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# Indifference curve

In microeconomics, an indifference curve is a graph showing combinations of two goods to which an economic agent (such as a consumer or firm) is indifferent, that is, it has no preference for one over the other. They are used to analyse the choices of economic agents.

For example, if a consumer was equally satisfied with 1 apple and 4 bananas, 2 apples and two bananas, or 5 apples and 1 banana, these combinations would all lie on the same indifference curve.

For a given pair of goods, many indifference curves can be drawn. The consumer is generally assumed to prefer combinations of goods representing higher levels of consumption. The rational consumer will make choices between the two goods to reach the highest indifference curve feasible given the choices available to her.

The theory of indifference curves was developed by Vilfredo Pareto and others in the first part of the 20th century. The theory was developed so that analysis of economic choices could be based upon preferences, which can be observed, rather than the older concept of utility which suffers from the disadvantage that it cannot be objectively measured.

## Indifference Curve Properties

Indifference curves are typically assumed to have the following features:

### Assumptions

These properties follow mathematically from the first three of the following list of assumptions. These assumptions, which are troublesome, are made in conceiving of indifference curves and demand functions:

Completeness: This assumption rests on the assertions that choice-makers have (1) infinite knowledge not just about the details of any apparent options, but about all (other) existing possibilities, and how much they would cost (including all implicit costs not reflected in the price), and (2) infinite knowledge about the set of factors which affect the personal satisfaction inherent in the option. This is thus subject to another selection problem: the total utility of a given choice depends on how many tangible and intangible factors one takes into account. Does one want to know how a commodity was made, who or what was destroyed by its production, or what the alternatives might have been, given that such knowledge will likely affect the object's desirability (utility)? Since not buying something but rather waiting for a future alternative (which might radically change the attractiveness of existing options) is always one option, the current utility is not even theoretically assessable. All these (thoroughly impossible) conditions would together mean that every pair of options has a unique ordering of utility.

Transitivity: Essentially, this says the pair ordering above extends to more than two options and is unique.

Non-satiation: This is the idea that people always want more --- not of something, but of everything and anything! This has elsewhere been called the philosophy of the cancer cell. Non-satiation is frequently relaxed when the specifics of the market show that this is the case.

Satiation: The marginal value a person gets from each commodity falls with the number of units. This is also called convexity. If one has much of something, one is not very happy with even more (but, according to the previous assumption, still a little).

Robotic behaviour: This seems separate from the other "rationality" criteria above. This is the assumption that a consumer not only can order options according to preference, but acts on such a utility-based rationale rather than, say, primarily out of habit or subject to an influence like "training" (e.g. due to marketing). In other words, the relationship between "utility" and effective "preference" is quietly assumed, in contradiction to what any psychologist or advertising agent knows. In reality, people making choices are well aware that they are not acting on the sum of their knowledge, but rather on habit, bias, and impulse as well. Consumers do not make their purchase decisions all at once, and thus do not have a "budget line" for most decisions. This "irrationality" applies to mass behaviour (subject to "fashion") even more than it does to individuals. Note however that a preference based on habit, bias or fashion does not necessarily contradict the theory.

Independence of budget and desires: It is assumed that consumers do not have control over the amount of their income. In reality, many people are in a position to earn extra income when they need to purchase something big, and to emphasize work which does not earn monetary compensation when they have enough.

Independence of purchase choices from non-monetary choices: More generally, since the given formalism is used to represent money-transactions only --- i.e. in the context of a market --- there is an assumption that a consumer's set of choices which concern monetary costs is entirely independent from the set of choices which do not have any cost involved. Instead, humans are social beings and thus use heuristics such as morality and social influence to make these decisions. If this is true, the rational choice theory cannot be repaired with any perturbation; it is simply inapplicable.

## Example Indifference Curves

Below is an example of three indifference curves:

The consumer would rather be on I3 than I2, and would rather be on I2 than I1, but does not care where they are on each indifference curve. The slope of an indifference curve, known by economists as the marginal rate of substitution, shows the rate at which consumers are willing to give up one good in exchange for more of the other good. For most goods the marginal rate of substitution is not constant so their indifference curves are curved. The curves are convex to the origin indicating a diminishing marginal rate of substitution.

If the goods are perfect substitutes then the indifference curves will be parallel lines since the consumer would be willing to trade at a fixed ratio. The marginal rate of substitution is constant.

If the goods are perfect complements then the indifference curves will be angled. An example would be something like if you had a cookie recipe that called for 3 cups flour to 1 cup sugar. No matter how much extra flour you had, you still could not reach a higher cookie level if there was not enough sugar. Another example of perfect complements is a left shoe and a right shoe. The consumer is no better off having several right shoes if she has only one left shoe. Additional right shoes have zero marginal utility without more left shoes. The marginal rate of substitution is either zero or infinite.

Consumer theory uses indifference curves and budget constraints to produce consumer demand curves.