Define production function and also discuss a production indifference curve and its properties with diagram

Q. What is meant by production function? Describe a production indifference curve and its properties. Use diagram in your answer (Nov’11 and Nov’10).

Productions function: Production is the process by which inputs are transformed in to outputs. Thus there is relation between input and output. The functional relationship between input and output is known as production function. In economics, equation that expresses the relationship between the quantities of productive factors (such as labour and capital) used and the amount of product obtained. It states the amount of product that can be obtained from every combination of factors, assuming that the most efficient available methods of production are used.

It can be expressed in algebraical form as under:

x =f (a¹, a²,…………………………… aⁿ)

This equation tells us the quantity of the product X which can be produced by the given quantities of inputs (lands labour, capital) that are used in the process of production. Here, it may be noted that production function shows only the maximum amount of output it which can be produced from given inputs. It is because production function includes only efficient production process.

A production indifference curve and its properties:

(1) Indifference Curves are Negatively Sloped: The indifference curves must slope down from left to right. This means that an indifference curve is negatively sloped. 

In fig. 3.4 the two combinations of commodity cooking oil and commodity wheat is shown by the points a and b on the same indifference curve. The consumer is indifferent towards points a and b as they represent equal level of satisfaction.

(2) Higher Indifference Curve Represents Higher Level: A higher indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction and combination on a lower indifference curve yields a lower satisfaction. 

In this diagram (3.5) there are three indifference curves, IC¹, IC² and IC³ which represents different levels of satisfaction. The indifference curve IC3 shows greater amount of satisfaction and it contains more of both goods than IC² and IC¹ (IC³ > IC² > IC¹).

(3) Indifference Curve is Convex to the Origin: This is an important property of indifference curves. They are convex to the origin (bowed inward). This is equivalent to saying that as the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes of X for Y along an indifference curve.

(4) Indifference Curve Cannot Intersect Each Other: Given the definition of indifference curve and the assumptions behind it, the indifference curves cannot intersect each other. It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible.

In fig 3.7, two indifference curves are showing cutting each other at point B. The combinations represented by points B and F given equal satisfaction to the consumer because both lie on the same indifference curve IC₂. Similarly the combinations shows by points B and E on indifference curve IC₁ give equal satisfaction top the consumer.

(5) Indifference Curves do not touch the Horizontal or Vertical Axis: One of the basic assumptions of indifference curves is that the consumer purchases combinations of different commodities. He is not supposed to purchase only one commodity. In that case indifference curve will touch one axis. This violates the basic assumption of indifference curves.