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Isoelastic Function
In mathematical economics, an isoelastic function, sometimes constant elasticity function, is a function that exhibits a constant elasticity, i.e. has a constant elasticity coefficient. The elasticity is the ratio of the percentage change in the dependent variable to the percentage causative change in the independent variable, in the limit as the changes approach zero in magnitude. For an elasticity coefficient r (which can take on any real value), the function's general form is given by : f(x) = , where k and r are constants. The elasticity is by definition :\text = \frac \frac = \frac , which for this function simply equals ''r''. Derivation Elasticity of demand is indicated by = \frac \frac , where r is the elasticity, Q is quantity, and P is price. Rearranging gets us: \frac = \frac Then integrating \int\frac =\int \frac r \ln(P) + C = \ln(Q) Simplify e^ = e^ (e^)^re^C = Q CP^r = Q Q(p) = kP^r Examples Demand functions An example in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
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. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
