The Demand for
Inputs to the
Production Process
Chapter 13
Ripon Kumar Mondal, PhD
LECTURE 9
Introduction
The demand for inputs to the agricultural production process is a derived demand.
That is, the input demand function is derived from the demand by buyers of the output
from the farm.
In general, the demand for an input or factor of production depends on
(1) the price of the output or outputs being produced,
(2) the price of the input,
(3) the prices of other inputs that substitute for or complement the input, and
(4) the parameters of the production function that describes the technical
transformation of the input into an output.
In some instances, the demand for an input might also depend on the availability
of dollars needed to purchase the input.
Ref. p.216
Introduction
For example, the demand by a farmer for seed, fertilizer, machinery,
chemicals, and other inputs is derived from the demand by users for the
corn produced by the farmer.
The demand for each of these inputs is a function not only of their
respective prices, but also the price of corn in the marketplace.
The demand by a dairy farmer for grain and forage is dependent not only
on the respective prices of grain and forage, but also on the price of the
milk being produced.
Ref: p216
A Single-Input Setting
In a single input setting, the derivation of a demand function for an input x
makes use of
(1) the production function that transforms the input x into the product y;
(2) the price of the output y, called p, and
(3) the own price of the input, called v.
Since there are no other inputs, in a single input setting prices of other
inputs do not enter.
Ref: P.216
A Single-Input Setting
A general statement of the problem is as follows.
Given a production function y = f(x,α) where x is the quantity of input used
and α represents the coefficients or parameters of the production function,
a constant product price (p) and a constant input price (v),
The corresponding input demand function can be written as x = g(α, p, v).
Notice that the function g, the input demand function, is a different function
from f, the production function.
The derivation of the input demand function for a specific production
function and set of prices makes use of the firm's first order conditions for
profit maximization.
Ref: p216
A Single-Input Setting
Assume that the farm manager uses only one input in the production of
a single output. The farmer is operating in a purely competitive
environment, and the price of the input and the output is assumed to be
fixed and given. The farmer is interested in maximizing profits.
The first order conditions for maximum profit require that the farmer equate
𝑝𝑀𝑃𝑃𝑥 = 𝑉𝑀𝑃𝑥 = 𝑣
where p is the output price and v is the input price.
Ref: p216
A Single-Input Setting
Now suppose that the price of the input (v) varies. What happens?
The intersection between VMPx and v represents the demand for the input
at that particular input price, which, in turn, traces out the demand curve or
input demand function for the input x under a series of alternative input
prices.
If the price of the output increases, the VMP curve will shift upward,
increasing the demand for x at any positive input price.
Ref: p216
A Single-Input Setting
Conversely, a decrease in the price of the output will reduce the demand
for the input x at any given input price.
The input demand function normally begins at the start of stage II and
ends at the start of stage III.
Ref: p216
A Single-
Input
Setting
Ref: p217
A Single-Input Setting
As the productivity of the underlying production function increases, the
MPPx will increase. This, in turn, will increase the demand by farmers for
input x.
Conversely, a decrease in the productivity of the underlying production
function will cause a reduction in the demand for x for a given input and
output price.
Ref: p217
