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Chapter 2 Handouts What is a derivative

Chapter 2 Handouts What is a derivative - MBA 6651...

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MBA 6651 Differentiation: What is It? Dr. Wendy Bailey 1 In this class we’ll use marginal analysis by applying basic techniques of calculus (the concept of the derivative). The textbook does the derivatives for you, but you do need to understand the basic concept so you can work the problems and understand why things are done the way they are. We’ll use lots of “marginals” in this class – marginal revenue, marginal cost, marginal product, etc. These “marginals” are usually derived using calculus, so you need to understand a little about what a derivative means. Basically, a “marginal” is simply a slope or rate of change in something else – it tells us how a very small change in an independent variable impacts a dependent variable. A dependent variable is one that “depends” or is determined by the values of other “independent” variables. Let’s consider the case of total revenue. Total revenue is a function of the quantity produced – so total revenue is the dependent variable here and quantity is our independent variable. If total revenue were a linear function (i.e., represented by a straight line if graphed), the rate of change would be a constant, since straight lines have a constant slope. Most of the functions we’ll see in this class will not be linear, so that complicates matters since the slope or rate of change will be different at every single point on the line. Look at the graph below: TR C TR B Q Essentially, the marginal (e.g., marginal revenue) used in principles of economics classes measures the slope of a chord (“secant” line), as shown by the red line above between points B and C. When the quantity goes up from 2 to 5 units here, total revenue changes from $16 to $25. We could measure the marginal revenue by using the formula MR = change in TR / change in Q = (25 – 16)/(5 – 2) = $9/3 = $3.00 Technically, however, we are measuring the change in revenue associated with a one-unit increase in output in this range , rather than at one spot exactly. The formula we use measures the slope of the red
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