Theory of Production and Costs
Concept of Production – Production Function –– short run versus long run production function- Law of Variable
Proportions – TP, AP, MP and their interrelationships – Isoquants- Properties- MRTS - Isocost Curve –Producer
Equilibrium- Law of Returns to ...
Part 1: Theory of Production and Costs
Concept of Production – Production Function –– short run versus long run production function- Law of Variable
Proportions – TP, AP, MP and their interrelationships – Isoquants- Properties- MRTS - Isocost Curve –Producer
Equilibrium- Law of Returns to Scale – Expansion Path – Internal and External Economies- Linearly
Homogeneous Production Function - Cobb-Douglas production function
Part 2: Theory of Costs
Cost function – Cost concepts- Explicit and implicit costs, opportunity cost, private cost, social cost, economic
cost, accounting cost, sunk cost, fixed and variable cost, marginal and average cost -Short run and Long run cost
curves - Modern theory of costs.
THEORY OF PRODUCTION
Production
Production may be defined as a process by which inputs are transformed into an output
Production Function
The production function examines the technological relationship between inputs and output.
It shows the maximum quantity of output, that can be produced as a function of inputs used in
the production process In functional form we write
Q = f(X1, X2,X3…….Xn) or Q = f(Xi) Where Q = output, X1, X2,X3…….Xn are inputs
If we consider Labour (L) and (K) are the two factors, then the production function takes the
following form, Q = f (L,K)
Short run and Long run Production Function
The short run is a time frame in which the quantity of one or more resources used in
production is fixed. For most firms, the capital, is fixed in the short run. Other resources used
by the firm (such as labor, raw materials, and energy) can be changed in the short run. When
one or more inputs are fixed in quantity we call it short run production function ( Example is
law of variable proportion). A typical short run production function with one variable factor
is given as
Qmax = f(L, Kconst) Qmax = f(K, Lconst)
When all inputs are freely variable, we call it long run production function. A long run
production function is given as Qmax = f(K, L). Here both factors are variable. ( Example for
long run production function is Returns to Scale)
Total Product or TP Curve
Total Product is defined as the sum total volume of Production or total number of
Units produced with the given fixed and variable inputs. In functional form we have
1
,Qmax = f(L, Kconst)
A TP curve shows the technological relationship between a variable input and TP(assuming
other inputs remaining the same). A TP curve given below concave upward till point j ,
which is the point of inflection. From J to L the concave downward indicating that TP
increases at a decreasing rate. Beyond L, TP decreases. However, when the technology
improves the TP shift upward to TP1.
TP2
TP1
Average Product
Average product is defined as the ratio of total product and number of units of
variable factor.
AP = TP / No of variable factors
Using the above functional form, APL= Q/L and APK = Q/K
Marginal Product
Marginal Product is defined as the Increment in total output due to the use of an extra
unit of variable factor.
MP = Change in Total Product / Change in Variable Factor
OR
MPL = ∆ Q/ ∆ L or dQ/dL or
MPK = ∆ Q/ ∆ K or dQ/dK or
Relationship between Marginal and Average Product
The AP and MP got three important relationship. They are (a) the AP increases if the MP is
greater than the AP , (b) the AP remains constant if the MP is equal to the AP , (a) the AP
decreases if the MP is less than the AP . ( See graph below). In the graph it is clear that as AP
increases MP>AP. When AP falls MP<AP. When AP got a maxima MP = AP. ( See
mathematical proof- for advanced students only)
MP
AP MP>AP
MP<AP
MP=AP
2
Variable Factor
,Law of Variable Proportions or Diminishing Returns
Statement of law.
The law of variable proportions examines input-output relationship when output is increased
by varying the quantity of one factor (variable input) while other factors are kept constant.
According to this law, if more and more units of a variable factor are employed with fixed
factors, total product (TP) increases at an increasing rate in the beginning, then increase at a
diminishing rate and finally starts falling.
Why does diminishing returns occur? – An example
Think about the effectiveness of extra workers in a small café. If more workers are
employed, production could increase but more and more slowly. However, there are
only so many chopping boards and space to make sandwiches. An extra worker may
just struggle to find a space to make sandwiches.
Assumptions of law.
The law operates on the basis of following assumptions or pre-conditions.(i) Technique of
production does not change. The law will not apply if there is improvement in technology. (ii)
Different quantities of one factor can be varied / combined with fixed factors. It is possible to
change the factor-proportions. (iii) All units of a variable factor are equally efficient. (iv)
Factors of production are not perfect substitutes. (v) There is short period of operation.
Table and Graph ( give from class room example)
I Stage Q= f(L,Kconst) = TP
TP II Stage
III Stage
Labour
MP
AP
APL
Labour
MPL
(Briefly explain the graph in your own words)
3
, Another graph ( any one is enough)
Three stages (phases) of law
The following three phases are noticed in the relation between variable factor and the physical
output as more and more units of variable factor (labour) are employed to a given quantity of
fixed factor (land).
Phase I. TP increases at an increasing rate. In other words, MP rises. In this phase both MP and
AP increase. When more and more units of variable factor are applied to fixed factors, the
underutilized fixed factors get fully utilized raising MP of variable factor. Thus the firm is
moving towards optimum combination of factor of production and thereby getting increasing
returns.
Why Increasing Returns in this stage: Because, the quantity of the fixed factor is abundant
relative to the quantity of the variable factor. Therefore, when more and more units of a variable
factor are added to the constant quantity of the fixed factor, the fixed factor is more intensively
and effectively utilised.
4
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