Page 94 - DECO405_MANAGERIAL_ECONOMICS

Unit 6: Production Theory

Before further discussion it is necessary to conceptualize three terms: total product, average Notes
product and marginal product.
1. Total product is the total quantity produced by that many units of a variable factor
(i.e., labour). For example, if on a farm 2000 Kg. of wheat were produced by 10 men, the
total product would be 2000 Kg.
2. Average product is the total output divided by the number of units of the variable factor
(or the number of men). Thus AP = TP/L. On the same farm, the average product would be
2000/10 = 200 Kg.

3. Marginal product is the change in total output resulting from the change (using one more
or one less unit) of the variable factor. If an eleventh man is now added to this farm and
the output rose to 2,100 Kg, the marginal product (of labour) would be 100 Kg. Thus,
MP = d(TP)/dL.
For a two-input production process, the total product of labour (TP ) is defined as the maximum
L
rate of output coming up from combining varying rates of labour input with a fixed capital
input K . (Note: A bar over K or over any other variable means, that variable has been fixed,
and therefore is no more variable.)

TP = f (K,L)
L
and total product of capital function is

TP = f (K,L)
K
Marginal product (MP) is the change in output per unit change in the variable input. Thus the
marginal product of labour and capital is

a
For the Cobb-Douglas production function, Q = AK L b
The marginal products are

and

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.,

and

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) in Table.

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