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This definition defines monotonic increasing preferences. Monotonic decreasing preferences can often be defined to be compatible with this definition. For instance, an agent's preferences for pollution may be monotonic decreasing (less pollution is better). In this case, the agent's preferences for lack of pollution are monotonic increasing.
Traditionally, comparative results in economics are obtained using the Implicit Function Theorem, an approach that requires the concavity and differentiability of the objective function as well as the interiority and uniqueness of the optimal solution. The methods of monotone comparative statics typically dispense with these assumptions.
The term monotonic transformation (or monotone transformation) may also cause confusion because it refers to a transformation by a strictly increasing function. 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 economics, a utility function is often used to represent a preference structure such that () if and only if. The idea is to associate each class of indifference with a real number such that if one class is preferred to the other, then the number of the first one is greater than that of the second one.
Given a utility function u(x,y), to calculate the MRS, one takes the partial derivative of the function u with respect to good x and divide it by the partial derivative of the function u with respect to good y. If the marginal rate of substitution is diminishing along an indifference curve, that is the magnitude of the slope is decreasing or ...
In mathematics, a homothetic function is a monotonic transformation of a function which is homogeneous; [2] however, since ordinal utility functions are only defined up to an increasing monotonic transformation, there is a small distinction between the two concepts in consumer theory. [1]: 147
Linear utilities functions are a small subset of Quasilinear utility functions. Goods with linear utilities are a special case of substitute goods. Suppose the set of goods is not finite but continuous. E.g., the commodity is a heterogeneous resource, such as land. Then, the utility functions are not functions of a finite number of variables ...
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter. [1] As a type of static analysis it compares two different equilibrium states, after the process of adjustment (if any). It does not study the motion towards equilibrium, nor the process of ...