How to draw a production function indicating three stage of production

Wikipedia has a good explanation, and includes a graph over the common three stages of production.

Go to Wikipedia and find: Production_function

To draw a production function indicating three stages of production, you can follow these steps:

Step 1: Understand the concept of a production function
A production function shows the relationship between inputs used in the production process and the resulting output. It helps analyze how much output can be produced from a given combination of inputs.

Step 2: Identify the stages of production
In the context of three stages of production, these are usually referred to as the "short run," the "optimal level of production," and the "long run." The specific characteristics of each stage may vary depending on the industry or context.

Step 3: Determine the input variables
Common input variables in production functions include capital (K) and labor (L). You can choose these variables for depicting the three stages of production.

Step 4: Determine the output variable
The output variable can represent the quantity of goods or services produced (Q). This is the vertical axis of your production function graph.

Step 5: Sketch the graph
On a graph, place the output (Q) on the vertical axis and the input variables (K and L) on the horizontal axis.

Short Run Stage:
In this stage, at least one input variable (e.g., capital) is fixed, while the other variable (e.g., labor) is variable. Since only labor can be adjusted, draw a curved increasing line representing the relationship between labor and output. As more labor is added, the output increases, but at a diminishing rate.

Optimal Level of Production:
In this stage, both capital and labor are variable and can be adjusted. Draw a line representing the most efficient combination of capital and labor that maximizes output. This line is usually upward sloping but with a less steep slope compared to the short run stage.

Long Run Stage:
In this stage, all inputs can be adjusted. Draw a line that represents the maximum output attainable using various combinations of capital and labor. This line typically has the least steep slope compared to the previous two stages.

Step 6: Label the graph
Add appropriate labels, such as "short run," "optimal level of production," and "long run," to indicate the respective stages. Also, label the axes as "Quantity of Output" (vertical axis) and "Quantity of Inputs" (horizontal axis), specifying the input variables used.

By following these steps, you can draw a production function indicating three stages of production. Remember that the specific shape of the curves depends on the nature of the production function in each industry or context.