# Consumer theory

Consumer theory is a theory of economics. It relates preferences (through indifference curves and budget constraints) to consumer demand curves. The models that make up consumer theory are used to represent prospectively observable demand patterns for an individual buyer on the hypothesis of constrained optimization. Prominent variables used to explain the amount demanded of a good are the price per unit of that good and money income of the consumer. A change in the price of a good is posited to change the amount demanded of that good in such a way that it can be broken down into two parts: the substitution effect (from a change in relative prices) and the income effect (from a change in purchasing power of the money income).

## Indifference curves and budget constraints

For an individual, indifference curves and an assumption of constant prices and a fixed income in a two-good world will give the following diagram. The consumer can choose any point on or below the budget constraint line BC. This line is diagonal since it comes from the equation . In other words, the amount spent on both goods together is less than or equal to the income of the consumer. The consumer will choose the indifference curve with the highest utility that is within the budget constraint. I3 has all the points outside of their budget constraint so the best that the consumer can do is I2. This will result in them purchasing X* of good X and Y* of good Y.

link between indifference curves budget constraint an consumers choice.

Income effect and price effect deal with how the change in price of a commodity changes the consumption of the good. The theory of consumer choice examines the trade-offs and decisions people make in their role as consumers as prices and their income changes.

## Price effects

These curves can be used to predict the effect of changes to the budget constraint. The graphic below shows the effect of a price increase for good Y. If the price of Y increases, the budget constraint will pivot from BC2 to BC1. Notice that because the price of X does not change, the consumer can still buy the same amount of X if he or she chooses to buy only good X. On the other hand, if the consumer chooses to buy only good Y, he or she will be able to buy less of good Y because its price has increased.

To maximize the utility with the reduced budget constraint, BC1, the consumer will re-allocate consumption to reach the highest available indifference curve which BC1 is tangent to. As shown on the diagram below, that curve is I1, and therefore the amount of good Y bought will shift from Y2 to Y1, and the amount of good X bought to shift from X2 to X1. The opposite effect will occur if the price of Y decreases causing the shift from BC2 to BC3, and I2 to I3.

link to shifting price of good y and quanity of goods consumed as a result

If these curves are plotted for many different prices of good Y, a demand curve for good Y can be constructed. The diagram below shows the demand curve for good Y as its price varies. Alternatively, if the price for good Y is fixed and the price for good X is varied, a demand curve for good X can be constructed.

example of going from indifference curves to demand curve

## Income effect

Another important item that can change is the income of the consumer. As long as the prices remain constant, changing the income will create a parallel shift of the budget constraint. Increasing the income will shift the budget constraint right since more of both can be bought, and decreasing income will shift it left.

link to shifting income of consumer and quntity of goods consumed as a result

Depending on the indifference curves the amount of a good bought can either increase, decrease or stay the same when income increases. In the diagram below, good Y is a normal good since the amount purchased increased as the budget constraint shifted from BC1 to the higher income BC2. Good X is an inferior good since the amount bought decreased as the income increases.

example of a normal good and an inferior good

is the change in the demand for good 1 when we change income from to , holding the price of good 1 fixed at :

## Price effect as sum of substitution and income effects

Every price change can be decomposed into an income effect and a substitution effect. The substitution effect is a price change that changes the slope of the budget constraint but leaves the consumer on the same equilibrium indifference curve. By this effect, the consumer is posited to substitute toward the good that becomes comparatively less expensive. If the good in question is a normal good, then the income effect from the rise in purchasing power from a price fall reinforces the substitution effect. If the good is an inferior good, then the income effect will offset in some degree the substitution effect. If the income effect for an inferior good is sufficiently strong, the consumer will buy less of the good when it becomes less expensive, a Giffen good (commonly believed to be a rarity).

example of substitution effect

In the figure, the substitution effect, , is the change in the amount demanded for when the price of good falls from to (increasing purchasing power for ) and, at the same time, the money income falls from to to keep the consumer at the same level of utility on :

The substitution effect increases the amount demanded of good from to . In the example, the income effect of the price fall in partly offsets the substitution effect as the amount demanded of goes from to . Thus, the price effect is the algebraic sum of the substitution effect and the income effect.

