Example 4 we now return to example 2 with one change

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Example 4: We now return to Example 2, with one change. Price is still in $/kg, but the horizontal scale is now in tonnes . If we sell 4 tonnes at $3/kg, what are our total rev- enues? To find out, we need to convert tonnes to kilograms: TR = P x Q =($3/kg) (4 tonnes 1000 kg/tonne) = (3 x 4 1000)[($/kg) tonnes (kg/tonne)] = (12,000)[($/kg) kg] = (12,000)($) = $12,000. M4-2 MATH MODULE 4: USING ECONOMIC UNITS
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MATH MODULE 4: USING ECONOMIC UNITS M4-3 Of course you probably did all of these calculations in your head, because the exam- ples are fairly straightforward. With more complicated transformations, however, it pays to keep track of the units systematically. Moreover, keeping the units in mind can help resolve some of the more important basic difficulties that students encounter in the early stages of mastering economics. Finally, and perhaps most important, keeping a firm grasp on the units is one of the best ways of increasing your theoretical capacity and your economic intuition. If you know the units in which your variables are mea- sured, it is much easier to translate from economics into mathematics and back. Hence the number-crunching is not just an abstract operation but becomes a representation of the actual economic processes you are analyzing. The next set of examples provides you with some practical tips for utilizing eco- nomic units effectively. Example 5: Stock and Flow Variables and the Time Dimension: Both stock and flow variables are important in economics. Population censuses, inventories and balance sheets pertain to a moment in time . They involve “taking stock” of the population, the physical assets of a firm, and the assets and liabilities of a firm, respectively, at that moment. They are stock variables, and their time dimension is zero. In contrast, the com- ponents of Gross Domestic Product (private consumption and investment, government consumption and investment, and net exports), or births, deaths, immigration and emi- gration, or the volume of sales of a particular good, are flow variables. They are mea- sured with reference to a particular period or duration of time. You will notice that in the early chapters of the text, supply and demand are explicit- ly specified with reference to a particular period, say a day or a week or a month. Even when the time period is not explicitly mentioned, however, supply and demand curves implicitly involve a flow of goods within a specific period of given duration. If you con- sume 1 pizza per week, you consume almost exactly 52 pizzas per year (52.143, or 52.286 in leap years). Consider the following linear demand curve, which represents the demand for a good over the period of a year, in which the ceteris paribus assumption holds, price P is measured in $/kg, and quantity demanded is measured in kg/year: Annual demand : P = 78 – 1/24 Q D . If P = 0, then Q D = 1872 kg/year. If there are 12 months in a year (abstracting from the fact that some months are longer than others), then on average we have: Monthly demand : P = 78 – 1/2 Q D . If P = 0, then Q D = 156 kg/month. Note that 156 kg is 1/12 of 1872 kg/year, and the slope of the demand curve expressed on a monthly basis is hence 12 times as steep as the “annual” curve.
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