Economics
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Production function is the relationship between quantities of input and output. It is expressed as Q=F(L,M,N,C,T) where Q stands for the output of a good per unit time , L for labour, M for management, N for land ( natural resources), C capital and T for technology , F states functional relationship. Production function is of two types rigid or flexible.
Q=(L,M,N,C,T) , Given T if quantities of all inputs L,M,N,C are increased n-fold the output Q also increase n-fold. Production function becomes nQ=f(nL,nM,nN,nC). If the production function is of kth degree the function is n^k.Q=f(nL,nM,nN,nC). If k=1 then it is called constant return to scale. If k>1 it is increasing return to scale. If k<1 it is decreasing return to scale.
It states that if one input is variable and all other inputs are fixed the firm’s production exhibits law of variable proportions.
Assumptions
Stage I
Increasing returns- In stage I it starts from the origin and reaches till point S where MP and AP curves meet. In this stage TP curve also increases rapidly. It denotes increasing average returns because the fixed factor is large in quantity than the variable factor.
Stage II
Law of Diminishing returns- It starts when the average product is at its maximum to the zero point of the marginal product. In the graph this stage is between SN and HM . In this stage the production is feasible and profitable.
Stage III
Negative marginal returns- In this stage production don’t takes place. The total product starts declining and marginal product becomes negative. In the graph this stage starts frm HM where MP curve is below the X-axis. To the right of point M the variable input is used excessively so production will not take place.
This law states that as the proportion of one factor in a combination of factors is increased after a point the average and the marginal product of that factor will diminish. The scarcity of one factor in relation to other factors is the root cause of law of diminishing return. Eg. In a tank fisheries as more and more fish are caught the quantity of fish decreases because their quantity is limited in a tank and I addition of labor or capital doesn't increase the amount of fish caught.
It describes the relationship between output and the scale of input in the long run when all input are increased in same proportion.
Assumptions
Explanation
Consider table below.
Unit
Scale of production
Total returns
Marginal returns
1
1 worker + 2 Acres of land
8
8
2
2 workers + 4 Acres of land
17
9
3
3 workers + 6 Acres of land
27
10
4
4 workers +8 Acres of land
38
11
5
5 workers + 10 Acres of land
49
11
6
6 workers + 12 Acres of land
59
10
7
7 workers + 14 Acres of land
68
9
8
8 workers + 16 Acres of land
76
8
This table reveals that in the beginning with the scale of production of (1 worker + 2 acres of land) total output is 8. To increase the output when the scale of production is doubled (2 workers + 4 acres of land) total returns are more than doubled and becomes 17. Now if the scale is trebled (3 workers + 6 acres of land) returns becomes more than three-fold. It shows increasing return to scale.
If the scale of production is increased further total return will increase in such a way that marginal returns become constant. In case of 4th and 5th units of the scale of production marginal return are 11 i.e. return to scale are constant. Increase in the scale of production beyond this limit will lead to diminishing returns.
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