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The midpoint method computes + so that the red chord is approximately parallel to the tangent line at the midpoint (the green line). In numerical analysis , a branch of applied mathematics , the midpoint method is a one-step method for numerically solving the differential equation ,
Shephard's lemma is a result in microeconomics having applications in the theory of the firm and in consumer choice. [1] The lemma states that if indifference curves of the expenditure or cost function are convex , then the cost-minimizing point of a given good ( i {\displaystyle i} ) with price p i {\displaystyle p_{i}} is unique.
Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...
Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve (more precisely, to the slope multiplied by −1) passing through the consumption bundle in question, at that point: mathematically, it ...
The Curriculum Open-Access Resources in Economics Project (CORE Econ) is an organisation that creates and distributes open-access teaching material on economics. The goal is to make teaching material and reform the economics curriculum. [1] Its textbook is taught as an introductory course at almost 500 universities. [2]
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
In 2008 economist Andrew Naganoff (Russian: Эндрю Наганов) proposed an integral form of the equation of exchange, where on the left side of the equation is () under the integral sign, and on the right side is a sum from i=1 to .
[3] Jan Tinbergen is one of the two founding fathers of econometrics. [4] [5] [6] The other, Ragnar Frisch, also coined the term in the sense in which it is used today. [7] A basic tool for econometrics is the multiple linear regression model. [8] Econometric theory uses statistical theory and mathematical statistics to evaluate and develop ...
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