# X ap l l tp l kg kgl day l days average product of

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X = AP L L [TP L (kg) = (kg/L-day) L-days] Average Product of Labour : AP L = TP L / L Q X / L [AP L (kg/labour-day)] Marginal Product of Labour : MP L = ∆TP L /∆ L Q x /∆ L [MP L (kg/labour-day)] INPUT MARKET 4. Total Revenue Product of Labour : TRP L P X Q X = ARP L L [TRP L (\$) = (\$/kg)(kg) = (\$/L-day) L-days] Average Revenue Product of Labour : ARP L = P X AP L = TRP L / L P X Q X / L [ARP L (\$/L-day) = (\$/kg)(kg/L-day)] Marginal Revenue Product of Labour : MRP L = ∆TRP L /∆ L = MR MP L [MRP L (\$/labour-day) = (\$/kg)(kg/labour-day)] 5. Total Factor Cost of Labour : TFC L P L Q L = AFC L L [TFC L (\$) = (\$/kg)(kg) = (\$/L-day) L-days] Average Factor Cost of Labour : AFC L = P L = TFC L / Q L [AFC L (\$/L-day) = (\$)/(L- days)] Marginal Factor Cost of Labour : MFC L = ∆TFC L / ∆Q L = MC MP L =(∆TC/∆ Q X ) (∆ Q x / ∆L ) [MFC L (\$/labour-day) = (\$/kg)(kg/labour- day)] 1.2 AN IMPORTANT SPECIAL CASE: LINEAR AVERAGE AND MARGINAL CURVES In general, there is no reason to assume that the functions with which economists are concerned, such as the average and marginal functions we outlined in Section 1.1 of this Module, are in fact linear. We use linear functions so frequently in our illustrations and examples basically because of their mathematical simplicity. Using them, we can often understand fairly difficult points in economic theory without requiring any more math- ematics than high school algebra. We do need to be alert to the fact that in some cases, results that are valid for linear functions do not necessarily hold if the functions have a more general, nonlinear form. But we will still continue to use linear functions exten- sively, because they have a relatively high economics-to-mathematics ratio. It is therefore important to understand clearly the relationships among linear aver- age and marginal curves and the quadratic total curves to which they correspond. We will focus here on an example based on a demand curve for a good, but the rules we derive apply to all of the sets of functions outlined in Subsection 1.1 of this Module. M5-2 MATH MODULE 5: TOTAL, AVERAGE, AND MARGINAL FUNCTIONS

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MATH MODULE 5: TOTAL, AVERAGE, AND MARGINAL FUNCTIONS M5-3 These basic rules are also discussed at a number of points in your text, including page 349, footnote 14; pages 364-5, Figures 12-7 and 12-8; and (as they relate to elasticity), page 115, Figure 4-23 and page 595, Figure A.4-1. Consider the demand curve with the form P = 10 – Q , data for which are in Table M.5-1. Total Revenue is given by TR = P Q = (10 – Q ) Q = 10 Q Q 2 . Total revenue, as Table M.5-1 and Figure M.5-1 show, thus has a quadratic form: its graph is a parabo- la opening downward, with a peak or maximum value of \$25 when Q = 5 kg, and a value of 0 at Q = 0 and Q =10.
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