Solution:

Production:

• Production in economic terms is generally understood as the transformation of inputs into outputs. The inputs are what the firm buys, namely productive resources, and outputs are what it sells.

• Production is not the creation of matter but it is the creation of value. Production is also defined as producing goods that satisfy some human want.

• Production is a sequence of technical processes requiring either directly or indirectly the the mental and physical skill of craftsman and consists of changing requiring either directly or indirectly the the mental and physical skill of a craftsman and consists of changing the shape, size, and properties of materials and ultimately converting them into more useful articles.

The Production Function:

• The production function expresses a functional relationship between quantities of inputs and outputs. It shows how and to what extent output changes with variations in inputs during a specified period.

• In the words of Stigler, "The production function is the name given to the relationship between rates of input of productive services and the rate of output of product. It is the economist's summary of technical knowledge."

• The production function is a technological or engineering concept which can be expressed in the form of a table, graph, and equation showing the amount of output obtained from various combinations of inputs used in production, given the state of technology.

• Algebraically, it may be expressed in the form of an equation as

  Q = f (L,M,N,K,T)

• Where Q stands for the output of a good per unit of time, L for labor, M for management (or organization), N for land (or natural resources), K for capital, and T for a given technology, and f refers to the functional relationship.

• The production function with many inputs cannot be depicted on a diagram. Moreover, given the specific values of the various inputs, it becomes difficult to solve such a production function mathematically.

• Economists, therefore, use a two-input production function. If we take two inputs, labor, and capital, the production function assumes the form

  Q = f(L, K)

• The production function as determined by technical conditions of production is of two types: it may be rigid or flexible.

• The former relates to the short run and the latter to the long run. The Nature of Production Function

• The production function depends upon the following factors:

  a) The quantities of inputs to be used.

  b) The state of technical knowledge.

  c) The possible processes of production.

  d) The size of the firm.

  e) The prices of inputs.

• Now if these factors change the production function automatically changes. Attributes of Production Function

• The following are the important attributes of production function:

  i. The production function is a flow concept.

  ii. A production function is a technical relationship between inputs and outputs expressed in physical terms.

  iii. The production function of a firm depends on the state of technology and inputs.

  iv. From the economic point of view, a rational firm is interested not in all the numerous. possible levels of output but only in that combination that yields maximum outputs.

  v. The short-run production function pertains to the given scale of production. The long-run production function pertains to the changing scale of production.

Short Run Production Function:

• In the short run, the technical conditions of production are rigid so that the various inputs used to produce a given output are in fixed proportions.

• However, in the short run, it is possible to increase the quantities of one input while keeping the quantities of other inputs constant to have more output. This aspect of the production function is known as the Law of Variable Proportions.

• The short-run production function in the case of two inputs, labor and capital with capital as fixed and labor as the variable input can be expressed as,

  Q = f (L,R)

• Where K refers to the fixed input.

• This production function is depicted in Figure 1 where the slope of the curve shows the marginal product of labor.

• A movement along the production function shows the increase in outputs as labor increases, given the amount of capital employed $k_1$, If the number of capital increases to $k_2$, at a point of time, the production function Q = f (L, K1 ) shifts upwards to Q = f (L, K2 ) , as shown in the figure.

• On the other hand, if labor is taken as a fixed input and capital as the variable input, the the production function takes the form,

  Q= f(KL)

• This production function is depicted in Figure 2 where the slope of the curve represents the marginal product of capital.