This document discusses production functions and the law of diminishing returns. It begins by defining production as the process of transforming resources into goods or services using inputs like land, labor, capital and entrepreneurship. It then discusses short-run and long-run production functions. The short-run production function treats one input like capital as fixed and analyzes how output changes with varying levels of the variable input, labor. It demonstrates diminishing marginal returns to labor through a hypothetical example. The long-run production function considers how output changes with two variable inputs, capital and labor, as demonstrated using the Cobb-Douglas production function.
2. INDEX
INTRODUCTION
PRODUCTION FUNCTION WITH ONE VARIABLE
LAW OF DIMINISHING RETURNS
OPTIMUM EMPLOYMENT OF LABOUR
PRODUCTION FUNCTION OF TWO VARIABLE INPUTS
3. INTRODUCTION
PRODUCTION
In economics we can say production is process by which resources are
transformed into a different commodity or services.
LAND LABOUR
CAPITAL ENTREPRENEUR
PRODUCT/SERVICES
4. INPUT & OUTPUT
A/C to BAUMOL
Input
“ Input is simply anything which the firm buys for use
in its production or other process”.
Example: Raw material,labour etc.
Output
An output is any good or services that comes out of
production process.
Example: Engineer of NIT After 4 year process.
5. Fixed & variable inputs
Fixed inputs
Fixed inputs whose supply is inelastic in short run, or
input is constant or fixed up to certain level of output.
(e.g. land).
variable inputs
Variable input is one whose supply is elastic in short
run.(labor & raw material, capital).
6. Production function
It is mathematical presentation of input output
relationship in the form of an equation , a table or
graph.
On ground level production function is very complex,
because it includes wide range of inputs.
Q=f(LB,L,K,M,T,t)
LB=land & building, L= labour, K =capital ,M= material,
T=technology, t=time
In economics we deals with two no. of inputs those are
K & L, other inputs taken as constant.
So Qc=f(K, L)
8. Short run production function
It is also term as single input variable function.
Q is f(K BAR,L) where K bar is constant.
Q=bl , where b= change in Q/change in L gives
constant return to labour.
The law of production under these conditions
called “law of variable promotions or law of
return to a variable input.
9. Law of diminishing returns to a variable
input.
When more & more variables input are used
with a given quantity of fixed inputs, total o/p
may initially increase at increasing rate, and
then constant rate, but it will eventually
increasing at diminishing rates.
That’s is the marginal increase in total o/p
decreases eventually when additional units of a
variable factor are used , given quantity of
fixed factors.
10. Assumption
Labour is the only variable I/P, K remain constant.
Labour is homogeneous.
State of technology is given.
Input prices are given.
lets consider Qc=f(L), K constant. For
Qc=-L³+15L²+10L hypothetical equation for labour o/p
relationship for X Firm. L=5
So Qc=-125+375+50=300
11. Cont……
MARGINAL PRODUCTIVITY OF LABOUR
MPL=Derivative of Q w.r.t.L=-3L²+30L+10, when we put
L in this equation we get different values of MPL.
But in this method labour should be perfectly divisible
and delta L approaches to 0.Since L=1 , SO calculas
method is not allowed.
Alternatively ,labour is increased at lest by one. So
MPL=TPL-(TPL-1) where TPL is(Total product).
Average productivity of labour obtained by dividing the
production function by L. that is APL=Qc/L
14. Application of the law of diminishing returns.
Diminishing law is an empirical law. It may not apply
universally to all kinds of productive activities.
Its operate in agricultural activities more regularly than
industrial production.
Despite the limitations of the law , if increase in I/p
units to the fixed factors , marginal returns to variable
input decreases eventually.
The law of diminishing returns helps to take business
decisions.
It determines optimum employment of labour.
15. Long run production function.
It is also known as production with two variables.
We know Q=f(K,L)
Q=A.Kª.L*b , Cobb-Douglus production function.
Where K is capital, L is labour,& A,a,b is parameters and
a+b=1.
example A= 50,a=0.5,b=.5
If K=2, L=5 then Q=158.
If K=5,L=5 the Q= 250.
If K=3, L =5 the Q=194