See M. H. Dobb, Theories of Value and Distribution Since Adam Smith (1975); M. Allingham, Value (1983); B. Fine, ed., The Value Dimension (1986).
Government levy on the amount a firm adds to the price of a goods or services as value is added—that is, at each step of their production and distribution. In the most common method of calculation, the seller subtracts the sum of taxes paid on items being purchased from the sum of all taxes that have been collected on the items being sold; the net tax liability is the difference between the tax collected and the tax paid. The burden of the value-added tax, like that of other sales taxes, tends to be passed on to the consumer. To limit the VAT's regressiveness, most countries set lower rates for consumer necessities than for luxury items. In 1954 France became the first country to adopt the value-added tax on a large scale. Though complex to calculate, the tax served as an improvement on earlier systems by which a product was taxed repeatedly at every stage of production and distribution. It has since been adopted throughout much of Europe and in many countries in South America, Asia, and Africa. All European Union member countries have a VAT. Seealso regressive tax.
Learn more about value-added tax (VAT) with a free trial on Britannica.com.
Philosophical theory of value. Axiology is the study of value, or goodness, in its widest sense. The distinction is commonly made between intrinsic and extrinsic value—i.e., between that which is valuable for its own sake and that which is valuable only as a means to something else, which itself may be extrinsically or intrinsically valuable. Many different answers have been given to the question “What is intrinsically valuable?” For hedonists, it is pleasure; for pragmatists, it is satisfaction, growth, or adjustment; for Kantians, it is a good will. Pluralists such as G.E. Moore and William David Ross assert that there are any number of intrinsically valuable things. According to subjective theories of value, things are valuable only insofar as they are desired; objective theories hold that there are at least some things that are valuable independently of people's interest in or desire for them. Cognitive theories of value assert that ascriptions of value function logically as statements of fact, whereas noncognitive theories assert that they are merely expressions of feeling (see emotivism) or prescriptions or commendations (see prescriptivism). According to naturalists, expressions such as “intrinsically good” can be analyzed as referring to natural, or non-ethical, properties, such as being pleasant. Moore famously denied this, holding that “good” refers to a simple (unanalyzable) non-natural property. Seealso fact-value distinction; naturalistic fallacy.
Learn more about axiology with a free trial on Britannica.com.
In mathematics, two theorems, one associated with differential calculus and one with integral calculus. The first proposes that any differentiable function defined on an interval has a mean value, at which a tangent line is parallel to the line connecting the endpoints of the function's graph on that interval. For example, if a car covers a mile from a dead stop in one minute, it must have been traveling exactly a mile a minute at some point along that mile. In integral calculus, the mean value of a function on an interval is, in essence, the arithmetic mean (see mean, median and mode) of its values over the interval. Because the number of values is infinite, a true arithmetic mean is not possible. The theorem shows how to find the mean value using a definite integral. Seealso Rolle's theorem.
Learn more about mean-value theorems with a free trial on Britannica.com.
In mathematical analysis, one of a set of discrete values of a parameter, math.k, in an equation of the form math.Lx = math.kx. Such characteristic equations are particularly useful in solving differential equations, integral equations, and systems of equations. In the equation, math.L is a linear transformation such as a matrix or a differential operator, and x can be a vector or a function (called an eigenvector or eigenfunction). The totality of eigenvalues for a given characteristic equation is a set. In quantum mechanics, where math.L is an energy operator, the eigenvalues are energy values.
Learn more about eigenvalue with a free trial on Britannica.com.