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A) Example of an isoquant map with two inputs that are perfect substitutes. B) Example of an isoquant map with two inputs that are perfect complements. An isoquant (derived from quantity and the Greek word isos , ίσος , meaning "equal"), in microeconomics , is a contour line drawn through the set of points at which the same quantity of ...
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...
Created Date: 8/30/2012 4:52:52 PM
For example, if the MRS xy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X. As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases).
Liskov's notion of a behavioural subtype defines a notion of substitutability for objects; that is, if S is a subtype of T, then objects of type T in a program may be replaced with objects of type S without altering any of the desirable properties of that program (e.g. correctness).
Substitution, written M[x := N], is the process of replacing all free occurrences of the variable x in the expression M with expression N. Substitution on terms of the lambda calculus is defined by recursion on the structure of terms, as follows (note: x and y are only variables while M and N are any lambda expression): x[x := N] = N
However, in first-order logic, these two sentences may be framed as statements that a certain individual or non-logical object has a property. In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to ...