Compensating Variation
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Compensating Variation
In economics, compensating variation (CV) is a measure of utility change introduced by John Hicks (1939). 'Compensating variation' refers to the amount of additional money an agent would need to reach their initial utility after a change in prices, a change in product quality, or the introduction of new products. Compensating variation can be used to find the effect of a price change on an agent's net welfare. CV reflects new prices and the old utility level. It is often written using an expenditure function, e(p,u): :CV = e(p_1, u_1) - e(p_1, u_0) : = w - e(p_1, u_0) : = e(p_0, u_0) - e(p_1, u_0) where w is the wealth level, p_0 and p_1 are the old and new prices respectively, and u_0 and u_1 are the old and new utility levels respectively. The first equation can be interpreted as saying that, under the new price regime, the consumer would accept ''CV'' in exchange for allowing the change to occur. More intuitively, the equation can be written using the value function, v(p, ...
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Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ...
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John Hicks
Sir John Richards Hicks (8 April 1904 – 20 May 1989) was a British economist. He is considered one of the most important and influential economists of the twentieth century. The most familiar of his many contributions in the field of economics were his statement of consumer demand theory in microeconomics, and the IS–LM model (1937), which summarised a Keynesian view of macroeconomics. His book ''Value and Capital'' (1939) significantly extended general-equilibrium and value theory. The compensated demand function is named the Hicksian demand function in memory of him. In 1972 he received the Nobel Memorial Prize in Economic Sciences (jointly) for his pioneering contributions to general equilibrium theory and welfare theory. Early life Hicks was born in 1904 in Warwick, England, and was the son of Dorothy Catherine (Stephens) and Edward Hicks, a journalist at a local newspaper. He was educated at Clifton College (1917–1922) and at Balliol College, Oxford (1922– ...
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Expenditure Function
In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods. Formally, if there is a utility function u that describes preferences over ''n '' commodities, the expenditure function :e(p, u^*) : \textbf R^n_+ \times \textbf R \rightarrow \textbf R says what amount of money is needed to achieve a utility u^* if the ''n'' prices are given by the price vector p. This function is defined by :e(p, u^*) = \min_ p \cdot x where :\geq(u^*) = \ is the set of all bundles that give utility at least as good as u^*. Expressed equivalently, the individual minimizes expenditure x_1p_1+\dots +x_n p_n subject to the minimal utility constraint that u(x_1, \dots , x_n) \ge u^*, giving optimal quantities to consume of the various goods as x_1^*, \dots x_n^* as function of u^* and the prices; then the expenditure function is :e(p_1, \dots , p_n ; u^*)=p ...
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Value Function
The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters of the problem. In a controlled dynamical system, the value function represents the optimal payoff of the system over the interval , t1/var> when started at the time-t state variable x(t)=x. If the objective function represents some cost that is to be minimized, the value function can be interpreted as the cost to finish the optimal program, and is thus referred to as "cost-to-go function." In an economic context, where the objective function usually represents utility, the value function is conceptually equivalent to the indirect utility function. In a problem of optimal control, the value function is defined as the supremum of the objective function taken over the set of admissible controls. Given (t_, x_) \in , t_\times \mathbb^, a typical optimal control problem is to : \text \quad J(t_, x_; u) = \int_^ I(t,x(t), u(t)) \, \mathr ...
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Equivalent Variation
Equivalent variation (EV) is a measure of economic welfare changes associated with changes in prices. John Hicks (1939) is attributed with introducing the concept of compensating and equivalent variation. The equivalent variation is the change in wealth, at current prices, that would have the same effect on consumer welfare as would the change in prices, with income unchanged. It is a useful tool when the present prices are the best place to make a comparison. The value of the equivalent variation is given in terms of the expenditure function (e(\cdot,\cdot)) as EV = e(p_0, u_1) - e(p_0, u_0) = e(p_0, u_1) - w where w is the wealth level, p_0 and p_1 are the old and new prices respectively, and u_0 and u_1 are the old and new utility levels respectively. Furthermore, if the wealth level does not change, e(p_0,u_0)=w=e(p_1,u_1) since under both old and new utility levels and prices, a consumer exhausts their Budget Constraint by Walras's law, so EV = e(p_0, u_1) - e(p_1 ...
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Normal Good
In economics, a normal good is a type of a Good (economics), good which experiences an increase in demand due to an increase in income, unlike inferior goods, for which the opposite is observed. When there is an increase in a person's income, for example due to a wage rise, a good for which the demand rises due to the wage increase, is referred as a normal good. Conversely, the demand for normal goods declines when the income decreases, for example due to a wage decrease or layoffs. Analysis There is a positive correlation between the income and demand for normal goods, that is, the changes income and demand for normal goods moves in the same direction. That is to say, that normal goods have an elastic relationship for the demand of a good with the income of the person consuming the good. In economics, the concept of elasticity, and specifically income elasticity of demand is key to explain the concept of normal goods. Income elasticity of demand measures the magnitude of the ...
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Inferior Good
In economics, an inferior good is a good whose demand decreases when consumer income rises (or demand increases when consumer income decreases), unlike normal goods, for which the opposite is observed. Normal goods are those goods for which the demand rises as consumer income rises. Inferiority, in this sense, is an observable fact relating to affordability rather than a statement about the quality of the good. As a rule, these goods are affordable and adequately fulfill their purpose, but as more costly substitutes that offer more pleasure (or at least variety) become available, the use of the inferior goods diminishes. Direct relations can thus be drawn from inferior goods to socio-economic class. Those with constricted incomes tend to prefer inferior goods for the reason of the aforementioned observable inferiority. Depending on consumer or market indifference curves, the amount of a good bought can either increase, decrease, or stay the same when income increases. Examples T ...
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Quasilinear Utility
In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function u(x_1, x_2, \ldots, x_n) = x_1 + \theta (x_2, \ldots, x_n) where \theta is strictly concave. A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for x_2, \ldots, x_n does not depend on wealth and is thus not subject to a wealth effect; The absence of a wealth effect simplifies analysis and makes quasilinear utility functions a common choice for modelling. Furthermore, when utility is quasilinear, compensating variation (CV), equivalent variation (EV), and consumer surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. Definition in terms of preferences A preference relation \succsim is quasilinear with respect to commodity 1 (called, in this case, the ''numeraire'' ...
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Consumer Surplus
In mainstream economics, economic surplus, also known as total welfare or total social welfare or Marshallian surplus (after Alfred Marshall), is either of two related quantities: * Consumer surplus, or consumers' surplus, is the monetary gain obtained by consumers because they are able to purchase a product for a price that is less than the highest price that they would be willing to pay. * Producer surplus, or producers' surplus, is the amount that producers benefit by selling at a market price that is higher than the least that they would be willing to sell for; this is roughly equal to profit (since producers are not normally willing to sell at a loss and are normally indifferent to selling at a break-even price). Overview In the mid-19th century, engineer Jules Dupuit first propounded the concept of economic surplus, but it was the economist Alfred Marshall who gave the concept its fame in the field of economics. On a standard supply and demand diagram, consumer su ...
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