Microennomics Expert
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Consumer Behavior
● Theory of consumer behavior
- How consumers allocate incomes among different goods and services to maximize their well-being.
Three distinct elements required to understand consumer behavior:
Consumer preferences (What she wants)
Budget constraints (How much income she has)
Consumer choices (How she allocates her income)
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Consumer Preferences
In Economics we assume:
- Preferences are given
- Consumers are rational,
- They have goals, and they make decisions that will enable them to achieve those goals.
- Does not mean that the goals are somehow rational or appropriate, nor does it mean that people do what others might think is right or best for them.
- Consumers maximize their satisfaction (i.e., utility), and as long as they are making decisions that achieve that goal, they are being rational.
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Consumer Preferences
● Market basket (or bundle) List with specific quantities of one or more goods.
| Alternative Market Baskets | ||
| A | 20 | 30 |
| B | 10 | 50 |
| D | 40 | 20 |
| E | 30 | 40 |
| G | 10 | 20 |
| H | 10 | 40 |
Market Basket
Units of Food
Units of Clothing
To explain the theory of consumer behavior, should ask whether consumers prefer one market basket to another.
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Consumer Preferences
Basic Assumptions about Preferences
Completeness:
- Consumers can compare and rank all possible baskets.
- For any two market baskets A and B, will prefer A to B, B to A, or will be indifferent (equally satisfied).
Transitivity:
- Consumers prefer basket A to basket B and basket B to basket C, then the consumer also prefers A to C.
- Necessary for consumer consistency.
More is better than less: (Nonsatiation)
- Goods are assumed to be desirable — i.e., to be good.
=> Consumers always prefer more of any good to less.
=> Consumers are never satisfied or satiated; more is always better, even if just a little better.
- There are goods, such as air pollution, that are undesirable - ignore these “bads” in the context of our immediate discussion.
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Describing Individual Preferences
More of each good is preferred to less,
A is clearly preferred to basket G,
E is clearly preferred to A.
However, A cannot be compared with B, D, or H without additional information.
Consumer Preferences
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U1: Shows all baskets that give the consumer the same level of satisfaction as does basket A;
- Baskets B and D, etc.
An Indifference Curve
Consumer Preferences
● Indifference curve Curve representing all combinations of market baskets that provide a consumer with the same level of satisfaction.
This consumer prefers:
E, to A,
A to H or G
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A set of indifference curves that describes a person's preferences.
An Indifference Map
Consumer Preferences
● Indifference map Graph containing a set of indifference curves showing the market baskets among which a consumer is indifferent.
Any market basket on U3, (A), is preferred to any basket onU2 (B), which in turn is preferred to any basket on U1, (D).
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The magnitude of the slope of an indifference curve: Marginal Rate of Substitution (MRS) between two goods.
Consumer Preferences
MRS falls from 6 (between A and B) to 4 (between B and D) to 2 (between D and E) to 1 (between E and G).
Convexity The decline in the MRS reflects a diminishing marginal rate of substitution.
- When the MRS diminishes along an indifference curve, the curve is convex.
● Marginal rate of substitution (MRS): Maximum amount of a good that a consumer is willing to give up in order to obtain one additional unit of another good.
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MRS is constant.
- The consumer views orange juice and apple juice as perfect substitutes: is always indifferent between a glass of one and a glass of the other.
Consumer Preferences
Perfect Substitutes and Perfect Complements
MRS is zero or infinite;
- The consumer views left shoes and right shoes as perfect complements: An additional left shoe gives no extra satisfaction unless without the matching right shoe.
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Consumer Preferences
Utility function:
a) can be represented by a set of indifference curves, with numerical indicators.
b) can be represented by a mathematical formula.
Ordinal utility function Utility function that generates a ranking of market baskets in order of most to least preferred.
Cardinal utility function Utility function describing by how much one market basket is preferred to another.
● Utility Numerical score representing the satisfaction that a consumer gets from a given market basket.
● Utility function Formula that assigns a level of utility to individual market baskets.
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Utility Function Mathematical Representation
Examples of utility functions
1) Smooth, symmetric: U(X,Y) = XY, U(X,Y) = X0.5 Y0.5
2) Perfect substitutes (Linear) : U(X,Y) = 2X+3Y
3) (next session) Perfect compliments: U(X,Y) = minimum {X,Y}
4) Quasi-Linear: U(X,Y) = X0.5 + Y/4
Let’s focus on Type-1 utility function first.
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Y
X
Utility
Utility Function Graphical Representation
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Y
X
Utility
The Function: U(X,Y) = X0.5 Y0.5
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Y
X
Utility
Graphical Representation: The Indifference Curves
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Y
X
U=1/12
U=6/12
U=9/12
Graphical Representation: The Indifference Curves
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Clothing (C)
Budget Constraints
The table shows market baskets associated with the budget line F + 2C = $80
● Budget constraints Constraints that consumers face as a result of limited incomes.
