand
U = X2Y
I = 1800; Py = 2
MUx = 2XY; MUy = X2
MRS = 2Y/X = Px/Py = Px/2
=> Y = (1/4)PxX
I = PxX + PyY
1800 = PxX + (2)(1/4)PxX
= (3/2)PxX
X = 1200/Px
Demand Curve Y Px
X = f(Px)
400 3
600 2
1200 1
Solve for Y & substitute 3 2 1
Px = X X

47. Consumer Demand : U = X2Y I = 1800; Py = 2 Price-Consumption Curve
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Consumer Demand
U = X2Y
I = 1800; Py = 2 :
Price-Consumption Curve
Demand Curve Y Px
In this case, consumption of Y is unaffected by changes in Px. Cross-price elasticity is zero. 3 2 1
Px = X X

48. Consumer Demand Price-Consumption Curve Demand Curve Y Px X X
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Consumer Demand
Price-Consumption Curve
Demand Curve Y Px
Or, cross-price elasticity can be positive ...
… with a smaller response in demand. 3 2 1 DX
DPx X X

49. Consumer Demand : U = X2Y I = 1800; Py = 2 Price-Consumption Curve
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Consumer Demand
U = X2Y
I = 1800; Py = 2 :
Price-Consumption Curve
Demand Curve Y Px 3 2 1 DX
DPx
Px = X X

50. Price Elasticity of Demand
Price Elasticity of Demand (Ep) Measures how sensitive quantity demanded is to changes in price.
Demand Equation: Qd = a – bP
Ep = (%DQ)/(%DP)
= (DQ/Q)/(DP/P)
= DQ/DP(P/Q)
= -b(P/Q)
Ep < 1 Inelastic: Total expenditure increases as price increases.
Ep > 1 Elastic: Total expenditure decreases as price increases.
Ep = 1 Unit Elastic: Total expenditure doesn’t change

51. Non-Price Determinants of Demand
What determines consumer demand?
Preferences
Income
Prices of Related Goods
Substitutes
Complements

52. Determinants of Price Elasticity
What determines price elasticity of demand?
Substitutes (+)
Budget share
Normal (+)
Inferior ( -)
Short v long run (+) ex. Oil
Network Effects
Bandwagon and Snob Effects
normal goods have higher elasticities, because income effect reinforces substitution effect.

53. Next Time 6/28 Theory of the Firm Besanko ,Chs 6-7. or
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Next Time
6/28 Theory of the Firm
Pindyck, Ch 6.
Besanko ,Chs 6-7. or
Varian, Chs 18,