Page 92 - DECO101_MICRO_ECONOMICS_ENGLISH

Unit 7: Production Theory

If h is assumed to be a variable, then the above function may be called the variable elasticity of Notes
substitution, VES function.

Still another form is the fixed proportion production function also called the Leontief function.
It is represented by
⎡ KL ⎤
,
Q = minimum ⎢ ⎣ ab ⎦ ⎥
where a and b are constants and ‘minimum’ means that Q equals the smaller of the two ratios.

Finally there is a very simple linear production function. Assuming that the inputs are perfect
substitutes so that all factors may be reducible to one single factor, say, labour, L, than the linear
production function may be,
Q = aL
where
‘a’ is the constant term and
L stands for labour.

In order to analyse the relationship between factor inputs and outputs, economists classify time
periods into short runs and long runs.
Before further discussion it is necessary to conceptualize three terms: total product, average
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 defi ned 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 fi xed, 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
Δ Q
MP = Δ L
L

Δ Q
MP = Δ K
K

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