= AP
L
3
L
[TP
L
(kg) = (kg/Lday)
3
Ldays]
Average Product of Labour
: AP
L
= TP
L
/
L
≡
Q
X
/
L
[AP
L
(kg/labourday)]
Marginal Product of Labour
: MP
L
= ∆TP
L
/∆
L
≡
∆
Q
x
/∆
L
[MP
L
(kg/labourday)]
INPUT MARKET
4.
Total Revenue Product of Labour
: TRP
L
≡
P
X
3
Q
X
= ARP
L
3
L
[TRP
L
($) = ($/kg)(kg) = ($/Lday)
3
Ldays]
Average Revenue Product of Labour
: ARP
L
= P
X
3
AP
L
= TRP
L
/
L
≡
P
X
3
Q
X
/
L
[ARP
L
($/Lday) = ($/kg)(kg/Lday)]
Marginal Revenue Product of Labour
: MRP
L
= ∆TRP
L
/∆
L
= MR
3
MP
L
[MRP
L
($/labourday) = ($/kg)(kg/labourday)]
5.
Total Factor Cost of Labour
: TFC
L
≡
P
L
3
Q
L
= AFC
L
3
L
[TFC
L
($) = ($/kg)(kg) = ($/Lday)
3
Ldays]
Average Factor Cost of Labour
: AFC
L
=
P
L
= TFC
L
/
Q
L
[AFC
L
($/Lday) = ($)/(L
days)]
Marginal Factor Cost of Labour
: MFC
L
= ∆TFC
L
/
∆Q
L
= MC
3
MP
L
=(∆TC/∆
Q
X
)
3
(∆
Q
x
/
∆L
) [MFC
L
($/labourday) = ($/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 dif±cult 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 economicstomathematics 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.
M52
MATH MODULE 5: TOTAL, AVERAGE, AND MARGINAL FUNCTIONS
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M53
These basic rules are also discussed at a number of points in your text, including page
349, footnote 14; pages 3645, Figures 127 and 128; and (as they relate to elasticity),
page 115, Figure 423 and page 595, Figure A.41.
Consider the demand curve with the form
P =
10 –
Q
, data for which are in Table
M.51. Total Revenue is given by TR =
P
3
Q
= (10 –
Q
)
3
Q
= 10
Q
–
Q
2
. Total revenue,
as Table M.51 and Figure M.51 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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 Fall '12
 Danvo
 Microeconomics, marginal functions

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