Marginal value

A marginal value is the change in a value associated with a specific change in some independent variable, or (when both variables are quantified) the ratio of these changes. These uses of the term “marginal” are especially common in economics, and result from conceptualizing constraints as a border or margin.

In the case of differentiability, at the limit, a marginal value is a mathematical differential, or the corresponding mathematical derivative.

Mathematical formulation

In a functional relationship such as $y=f(x)$, where $x$ is the independent variable and $y$ is the dependent variable the marginal value of $y$ is given by $dy/dx$. 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 $y=ab^{x}$, the marginal value of $y$ will be different for different values of $x$.

See also

• Marginal concepts