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Introductory Mathematics and Statistics for Islamic Finance, + Website by Noureddine Krichene, Abbas Mirakhor

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Chapter 4Partial Derivatives

Economic and financial relations feature interdependence of many variables. For instance, the utility function of a consumer may include many products and is written as

(4.1) equation

where img, img, and img denote the quantities of oranges, tomatoes, and grape juice, respectively, consumed by the consumer. In economics, we are interested in how a dependent variable responds when only one variable in the relationship changes; the assumption of maintaining all other fixed variables is called the ceteris paribus condition. In this case we may be interested in computing the change in utility due to a change in the consumption of oranges, keeping the consumption of tomatoes and grape juice fixed. This rate of change is called the partial derivative of utility in respect to a change in oranges consumed. It is denoted as img to indicate it is a partial derivative. We call it marginal utility of oranges.

Likewise, any production process involves the interplay of many variables. Production ...

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