Marginal Analysis

Marginal analysis A marginal change is a proportionally very small addition or subtraction to the total quantity of some variable. Marginal analysis is the analysis of the relationships between such changes in related economic variables. Important ideas developed in such analysis include marginal cost, marginal revenue, marginal product, marginal rate of substitution, marginal propensity to save, and so on. In microeconomic theory, marginal concepts are employed primarily to explicate various forms of optimizing behaviour. The Marginal Value is found by taking the first order derivative of the total quantity. Some important Marginal Concepts: Marginal Product of an input is the extra output that can be produced by using one more unit of the input, assuming that the quantities of no other inputs to production change. The marginal product of a given input can be expressed as

Where is the change in the firm's use of the input and output produced.

is the change in quantity of

If the output and the input are infinitely divisible, so the marginal units are infinitesimal, the marginal product is the mathematical derivative of the production function with respect to that input. Suppose a firm's output Y is given by the production function where K and L are inputs to production. Then the marginal product of capital and marginal product of labour are given by:

Marginal revenue is the additional revenue that will be generated by increasing product sales by 1 unit. Marginal revenue is equal to the ratio of the change in revenue for some change in quantity sold to that change in quantity sold. This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. .

By the product rule, marginal revenue is then given by .

Marginal propensity to save refers to the increase in saving that results from an increase in income i.e. the marginal propensity to save might be defined as the proportion of each additional dollar of household income that is used for saving.

Where, dS = Change in Savings and dY = Change in income. Marginal propensity to consume is the proportion of additional income that an individual desires to consume.

Where dC = change in consumption and dY = the change in disposable income that produced the consumption.

Optimisation Stationary Points For a continuous and differentiable function f(x) a stationary point x*is a point at which the first derivative of the function becomes 0, i.e. f ’(x) = 0 at x = x*. x*belongs to its domain of definition. A stationary point may be a minimum, maximum or an inflection point.

Figure showing the three types of stationary points (a) inflection point (b) minimum (c) maximum. Maxima & Minima The second derivative can be used to determine the nature of stationary points i.e. whether they are maximum points, minimum points or points of inflection. If d2y/ dx2 is positive, then it is a minimum point If d2y/ dx2 is negative, then it is a maximum point If d2y/ dx2 = zero then is point of inflexion Isoquants Isoquants are locus of points which give the combinations of 2 inputs, Labour and Capital which yield the same amount of output.

Characteristics of Isoquants: 1) They do not intersect. 2) Downward sloping, i.e. f’(x)<0 in the economically feasible region otherwise upward sloping, i.e. f’(x)>0 . 3) Convex to the origin, i.e. f”(x)>0 4) Marginal rate of technical substitution, which is also the slope is decreasing