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Positive economics as a science concerns the investigation of economic behavior. [4] It deals with empirical facts as well as cause-and-effect relationships. It emphasizes that economic theories must be consistent with existing observations and produce precise, verifiable predictions about the phenomena under investigation.
Engel's argument is formalized in neoclassical consumer theory, which conceives of the relationship between income and consumption patterns in terms of utility optimization. In such models, consumers allocate their expenditures to goods and services with the highest marginal utility. After basic needs are satiated, the marginal utility from ...
In economics, a normal good is a type of a 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.
This follows from the fact that at the optimal solution the gradient of the objective function is a linear combination of the constraint function gradients with the weights equal to the Lagrange multipliers. Each constraint in an optimization problem has a shadow price or dual variable.
This is the case in economics with respect to the ordinal properties of a utility function being preserved across a monotonic transform (see also monotone preferences). [5] In this context, the term "monotonic transformation" refers to a positive monotonic transformation and is intended to distinguish it from a "negative monotonic ...
The Lorenz curve is invariant under positive scaling. If X is a random variable, for any positive number c the random variable c X has the same Lorenz curve as X. The Lorenz curve is flipped twice, once about F = 0.5 and once about L = 0.5, by negation. If X is a random variable with Lorenz curve L X (F), then −X has the Lorenz curve:
An economic theory that defines wealth by the amount of precious metals owned. [48] business cycle. Also called the economic cycle or trade cycle. The downward and upward movement of gross domestic product (GDP) around its long-term growth trend. [49] The length of a business cycle is the period of time containing a single boom and contraction ...
The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.