In economics, the **throw away paradox** is a situation in which a person can gain by throwing away some of his property. It was first described by Robert J. Aumann and B. Peleg^{ [1] } as a note on a similar paradox by David Gale.^{ [2] }

There is an economy with two commodities (x and y) and two traders (e.g. Alice and Bob).

- In one situation, the initial endowments are (20,0) and (0,10), i.e, Alice has twenty units of commodity x and Bob has ten units of commodity y. Then, the market opens for trade. In equilibrium, Alice's bundle is (4,2), i.e, she has four units of x and two units of y.
- In the second situation, Alice decides to discard half of her initial endowment - she throws away 10 units of commodity x. Then, the market opens for trade. In equilibrium, Alice's bundle is (5,5) - she has more of
*every*commodity than in the first situation.

The paradox happens in the following situation. Both traders have the same utility function with the following characteristics:

- It is a homothetic utility function.
- The slope of the indifference curves at is -1.
- The slope of the indifference curves at is -1/8.

One such function is , where is a certain parameter between 0 and 1, but many other such functions exist.

The explanation for the paradox is that when the quantity of x decreases, its price increases, and the increase in price is more than sufficient to compensate Alice for the decrease in quantity.

Within economics, the concept of **utility** is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or satisfaction within the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a **utility function** that represents a consumer's preference ordering over a choice set. Utility has thus become a more abstract concept, that is not necessarily solely based on the satisfaction/pleasure received.

In economics, an **indifference curve** connects points on a graph representing different quantities of two goods, points between which a consumer is *indifferent*. That is, any combinations of two products indicated by the curve will provide the consumer with equal levels of utility, and the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come. The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles.

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In economics, the **marginal rate of substitution** (**MRS**) is the rate at which a consumer can give up some amount of one good in exchange for another good while maintaining the same level of utility. At equilibrium consumption levels, marginal rates of substitution are identical. The marginal rate of substitution is one of the three factors from marginal productivity, the others being marginal rates of transformation and marginal productivity of a factor.

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In economics, **convex preferences** are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions.

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In economics and other social sciences, **preference** is the order that a person gives to alternatives based on their relative utility, a process which results in an optimal "choice". Instead of the prices of goods, personal income, or availability of goods, the character of the preferences is determined purely by a person's tastes. However, persons are still expected to act in their best interest.

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The * Journal of Mathematical Economics* is a bimonthly peer-reviewed academic journal of mathematical economics published by Elsevier. It covers work in economic theory which expresses economic ideas using formal mathematical reasoning. The journal was established in 1974, with Werner Hildenbrand as the founding editor-in-chief. The current editor-in-chief is Atsushi Kajii. According to the

In economics and consumer theory, a **linear utility function** is a function of the form:

Efficiency and fairness are two major goals of welfare economics. Given a set of resources and a set of agents, the goal is to divide the resources among the agents in a way that is both Pareto efficient (PE) and envy-free (EF). The goal was first defined by David Schmeidler and Menahem Yaari. Later, the existence of such allocations has been proved under various conditions.

**Resource monotonicity** is a principle of fair division. It says that, if there are more resources to share, then all agents should be weakly better off; no agent should lose from the increase in resources. The RM principle has been studied in various division problems.

In theoretical economics, an **abstract economy** is a model that generalizes both the standard model of an exchange economy in microeconomics, and the standard model of a game in game theory. An *equilibrium* in an abstract economy generalizes both a Walrasian equilibrium in microeconomics, and a Nash equilibrium in game-theory.

- ↑ Aumann, R.J.; Peleg, B. (1974). "A note on Gale's example".
*Journal of Mathematical Economics*.**1**(2): 209. doi:10.1016/0304-4068(74)90012-3. - ↑ Gale, David (1974). "Exchange equilibrium and coalitions".
*Journal of Mathematical Economics*.**1**: 63–66. doi:10.1016/0304-4068(74)90036-6.

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