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^{[ citation needed ]} 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 happiness 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 single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and is based on choice rather than on the pleasure received, and so is more rigorously specified than the original concept but makes it less useful for ethical decisions.

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.

The theory of **consumer choice** is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption as measured by their preferences subject to limitations on their expenditures, by maximizing utility subject to a consumer budget constraint.

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.

In microeconomics, the **law of demand** is a fundamental principle which states that there is an inverse relationship between price and quantity demanded. In other words, "conditional on all else being equal, as the price of a good increases **(↑)**, quantity demanded will decrease **(↓)**; conversely, as the price of a good decreases **(↓)**, quantity demanded will increase **(↑)**". Alfred Marshall worded this as: "When then we say that a person's demand for anything increases, we mean that he will buy more of it than he would before at the same price, and that he will buy as much of it as before at a higher price". The law of demand, however, only makes a qualitative statement in the sense that it describes the direction of change in the amount of quantity demanded but not the magnitude of change.

In economics, an **ordinal utility** function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask *how much* better it is or how good it is. All of the theory of consumer decision-making under conditions of certainty can be, and typically is, expressed in terms of ordinal utility.

There are two **fundamental theorems of welfare economics**. The **first** states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal. The requirements for perfect competition are these:

- There are no externalities and each actor has perfect information.
- Firms and consumers take prices as given.

In cooperative game theory, the **core** is the set of feasible allocations that cannot be improved upon by a subset of the economy's agents. A coalition is said to *improve upon* or *block* a feasible allocation if the members of that coalition are better off under another feasible allocation that is identical to the first except that every member of the coalition has a different consumption bundle that is part of an aggregate consumption bundle that can be constructed from publicly available technology and the initial endowments of each consumer in the coalition.

**Walras's law** is a principle in general equilibrium theory asserting that budget constraints imply that the *values* of excess demand must sum to zero regardless of whether the prices are general equilibrium prices. That is:

The property of **local nonsatiation** of consumer preferences states that for any bundle of goods there is always another bundle of goods arbitrarily close that is preferred to it.

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.

**Competitive equilibrium** is a concept of economic equilibrium introduced by Kenneth Arrow and Gérard Debreu in 1951 appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated.

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". Preferences are evaluations, they concern matters of value, typically in relation to practical reasoning. 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. Rationality suggests that people act in ways which serves their best interest when they are faced with a decision. Meaning when given a set of options, you must necessarily have a set of preferences.

A **Robinson Crusoe economy** is a simple framework used to study some fundamental issues in economics. It assumes an economy with one consumer, one producer and two goods. The title "Robinson Crusoe" is a reference to the 1719 novel of the same name authored by Daniel Defoe.

In microeconomics, an **excess demand function** is a function expressing excess demand for a product—the excess of quantity demanded over quantity supplied—in terms of the product's price and possibly other determinants. It is the product's demand function minus its supply function. In a pure exchange economy, the excess demand is the sum of all agents' demands minus the sum of all agents' initial endowments.

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 Andres Carvajal. 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.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.