Consumer theory can also be used to analyze a consumer's choice between leisure and labor. Leisure is considered one good (often put on the horizontal-axis) and consumption is considered the other good. Since a consumer has a finite and scarce amount of time, she must make a choice between leisure (which earns no income for consumption) and labor (which does earn income for consumption).

The previous model of consumer choice theory is applicable with only slight modifications. First, the total amount of time that an individual has to allocate is known as her time endowment, and is often denoted as T. The amount an individual allocates to labor (denoted L) and leisure (l) is constrained by T such that:
:
or
:
A person's consumption is the amount of labor they choose multiplied by the amount they are paid per hour of labor (their wage, often denoted w). Thus, the amount that a person consumes is:
:
When a consumer chooses no leisure then and .

From this labor-leisure tradeoff model, the substitution and income effects of various changes in price caused by welfare benefits, labor taxation, or tax credits can be analyzed.

## References

• Volker Böhm and Hans Haller (1987). "Demand theory," The , v. 1, pp. 785-92.
• John R. Hicks (1939, 2nd ed. 1946). Value and Capital.

Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
Preference (or "taste") is a concept, used in the social sciences, particularly economics. It assumes a real or imagined "choice" between alternatives and the possibility of rank ordering of these alternatives, based on happiness, satisfaction, gratification, enjoyment, utility
An indifference curve in microeconomic theory is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another.
A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.
supply and demand describe market relations between prospective sellers and buyers of a good. The supply and demand model determines price and quantity sold in the market.
In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and quantitative relationships between them.
Mathematical problem may mean two slightly different things, both closely related to mathematical games:
general meaning
a question that can be answered with the help of mathematics ; formal meaning : any tuple (S, C( ), r

A hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena.
Purchasing power is the amount of value of a good/services compared to the amount paid. As Adam Smith noted, having money gives one the ability to "command" others' labor, so purchasing power to some extent is power over other people, to the extent that they are willing to trade their
An indifference curve in microeconomic theory is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another.
Income, generally defined, is the money that is received as a result of the normal business activities of an individual or a business.

Internationally, the accounting term income is synonymous to term revenue minus expenses.
In economics, utility is a measure of the relative satisfaction or desiredness from consumption of goods. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility.
Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate.
In consumer theory, an inferior good is a good that increases in demand when the consumers income falls, unlike normal goods, for which the opposite is observed. Inferiority, in this sense, is an observable fact rather than a statement about the quality of the good.
In economics, normal goods are any goods for which demand increases when income increases, i.e. with a positive income elasticity of demand. The term does not necessarily refer to the quality of the good.
In consumer theory, an inferior good is a good that increases in demand when the consumers income falls, unlike normal goods, for which the opposite is observed. Inferiority, in this sense, is an observable fact rather than a statement about the quality of the good.
A Giffen good is an inferior good for which a rise in its price makes people buy even more of the product as a consequence of the income effect. Evidence for the existence of Giffen goods is limited, but there is an economic model that explains how such a thing could exist.
A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.
Convex preferences refer to a property of utility functions commonly represented in an indifference curve as a bulge toward the origin for normal goods (for unwanted goods, the curve bulges away from the origin).
An indifference curve in microeconomic theory is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another.
Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold.
Price points are prices at which demand is relatively high. In introductory microeconomics, a demand curve is downward sloping to the right and either linear or gently convex to the origin.
supply and demand describe market relations between prospective sellers and buyers of a good. The supply and demand model determines price and quantity sold in the market.
In microeconomics, the utility maximization problem is the problem consumers face: "how should I spend my money in order to maximize my utility?"

Suppose their consumption set

has L commodities.
Value and Capital is a book by the British economist John Richard Hicks, published in 1939. It is considered a classic exposition of microeconomic theory. A central result in consumer-demand theory that the book builds on is that goods have value even with only ordinal