Maximizing Profits through Input-Output Dynamics

Production is the process by which inputs are transformed into ‘output’. Production is carried out by producers or firms. A firm acquires different inputs like labour, machines, land, raw materials etc. It uses these inputs to produce output.

In this chapter, we will discuss the relationship between inputs and output and the cost structure of the firm to identify the output at which the firm’s profits are maximum.

Factors of Production: Maximizing Output Efficiency in Firm Operations

• The Production Function: It is a relationship between inputs used and output produced by the firm. 
  • For various quantities of inputs used, it gives the maximum quantity of output that can be produced. 
  • Example: Suppose a farmer uses inputs to produce wheat, land and labor. 
    • A production function tells us the maximum amount of wheat (Q) he can produce for a given amount of land (K) that he uses, and a given number of hours of labor (L) that he performs i.e., (Q=K×L).
  • So, the production function tells us the exact relation between inputs and output. 
    • If either K or L increases, q will also increase. 
  • It deals only with the efficient use of inputs. 
  • Efficiency implies that it is not possible to get any more output from the same level of inputs.
• Technology Influence Production Function: It is the technological knowledge that determines the maximum levels of output that can be produced using different combinations of inputs.
  • If the technology improves, the maximum levels of output attainable for different input combinations increase.
• Factors of Production: The inputs that a firm uses in the production process are called factors of production.
• • In order to produce output, a firm may require any number of different inputs. 
  • However, for the time being, here we consider a firm that produces output using only two factors of production, labour and capital. 
  • For the maximum quantity of output (q) using two factors of production Labour (L) and Capital (K), we may write the production function as q = f (L, K). 
  • Refer to Figure, for different values of the two factors, the table shows the corresponding output levels. 
  • It shows that both inputs are necessary for the production. 
  • If any of the inputs becomes zero, there will be no production.
  • With both inputs positive, the output will be positive. 
  • As we increase the amount of any input, output increases. 

The Short Run and The Long Run: Flexibility in Factors of Production for Optimal Output

• Short Run: In the short run, at least one of the factors – labor or capital – cannot be varied, and therefore, remains fixed.
  • In order to vary the output level, the firm can vary only the other factor. 
  • The factor that remains fixed is called the fixed factor whereas the other factor which the firm can vary is called the variable factor.
• Long Run: In the long run, all factors of production can be varied. A firm in order to produce different levels of output in the long run may vary both inputs simultaneously. So, in the long run, there is no fixed factor.

Total Product, Average Product And Marginal Product

Total Product: Factors of Production Dynamics

• When we vary a single input and keep all other inputs constant. 
• Then for different levels of that input, we get different levels of output. 
• Total Product (TP): This relationship between the variable input and output, keeping all other inputs constant, is often referred to as the Total Product (TP) of the variable input.
  • This is also sometimes called total return to or total physical product of the variable input.

Average Product: Factors of Production Influence

• It is defined as the output per unit of variable input. We calculate it as APL (Refer to figure)

Marginal Product: Factors of Production Impact

• Marginal Product of an Input: It is defined as the change in output per unit of change in the input when all other inputs are held constant.
  • When capital is held constant, the marginal product of labour (MPL)  is 1. (Refer to Figure).
  • Since inputs cannot take negative values, marginal product is undefined at zero level of input employment.
•  MPL at Constant Capital and Total Product: 
  • For any level of an input, the sum of marginal products of every preceding unit of that input gives the total product. 
  • So total product is the sum of marginal products.
• The Average Product: It is of an input at any level of employment is the average of all marginal products up to that level.
  • Average and marginal products are often referred to as average and marginal returns, respectively, to the variable input.