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Analogously point b is dened by the coor dinates 8 4

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units above (“north of”) the horizontal axis. Analogously, point B is de±ned by the coor- dinates (8, 4). We call point C (0, 12), where the function cuts (or intersects ) the vertical axis, the vertical intercept , and point H (12, 0), where the function cuts (or intersects ) the horizontal axis, the horizontal intercept . Figure M.1-2(b) gives the signs of the coordinates in all four quadrants of the plane and along the two axes. In the southwest quadrant, for example, both x and y coordi- nates are negative, while in the southeast quadrant, the x coordinate is positive and the y coordinate is negative. [Negative values can have economic signi±cance. For instance, inputs into production are treated as “negative outputs” in economic activity analysis. And a person could say, “I would be prepared to pay a price of minus $2 for a Barry Manilow CD,” meaning that she would accept it only if it were not only free but also accompanied by a toonie.] As an exercise, you may want to plot the following 6 points on a 4-quadrant graph, and then compare them with the corresponding ones in Figure M.1-2(a): (4, –8), (–4, 8), (–4, –8), (8, –4), (–8, 4), and (–8, –4). 1.3 TYPES OF FUNCTIONS We can categorize the functions economists use in several ways. 1.3.1 One basic way relates to whether they are increasing, decreasing, constant, or increas- ing-and-decreasing (or decreasing-and-increasing ) . Figure M.1-3 shows examples of each type. Implicitly, when we speak of an “ increasing function,” we mean that the value of the function ( y ) increases as we move from left to right , to higher values of x. Figure M.1-3(a) depicts what mathematicians call a “ monotonically strictly increasing ” function: English translation, it has a positive slope throughout. In contrast, Figure M.1-3(b) depicts a monotonically strictly decreasing ” function: it has a negative slope throughout. Suppose that a function is never negatively sloped, but that it does have a horizontal portion. We can call it a “ non-decreasing function.” The constant (or horizontal) function in Figure M.1-3(c) can be described as simultaneously non-increasing and non-decreasing. Figure M.1-3(d) shows a (non-monotonic) decreasing-and-increasing function. You have already encountered all of these types of function in your introductory eco- nomics course, and you will see them all again. Figure M.1-3(a) could represent a sup- ply curve or a Total Cost function. Figure M.1-3(b) could be a demand curve, or a (not very well-behaved) production possibilities frontier, or a marginal physical product curve. Figure M.1-3(c) could be a perfectly elastic supply or demand curve, or the long- run average cost curve for an industry characterized by constant costs. And Figure M.1- 3(d) could be a marginal, average variable or average total cost curve. In each case, the mathematical properties of the function remain the same, but the economic interpretations will often be quite different.
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