Chapter 2 Handouts What is a derivative

If total revenue were a linear function ie

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Unformatted text preview: ere 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: Graph of the function TR = 10Q – Q2 TR If Q = 2, TR = 10(2) – (2)2 = 20 – 4 = 16 If Q = 5, TR = 10(5) – (5)2 = 50 – 25 = 25 C 25 TR B 16 2 5 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...
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