Page 93 - DECO101_MICRO_ECONOMICS_ENGLISH

Micro Economics

Notes For the Cobb-Douglas production function,

Q = AK L b
a
The marginal products are
dQ dQ
MP = = aAK a1 b = bAK L
−
ab-1
L and MP =
K
dK L dL
Average Product (AP) is total product per unit of variable input. It is found by dividing the rate
of output by rate of variable input, i.e.,
TP TP
AP = L and AP = K
K
L
L K
By holding the quantity of input constant and changing the other, we can derive TP of the variable
input.
Example: By holding capital constant at one unit (K = 1) and increasing units of
labour used from 0 to 6 units, we get total product of labour as in column (2) below in
Table.

TP, MP and AP of Labour
(1) (2) (3) (4) (5)
Labour Output or TP MP of labour AP of labour Output Elasticity
(No. of work- of labour
ers)
0 0 - - -
1 3 3 3 1
2 8 5 4 1.25
3 12 4 4 1
4 14 2 3.5 0.57
5 14 0 2.8 0
6 12 -2 2 -1
Marginal Product of Labour (MP ) is the change in total product or extra output per unit change
L
in labour used. Average Product of Labour (AP ) equals total product divided by the quantity of
L
labour used.
Δ TP
MP = Δ L
L

TP
AP = L
L
Output elasticity of labour (E ) measures the percentage change in output divided by percentage
L
change in quantity of labour used.
Δ
%Q
E =
Δ
%L
L
or
Δ
Δ Q/ Q Δ Q/ L MP
E = = = L
Δ L/ L Q/ L AP
L
L
This means that from zero units of labour (and with K = 1), TP or output grows proportionally to
the growth in the labour input. For the second unit of labour E = 1.25 (that is, TP or output grows
L
more than proportionally to the increase in L), and so on.

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