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53 relations: Affine variety, Algebraic expression, Algebraic geometry, Argument of a function, Binary relation, Calculus, Chain rule, Contour line, Cubic function, Demand curve, Derivative test, Differentiable manifold, Domain of a function, Economics, Function (mathematics), Functional equation, HarperCollins, Implicit curve, Implicit function theorem, Indifference curve, Inverse function, Isoquant, Isosurface, Labor demand, Labour supply, Lambert W function, Level set, Logarithmic differentiation, Marginal rate of substitution, Marginal rate of technical substitution, Mathematical analysis, Mathematics, McGraw-Hill Education, Multivalued function, Neighbourhood (mathematics), Parametrization, Partial derivative, Physical capital, Polygonizer, Polynomial, Profit (economics), Quadratic equation, Quartic function, Quintic function, Smoothness, Springer Science+Business Media, Submanifold, Supply (economics), Tangent space, Total derivative, ..., Unit circle, Utility, Value (mathematics). Expand index (3 more) »
Affine variety
In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine ''n''-space k^n of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal.
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Algebraic expression
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Argument of a function
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Contour line
A contour line (also isocline, isopleth, isarithm, or equipotential curve) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.
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Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
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Demand curve
In economics, the demand curve is the graph depicting the relationship between the price of a certain commodity and the amount of it that consumers are willing and able to purchase at any given price.
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Derivative test
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional equation
In mathematics, a functional equation is any equation in which the unknown represents a function.
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HarperCollins
HarperCollins Publishers L.L.C. is one of the world's largest publishing companies and is one of the Big Five English-language publishing companies, alongside Hachette, Macmillan, Penguin Random House, and Simon & Schuster.
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Implicit curve
In mathematics an implicit curve is a plane curve which is defined by an implicit equation relating the coordinate variables x and y. For example, the unit circle is defined by the implicit equation x^2+y^2.
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Implicit function theorem
In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables.
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Indifference curve
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Isoquant
An isoquant (derived from quantity and the Greek word iso, meaning equal) is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. While an indifference curve mapping helps to solve the utility-maximizing problem of consumers, the isoquant mapping deals with the cost-minimization problem of producers. Isoquants are typically drawn along with isocost curves in capital-labor graphs, showing the technological tradeoff between capital and labor in the production function, and the decreasing marginal returns of both inputs. Adding one input while holding the other constant eventually leads to decreasing marginal output, and this is reflected in the shape of the isoquant. A family of isoquants can be represented by an isoquant map, a graph combining a number of isoquants, each representing a different quantity of output. Isoquants are also called equal product curves. An isoquant shows that extent to which the firm in question has the ability to substitute between the two different inputs at will in order to produce the same level of output. An isoquant map can also indicate decreasing or increasing returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. Conversely, if the distance is decreasing as output increases, the firm is experiencing increasing returns to scale; doubling both inputs results in placement on an isoquant with more than twice the output of the original isoquant. As with indifference curves, two isoquants can never cross. Also, every possible combination of inputs is on an isoquant. Finally, any combination of inputs above or to the right of an isoquant results in more output than any point on the isoquant. Although the marginal product of an input decreases as you increase the quantity of the input while holding all other inputs constant, the marginal product is never negative in the empirically observed range since a rational firm would never increase an input to decrease output. An isoquants shows all those combinations of factors which produce same level of output. An isoquants is also known as equal product curve or iso-product curve.
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Isosurface
An isosurface is a three-dimensional analog of an isoline.
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Labor demand
In economics, the labor demand of an employer is the number of labor-hours that the employer is willing to hire based on the various exogenous (externally determined) variables it is faced with, such as the wage rate, the unit cost of capital, the market-determined selling price of its output, etc.
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Labour supply
In mainstream economic theories, the labour supply is the total hours (adjusted for intensity of effort) that workers wish to work at a given real wage rate.
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Lambert W function
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(z).
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Level set
In mathematics, a level set of a real-valued function ''f'' of ''n'' real variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline.
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Logarithmic differentiation
In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself.
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Marginal rate of substitution
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.
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Marginal rate of technical substitution
In microeconomic theory, the Marginal Rate of Technical Substitution (MRTS)—or Technical Rate of Substitution (TRS)—is the amount by which the quantity of one input has to be reduced (-\Delta x_2) when one extra unit of another input is used (\Delta x_1.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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McGraw-Hill Education
McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.
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Multivalued function
In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Parametrization
Parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.
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Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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Physical capital
In economics, physical capital or just capital is a factor of production (or input into the process of production), consisting of machinery, buildings, computers, and the like.
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Polygonizer
In computer graphics, a polygonizer is a software component for converting a geometric model represented as an implicit surface to a polygon mesh.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Profit (economics)
In economics, profit in the accounting sense of the excess of revenue over cost is the sum of two components: normal profit and economic profit.
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Quadratic equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
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Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
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Quintic function
In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Submanifold
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties.
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Supply (economics)
In economics, supply is the amount of something that firms, consumers, labourers, providers of financial assets, or other economic agents are willing to provide to the marketplace.
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Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
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Total derivative
In the mathematical field of differential calculus, a total derivative or full derivative of a function f of several variables, e.g., t, x, y, etc., with respect to an exogenous argument, e.g., t, is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Utility
Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time.
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Value (mathematics)
In mathematics, value may refer to several, strongly related notions.
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References
[1] https://en.wikipedia.org/wiki/Implicit_function
