Marginal value
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Marginal value is a term widely used in economics, to refer to the change in economic value associated with a unit change in output, consumption or some other economic choice variable.
The concept of marginal value is similar to the mathematical concept of the derivative of a differentiable function, or to related concepts such as the arc derivative (slope of a secant line for more general functions).
Marginal Value is the maximum amount of one good you would give up to get one more unit of a different good. (Purdue University, 2008)
[edit] Mathematical formulation
In a functional relationship like y = f(x), where x is the independent variable and y is the dependent variable the marginal value of y is given by 
. In the case where x is a discrete variable, the marginal value of y will be the change in the value of y for a one unit change in the value of x.
For example, the utility function, in its simplest form, is provided by U = f(x), where U: the level of utility a consumer attains and x: the quantity of a good the consumer consumes. Here the marginal value of U will be called marginal utility (MU) and be expressed as MU = (Change in U)/(Change in x). In this case, the change in x represents a discrete one unit increase in consumption.
As another example consider the consumption function. In its simplest form, it is given by c = f(y), where c: level of consumption and y: level of income. In economic terms the marginal value of consumption is called the marginal propensity to consume (MPC). This will be given by MPC = (Change in consumption)/(Change in income).
For a linear functional relationship like y = a + bx, the marginal value of y will simply be the co-efficient of x (in this case, b) and this will not change as x changes. However, in the case where the functional relationship is non-linear, say y = abx, the marginal value of y will be different for different values of x.
