production function with 2 variable inputs return to scale
TRANSCRIPT
Production function with 2 variable inputs return to scale
Production function
Isoquant and shape of isoquants
Return to scale
Properties of isoquant curves
Isoquants Map
Refrences
Thank you
WHAT IS PRODUCTION FUNCTION
Production means transforming inputs (labour, capital, raw materials, time etc.)into an output. This concept of
production is however limited to only ‘manufacturing’.
In other words , a process by which men, material, capital and time are converted
into value added product is called production.
It is a mathematical presentation of input output relationship.
The production function represent the technology of a firm, of an industry or the economy as a whole.
A production function may take the form of a schedule or a table, a graphed line or curve or a mathematical model.
A real life production function is generally very complex. It includes a wide range of input they are:-
Land and Building
Labour
Capital
Raw Material
Time
Technology
It is expressed by :-
Q = f(LB, L, K, M, T, t)
There is a relationship between production and productivity.
Long-run production K& L are variable.
Isoquants analyze and compare the different combinations of K & L and output
ISOQUANT
It is derived from Greek word iso, meaning equal.
The isoquant mapping deals with the cost-minimization problem of producers.
Adding one input while holding the other constant eventually leads to decreasing marginal output, and this is reflected in the shape of the isoquant.
Isoquant are also called equal product curves.
As with indifference curves, two isoquant can never cross.
Every possible combination of inputs is on isoquant.
An isoquant map can also indicate decreasing or increasing returns to scale based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases.
INPUT X
Q1
Q2
Q3
INPUT
Y
An isoquant map where Q3>Q2>Q1. Typically inputs X and Y would refer to labour and capital respectively. More of input X, and Y, or both is required to move from isoquant Q1 to Q2, or from Q2 to Q3.
Example of an isoquant map with two inputs that are substitute
I N P U T X
INPUT
Y
Q1 Q2 Q3
Measuring the relationship between the scale (size) of a firm and output
1) Increasing returns to scale: output more than doubles when all inputs are
doubled
Larger output associated with lower cost (autos)
One firm is more efficient than many (utilities)
The isoquants get closer together
Labor (hours)
Capital(machine
hours)
10
20
30
5 10
2
4
0
A
Increasing returns to scale
Measuring the relationship between the scale (size) of a firm and output
2) Constant returns to scale: output doubles when all inputs are doubled
Size does not affect productivity
May have a large number of producers
Isoquants are equidistant apart
Labor (hours)
Capital(machine
hours)
Constant Returns:Isoquants are equally spaced
10
20
30
155 10
2
4
0
A
6
Measuring the relationship between the scale (size) of a firm and output
3) Decreasing returns to scale: output less than doubles when all inputs are doubled
Decreasing efficiency with large size
Reduction of entrepreneurial abilities
Isoquants become farther apart
Labor (hours)
Capital(machine
hours)
Decreasing Returns:Isoquants get further apart
1020
30
5 10
2
4
0
A
1. Isoquants have a negative slope- An isoquant has a negative slope in the
economic region and in the economic range of isoquant.
The negative slope of isoquant implies substitutability between the input. It means that if one of the input is reduced, the other input has to be increased that the total output remains unaffected.
2. Isoquant are convex to origin-convexity of isoquant implies two things:substitution between two inputsDiminishing marginal rate of technical substitution (MRTS)
The MRTS is defined as:MRTS= -K\-L= slope of the
isoquant
3. Isoquant are non-intersecting and non-tangential- The intersection or tangency between any two isoquant implies that a given quantity of a commodity can be produced with a smaller as well as larger input-combination.
4. Upper isoquant represent higher level of output- Between any two isoquant, the upper one represent higher level of output than the lower one. The reason is upper isoquant has larger input combination which in general produce larger output.
QUANTITY L
Q1= 100
Q2= 200
QUANTITY
K
B
C
DA
X
Y
In this fig Q2 will always indicate high level of output than Q1. Q2 consist of more of either capital or labour or both. Consider point a on Q1 and compare it with any point at Q2. The point on Q2 consider more capital (a b). Point d more of labour (a d) and point c more of both, capital and labour. Therefore Q2 represent higher level of output(200 units) than Q1 indicating 100 units.
0
Q1
Q2
CAPITAL(K)
LABOUR (L)
An isoquant map is a set of isoquant presented on a two-dimensional plane as shown by isoquant Q1, Q2, Q3.Each isoquant shows various combination of two input that can be used to produce a given quantity of output.
Q3
