**The Law of Variable Proportions**

The law of variable proportions, also known as the law of diminishing returns, is an economic concept that explains the relationship between the inputs used in production and the resulting output. According to this law, as more and more units of a variable input are added to a fixed input, the marginal product of the variable input will eventually decline.

**Explanation with the Help of a Diagram:**

To understand the law of variable proportions, let's consider a hypothetical scenario where a farmer is cultivating a fixed piece of land. The farmer has a fixed amount of land (a fixed input) and decides to increase the number of workers (a variable input) to cultivate the land more efficiently.

1. **Stage 1 - Increasing Marginal Product**: Initially, when the farmer adds more workers to the land, the marginal product (additional output generated by each additional unit of input) increases. This happens because the workers can specialize in different tasks, leading to improved productivity. The graph for this stage shows an upward-sloping curve.

2. **Stage 2 - Diminishing Marginal Product**: As the number of workers continues to increase, a point is reached where the marginal product starts to decline. This is because the fixed amount of land becomes overcrowded with workers, and there may not be enough resources (such as tools or space) to accommodate the increased workforce efficiently. The graph for this stage shows a plateau or a gently sloping curve.

3. **Stage 3 - Negative Marginal Product**: Beyond a certain point, adding more workers becomes counterproductive. The fixed input (land) is unable to support the increasing variable input (workers), leading to a decrease in the marginal product. The graph for this stage shows a downward-sloping curve.

The law of variable proportions can be visualized through a graph, where the x-axis represents the quantity of the variable input (workers) and the y-axis represents the resulting output. Initially, the graph shows an increasing marginal product, then a plateau, and finally a declining marginal product.

It is important to note that the law of variable proportions assumes that all other factors of production remain constant except for the variable input being analyzed. In reality, various factors can influence production, such as technology, capital, and management practices. Nonetheless, the law of variable proportions provides valuable insights into the relationship between inputs and output in the short run.