“ In its broadest formulation this theory is a crucial element of the economic theory of social organization ,for it underlies every question of market organization and the role of governmental control over economic life” - George J.Stigler
The Production Function
A production function defines the relationship between inputs and the maximum amount that can be produced within a given time period with a given technology.
A production function indicates the output Q that a firm produces for every specified combination of inputs. For simplicity, we will assume that there are two inputs, labor L and capital K. We can then write the production function as
Q= F (K, L)
A bakery takes inputs like flour, water, yeast, labor, and heat and makes loaves of bread.
An earth-moving company takes capital equipment, ranging from shovels to bulldozers, and labor and digs holes.
A computer manufacturer buys parts, generally “off-the-shelf” like disk-drives and memory, along with cases and keyboards and other parts that may be manufactured specially for the computer manufacturer, and uses labor to produce computers.
Starbucks takes coffee beans, water, some capital equipment, and labor and produces brewed coffee.
Short run function vs Long Run function
The short run refers to a period of time in which one or more factors of production cannot be changed. Factors that cannot be varied over this period are called fixed inputs.
A firm's capital, for example, usually requires time to change-a new factory must be planned and built, machinery and other equipment must be ordered and delivered, all of which can take a year or more.
Total Productivity: Total output
Average productivity: Average output of the firm
Marginal Productivity: Increase in productivity following one unit increase of labor or any other factor of production
The figures illustrate TP, MP, and AP graphically.
Stage I – TP & AP are Increasing and MP is first increasing and then decreasing.
Stage II – TP is increasing, AP is decreasing and MP is also decreasing.
Stage III -- TP is diminishing, AP is decreasing & MP is negative
Production in the Long Run
In the long run, all inputs are variable.
The long run production process is described by the concept of returns to scale .
Returns to scale describes what happens to total output as all of the inputs are changed by the same proportion.
If all inputs into the production process are doubled, three things can happen:
output increases more than proportionately with an increase in the inputs
increasing returns to scale (IRTS)
output increases in the same proportion as the inputs
constant returns to scale (CRTS)
output increases less than proportionately with an increase in the inputs
decreasing returns to scale (DRTS)
Production in the Long Run
Graphically, the returns to scale concept can be illustrated using the following graphs.
Q X,Y IRTS Q X,Y CRTS Q X,Y DRTS
Economists hypothesize that a firm’s long run production function may exhibit at first increasing returns, then constant returns, and finally decreasing returns to scale.
Law of Diminishing Returns
As the use of an input increases (with other inputs fixed), a point will eventually be reached at which the resulting additions to output decrease. When the labor input is small (and capital is fixed), small increments in labor input add substantially to output as workers are allowed to develop specialized tasks. Eventually, however, the law of diminishing returns applies. When there are too many workers, some workers become ineffective, and the marginal product of labor falls.
The law of diminishing marginal product
If one factor of production is substituted for other factor of production ,the marginal product of one factor declines as the marginal product of other increases.
Condition: Isoquants must be convex at every point in order to satisfy the principle of diminishing rate of marginal product
ISOQUANT An Isoquant is a curve representing the various combinations of two inputs that produce the same amount of output. Q = f( L ,K) Example- diff combinations of L n k ,required to produce 45 units of goods X, join the points by a curve……
Types of isoquants
Input – output isoquant – zero substitutability between inputs
Linear isoquants – perfect substitutability between factors of production
Kinked isoquant – limited substitutability of capital and labor …also called as activity analysis isoquant..
smooth convex isoquant – continuous substitutability of K & l only over a certain range..
P roperties of isoquants
Downward - sloping to the right
higher isoquants represents larger output
No two isoquants intersects or touch each other
Isoquants are convex to the origin
slope of isoquant = d k /d L = M R TS(l,k)
Isoquant map & ridge lines
when the whole array of isoquants are represented on a graph …output varies as factor input change…….
higher isoquant represent higher level of output….
locus of points of isoquants where MP of input is zero….
ridge lines bound the economic region of production…
An isoquant map Units of capital ( K ) Units of labour (L) I 1 I 2 I 3 I 4 I 5
Marginal Rate of Substitution
It measures the rate at which one facto of production can be substituted for other factor of production, output being constant
It is the slope of the Isoquant at any point .
P Q S R T K L K3 K2 K1 O isoquant
It is the locus of all combinations of factors of production, assuming that price of factors of production are given and constant
Cost Equation of the firm
C = w.L + r.L
With the given cost C the firm can purchase any combination of labor and capital on the line AB. Thus AB is the isocost line .Points on a given isocost line show alternative production processes of equal cost. The slope of the isocost line is Pl/ Pk i.e. OA/OB K L O A B C/r C/w
K L O B A E F C D If the unit prices of the factors remain constant and the total cost level changes the isocost line shift parallely, its slope remaining the same. As the cost level increases (decreases) the isocost line shifts parallel to the right side (left side) and we will get one isocost line for each cost level.
Maximization of Output Subject to Cost Constraint
The firm is in equilibrum when it maximises its output given its total cost outlay
Principle : To maximise output subject to a given total cost and given inut prices, the producer must purchase inputs in quantities such that the marginal rate of technical subsitution of capital for labor is equal to the input-price ratio.Thus
MRTS l or k = MPl/MPk=w/r
Output is maximise where isoquant is tangent to the isocost line
E K O L B e1 e3 e2 e4 q2 q1 q0
Minimisation of Cost for a Given level of Output
The entrepreneur in this case wants to produce a given level of output with the minimum possible cost outlay.
Principle: The entrepreneur must employ inputs in such amounts as to equate the marginal rate of technical substitution and the input-price ratio
MRTS l or k = MP l/ MP k= w/r
E is the least cost point for the output level Q0.The least cost combinaton is fulfilled vwhen the isoquant is tangent to the lowest possible isocost line AB
K O L B D H A c G L E e2 e1 e3 e4 Q0
The Expansion path is the locus of all input combinations for which the Marginal Rate of Technical Subsitution(MRTS) is equal to the factor price ratio.
Equation of the expansion path:
g ( L, k ) = 0
Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 200 300 400 500 600 700 Expansion path