# 2 Most Important Concepts of Calculus in Managerial Economics

January 27, 2019 0 Comment

#### 1. Derivative:

Derivative is a measure of change in variable y for a very small change in variable x. usually, the English letter ‘d’ represents small change. Derivatives of a few functional forms are described below:

#### 2. Partial Derivative:

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. Algebraically, partial derivative of two variables (say, x and y), can be described as derivative of the function with respect to x (or y), holding (or x) constant.

Suppose a person is interested in prediction of demand for a particular product. There may be various factors that influence its demand like price of the product (P), advertising expenditure (A), income of the prospective customers (I) etc.

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Now, if the person wants to measure the rate of change in demand for the product as a result of change in only one variable out of the entire set of independent determinants of demand, he will have to use the tool called partial derivative.

Assume that demand D depends upon three variables P, A and I, i.e., D = ? (P, A, I). If the person wants to measure the effect of change in advertising expenditure only, keeping the other variables i.e., A and I, then the rate of change of D with respect to A only (holding P and I constant) is called the partial derivative of D with respect to A and is denoted by ?A (P, A, I). Similarly, partial derivative of D with respect to P and I are denoted by ?P (P, A, I) and fI (P, A, I).

Let f(x, y) be a function of two variables x and y. Then partial derivatives are defined as

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