● Budget line All combinations of goods for which the total amount of money spent is equal to income.
| Market Baskets and the Budget Line | |||
| A | 0 | 40 | $80 |
| B | 20 | 30 | $80 |
| D | 40 | 20 | $80 |
| E | 60 | 10 | $80 |
| G | 80 | 0 | $80 |
Market Basket
Food (F)
Total Spending
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Budget Constraints
Budget line: The combinations of goods that can be purchased given the consumer’s income and the prices of the goods.
Line AG: The budget associated with
(I= $80, PF = $1, PC = $2)
The slope of the budget line ( between B and D) is −PF/PC = −10/20 = −1/2.
What is the effect of change in income?
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Budget Constraints
Price Changes: A change in the price of one good (I unchanged) causes the budget line to rotate about one intercept.
Example:
Price of food falls from $1.00 to $0.50 => The budget line rotates from L1 to L2.
Price increases from $1.00 to $2.00, => The budget the line rotates from L1 to L3.
The Effects of Changes in Income and Prices
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Consumer Choice
Utility is Maximized at A.
- At this point, the budget line and indifference curve U2 are tangent.
- At point A: MRS between the two goods equals the price ratio.
- What about point B?
Should satisfy two conditions:
Be on the budget line
Maximize utility
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Consumer Choice
● Marginal benefit Benefit from the consumption of one additional unit of a good.
● Marginal cost Cost of one additional unit of a good.
Satisfaction is maximized when the marginal benefit — the benefit associated with the consumption of one additional unit of food — is equal to the marginal cost — the cost of the additional unit of food. (The marginal benefit is measured by the MRS.)
Satisfaction is maximized (given the budget constraint) at the point where
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Consumer Choice Mathematical Representation
An individual consumes two goods, X and Y with a utility function given by the expression:
U(X,Y) = X0.5 Y0.5
The current price of X and Y is 25 and 5 respectively. The individual currently has an income of 750.
To calculate the optimal quantities of X and Y given the income constraint and the. We simply need to maximize the Utility subject to the constraint. (Recall the Math review)
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Consumer Choice Mathematical Representation
Max U(X,Y) = X0.5 Y0.5
Subject to 25X+5Y=750
From the Math review:
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Marginal Utility
● Marginal utility (MU) Additional satisfaction obtained from consuming one additional unit of a good.
- Diminishing marginal utility More of a good is consumed, the consumption of additional amounts will yield smaller additions to utility.
What does this mean?
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Corner Solution
Corner solution: Is the solution to the consumer choice when the optimal solution is not the tangency.
- Situation in which the marginal rate of substitution of one good for another in a chosen market basket is not equal to the slope of the budget line.
a) The budget line is straight yet due to a specific type of utility function the consumer only consumes one of the goods – consumes on a corner.
b) The budget line is kinked.
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Corner Solution: Straight budget line Example-1 (Graphical)
Linear utility function (perfect substitute)
MRS is constant, the slope of budget line is constant too
Therefore:
MRS > (PX/PY) (Left Graph)
MRS < (PX/PY) (Right Graph)
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Corner solution: Example-1 (Numerical)
Consider a consumer and two goods: x, y. The Consumer utility function is:
U(x,y) = 3x + 2y.
The price of x is $2 and y is $1. The consumer has an income of $10.
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Corner Solution: Straight budget line Example-2
Some utilities are not linear yet lead to corner solution.
The quasi-linear utility quite often leads to corner solution.
Graphical representation: The utility is not linear yet for the given budget line of AB, the highest level of satisfaction is achieved at B on indifference curve U1, where the MRS is greater than the ratio of the price of ice cream to the price of frozen yogurt.
Question: What is different about the indifference curve in the graph?
See next iClicker question for mathematical representation.
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A College Trust Fund
Corner Solution: Kinked budget line Example-1 (Graphical)
A college trust fund that must be spent on education:
From A to B, a corner solution.
If the trust fund could be spent on other consumption as well as education, the student would be better off at C.
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Corner Solution: Kinked budget line Example-1 (Numerical)
A consumer is considering choosing a calling plan for her cell phone. The plan has a fixed monthly fee of $60, and it gives 800 free minutes per month and charges $0.2 for each additional minute. The consumer has a monthly income of $100, and she spend it on cell phone and another composite good y, where Py =$1. Her utility function is given by U(x,y) = x0.1 y0.9, where x is the minutes of cell phone she uses in a month.
Graph the budget line for calling.
Find her optimal bundle.
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Inefficiency of Gasoline Rationing
Corner Solution: kinked budget line Rationing (Graphical)
Gasoline rationed at $1 per gallon to a max of 2000 gallons.
- Without gasoline rationing, up to 20,000 gallons of gasoline are available for consumption (point B).
=> The consumer chooses point C on indifference curve U2, consuming 5000 gallons of gasoline.
With a limit of 2000 gallons of gasoline under rationing (at point E), the consumer moves to D on the lower indifference curve U1.
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Comparing Gasoline Rationing to the Free Market
Corner Solution: kinked budget line Rationing (Graphical)
If Price of gasoline in a competitive market = $2.00
Max consumption of gasoline is 10,000 gallons per year,
the consumer is better off under rationing
utility of F is lower than utility D
If Price of gasoline in a competitive market = $1.5
Consumer worse off under rationing
Utility of G, is higher than utility of D.
See Q-8 on PS2
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