# The production function graphs relationship between

### Production function - Wikipedia

The production function expresses a functional relationship between form of a table, graph and equation showing the amount of output obtained from various. curves are derived. • understand the relationship between the different cost curves . not only apply to the production function which was used here. It originates The graph is not an exact representation of the figures that appear in Table. Graph of total, average, and marginal product. In economics, a production function gives the technological relation between quantities of.

## The Production Function

Point B is just tangent to the steepest ray from the origin hence the average physical product is at a maximum. Beyond point B, mathematical necessity requires that the marginal curve must be below the average curve See production theory basics for further explanation.

Stages of production[ edit ] To simplify the interpretation of a production function, it is common to divide its range into 3 stages.

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.

### Production functions

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.

## Production functions

In this case, he would spend a thousand dollars for the seed, but realize a total yield of only seventy bushels. At a price of four dollars a bushel, he would receive two hundred and eighty dollars for his crop, but lose seven hundred and twenty dollars because of negative returns relative to input costs.

- Production Function and Its Aspects (With Diagram)
- Production function

A production function is a mathematical relationship that describes the way in which the quantity of a given product depends upon the quantities of the inputs used to produce it. Production functions are a graphic way to find a level of input that maximizes profits.

### Production Function and Its Aspects (With Diagram)

When the value of increased output is greater than the costs of a unit of increased input, the extra input is worthwhile. When the value of increased output is lower than the costs of a unit of increased input, the extra input is not worthwhile. That is the point of diminishing returns. The marginal product is positive when total production is increasing.

If the total product remains constant as input is added, the marginal product is zero. In some cases, total product may decrease with additional inputs. In such cases, the marginal product is negative.

When additional inputs result in a decreasing level of increase in total product, the marginal product is decreasing even though total product is still increasing. The average product is the amount of production relative to each unit of input at a specific level of production or level of input.

When the average product increases, the marginal product must be greater than the average product. When the average product is decreasing, the opposite is true. There are three regions in a production function. In region one, the production function extends to the point where the maximum average product occurs.

**Per capita production function graph explained**

It is always profitable to continue to add inputs as long as the average product increases correspondingly. In the third region of the graph, total production is decreasing, and the marginal product is negative.