As a basic premise for analyzing consumer behavior, we will assume that:
all individuals make consumption decisions with the goal of maximizing their total satisfaction from consuming various goods and services, subject to the constraint that their spending on goods exactly equals their incomes;
there is no saving or borrowing;
buyers know the full range of products and services available, as well as the capacity of each product to provide utility;
buyers know the price of each good and their incomes during the time period in question.
A particular combination of specific quantities of goods or services.
Consumers are able to rank all conceivable bundles of commodities.
Consumer preferences are transitive if from A > B and B > C follows that A > C.
Consumers always prefer to have more of a good rather than less of the good.
Utility is the name economists give to the benefits consumers obtain from the goods and services they consume. While utility implies usefulness, many of the products most of us consume may not be particularly useful.
An equation that shows an individual’s perception of the level of utility that would be attained from consuming each conceivable bundle of goods: U = f (X, Y).
A set of points representing different combinations of goods and services, each of which provides an individual with the same level of utility. Therefore, the consumer is indifferent among all combinations of goods shown on an indifference curve.
Indifference curves are assumed to have two important properties — they are:
Downward sloping
Convex
MRS measures the number of units of Y that must be given up per unit of X added so as to maintain a constant level of utility.
For a unit increase (decrease) in X, the MRS measures the decrease (increase) in Y needed to keep utility constant (\(MRS = \Delta Y/\Delta X\)).
For very small changes in X, the MRS is the absolute value of the slope of the indifference curve at the given value of X.
The MRS decreases as the consumer moves down an indifference curve.
An indifference map is made up of two or more indifference curves.
The higher (or further to the right) an indifference curve, the greater the level of utility associated with the curve.
Combinations of goods on higher indifference curves are preferred to combinations on lower curves.
MU is the addition to total utility (U) that is attributable to consuming one more unit of a good (X), holding constant the amounts of all other goods consumed.
\[MU_X = \frac{\Delta U}{\Delta X} \]
The marginal rate of substitution of X for Y can be interpreted as the ratio of the marginal utility of X divided by the marginal utility of Y:
\[MRS = -\frac{\Delta Y}{\Delta X} = \frac{MU_X}{MU_Y} \]
The budget line is the set of all combinations or bundles of goods that can be purchased at given prices if the entire income is spent.
The budget line divides the commodity space into the set of attainable bundles and the set of unattainable bundles.
An increase (decrease) in income causes a parallel outward (inward) shift in the budget line.
An increase (decrease) in the price of X causes the budget line to pivot inward (outward) around the original vertical intercept.
A consumer maximizes utility subject to a limited income at the combination of goods for which the indifference curve is just tangent to the budget line. At this combination:
\[ -\frac{\Delta Y}{\Delta X} = MRS = \frac{MU_X}{MU_Y} \]
To obtain maximum satisfaction from a limited income, a consumer allocates income so that the marginal utility per dollar spent on each good is the same for all commodities purchased, and all income is spent.
\[ \frac{MU_1}{P_1} = \frac{MU_2}{P_2} = \frac{MU_3}{P_3} = \ldots = \frac{MU_n}{P_n}\]
Suppose you attend the afternoon baseball game and have only $40 to spend on hot dogs and Cokes. You missed lunch, and $40 is not going to be enough money to buy all the Cokes and hot dogs you would want to consume. The only rational thing to do is to maximize your utility subject to your $40 budget constraint.
On the back of your baseball program you make a list of the marginal utility you expect to receive from various levels of hot dog and Coke consumption. You then divide the marginal utilities by the prices of hot dogs and Cokes, $5 and $4, respectively. The back of your baseball program looks like the table on the next slide:
| Units per game | \(MU_{h}\) | \(MU_hD\) | \(MU_c\) | \(MU_cD\) |
|---|---|---|---|---|
| 1 | 40 | 8 | 120 | 30 |
| 2 | 30 | 6 | 80 | 20 |
| 3 | 25 | 5 | 40 | 10 |
| 4 | 20 | 4 | 32 | 8 |
| 5 | 15 | 3 | 16 | 4 |
| 6 | 10 | 2 | 8 | 2 |
What is the optimal bundle of hot dogs and coke given the budget constraint?
The demand curve of an individual for a specific commodity relates utility-maximizing quantities purchased to market prices, holding constant income and the prices of all other goods.
The slope of the demand curve illustrates the law of demand: Quantity demanded varies inversely with price.
The market demand can be considered a list of prices and the quantities consumers are willing and able to purchase at each price in the list, other things being held constant.
The market demand curve is the horizontal summation of the demand curves of all consumers in the market.
It therefore shows how much all consumers demand at each price over the relevant range of prices.
For any particular quantity demanded, the price on the vertical axis of the market demand curve measures two things:
the maximum price consumers will pay to buy that quantity of the good,
the dollar value of the benefit to buyers of that particular unit of the good.
A market demand curve, then, gives the marginal benefit (value) individuals place on the last unit consumed.
A situation where the utility-maximizing bundle lies at one of the endpoints of the budget line and the consumer chooses to consume zero units of one of the goods.
\[ \frac{MU_1}{P_1} < \frac{MU_2}{P_2} = \frac{MU_3}{P_3} = \ldots = \frac{MU_n}{P_n}\]