When we spend this 6week we can purchase 6wk 2kg 3

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When we spend this $6/week, we can purchase ($6/wk) ÷ ($2/kg) = 3 additional kgs of X per week. [Notice that the mathematical cancellation of the $s corresponds to the actual “cancellation” of the money as we go from Y to $ to X .] The numerical value of the slope of the budget line is –1/3, and it is measured in cases/kg . Example 7: Why Total Revenue is Sometimes Measured as an Area, and Sometimes as the Height of a Line 48 TR ($/period) Q (kg/period) P ($/kg) Q (kg/period) Slope = 48 = 6 ($/kg) 8 16 32 64 0 TR 8 0 32 6 8 8 FIGURE M.4-3
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This question is touched on in Module 5, but it is useful to review it here as well, in the context of using economic units. In Figure M.4-3, the upper diagram contains the graph of a Total Revenue (TR) function with the equation TR = P x Q D = 8 Q D – 0.25( Q D ) 2 . Directly below it is the corresponding demand curve, which has the equation P = TR/ Q D = 8 – 0.25 Q D . Total Revenue TR is measured in $/period, Q D is in kg/period, and P is in $/kg. Let’s compare the two parts of the diagram when Q D = 8 kg/period. In the lower dia- gram, we see that this corresponds to a price of $6/kg. At this point, Total Revenue TR = P Q D = ($6/kg) (8 kg/period) = (6 8)[($/kg) (kg/period)] = (48)($/period) = $48/period, since the kgs cancel. This corresponds to the shaded area in the lower dia- gram. In the upper diagram, the vertical axis is measured in $/period, and so when Q D = 8 kg/period, TR is the height of the TR function, 48 units above the origin. What is the slope of the ray or straight line from the origin to the point (8, 48)? Slope = Rise/Run = TR/ Q D = ($48/period)/(8 kg/period) = 6($/kg) = P , since the “periods” cancel out. So the slope of the ray from the origin is equal to 6 in numerical value, and the units in which it is measured are $/kg . In short, there is no real puzzle, provided that we keep track of the units in which the variables are measured. Example 8: Input Markets, Output Markets, and Profit-Maximizing Production [This Example relates to material contained in Chapters 9-12 and 14 of the text. You may want simply to skip it for now, if you are working through the Module near the start of the course.] In our experience, this topic is one of the more challenging ones for students of microeconomics, even at the intermediate level. There are two main reasons. First, it is reasonably difficult. Second, and of equal importance, it is typically accompanied by a small tidal wave of new concepts, definitions, and notation. Yet the basic idea is fairly simple. A profit-maximizing firm purchases inputs , combines the inputs to produce outputs , and sells the outputs . A given combination of inputs produces a certain level of outputs. The firm must choose the level of inputs (and hence the corresponding level of outputs) that maximizes its profits. The “decisions” on inputs and outputs are in fact a single decision. The profit-maximizing level of inputs purchased produces the profit-maxi- mizing level of outputs sold.
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