# The production function gives relationship between quantity

The production function relates the quantity of factor inputs used by a business The short run is a time period where at least one factor of production is in fixed. The production function illustrates the relationship between the quantity of inputs used and the quantity of The marginal product of labor is the increase in the amount of output from an additional unit of labor. Gives a new equilibrium. This will give us standard two-dimensional graphs. With a production function that shows constant returns to scale . Quantity of output is under the firm's control and actual input demand changes as . relationships between. SC and SAC and.

### Production function - Wikipedia

In Stage 1 from the origin to point B the variable input is being used with increasing output per unit, the latter reaching a maximum at point B since the average physical product is at its maximum at that point.

Because the output per unit of the variable input is improving throughout stage 1, a price-taking firm will always operate beyond this stage. In Stage 2, output increases at a decreasing rate, and the average and marginal physical product both decline.

However, the average product of fixed inputs not shown is still rising, because output is rising while fixed input usage is constant.

In this stage, the employment of additional variable inputs increases the output per unit of fixed input but decreases the output per unit of the variable input. In Stage 3, too much variable input is being used relative to the available fixed inputs: The output per unit of both the fixed and the variable input declines throughout this stage.

At the boundary between stage 2 and stage 3, the highest possible output is being obtained from the fixed input.

Shifting a production function[ edit ] By definition, in the long run the firm can change its scale of operations by adjusting the level of inputs that are fixed in the short run, thereby shifting the production function upward as plotted against the variable input. If fixed inputs are lumpy, adjustments to the scale of operations may be more significant than what is required to merely balance production capacity with demand.

For example, you may only need to increase production by million units per year to keep up with demand, but the production equipment upgrades that are available may involve increasing productive capacity by 2 million units per year.

Shifting a production function If a firm is operating at a profit-maximizing level in stage one, it might, in the long run, choose to reduce its scale of operations by selling capital equipment.

### Production Function: Meaning, Definitions and Features

By reducing the amount of fixed capital inputs, the production function will shift down. However, here one thing that becomes most important to quote is that like demand function a production function is for a definite period. It shows the flow of inputs resulting into a flow of output during some time. The production function of a firm depends on the state of technology.

With every development in technology the production function of the firm undergoes a change.

The new production function brought about by developing technology displays same inputs and more output or the same output with lesser inputs. Sometimes a new production function of the firm may be adverse as it takes more inputs to produce the same output. Mathematically, such a basic relationship between inputs and outputs may be expressed as: Hence, the level of output Qdepends on the quantities of different inputs L, C, N available to the firm.

In the simplest case, where there are only two inputs, labour L and capital C and one output Qthe production function becomes.

As long as the natural laws of technology remain unchanged, the production function remains unchanged. This is a technological relation showing for a given state of technological knowledge how much can be produced with given amounts of inputs.

Lipsey Thus, from the above definitions, we can conclude that production function shows for a given state of technological knowledge, the relation between physical quantities of inputs and outputs achieved per period of time.

Features of Production Function: Following are the main features of production function: The factors of production or inputs are substitutes of one another which make it possible to vary the total output by changing the quantity of one or a few inputs, while the quantities of all other inputs are held constant.

It is the substitutability of the factors of production that gives rise to the laws of variable proportions. The factors of production are also complementary to one another, that is, the two or more inputs are to be used together as nothing will be produced if the quantity of either of the inputs used in the production process is zero. The principles of returns to scale is another manifestation of complementarity of inputs as it reveals that the quantity of all inputs are to be increased simultaneously in order to attain a higher scale of total output.

• Production Function: Meaning, Definitions and Features

It reveals that the inputs are specific to the production of a particular product.