Because TVC initially increases at decreasing rate (because of bettet utilisation of fixed factor and increase in efficiency of variable factor)
And later it increases at increasing rate ( Because of fall in efficiency of variable factors due to limitation of fixed factor).

Introduction

The Total Variable Cost (TVC) curve is an important concept in economics that illustrates the relationship between the quantity produced and the total variable cost incurred. It is known for its distinctive inverted S-shape, which indicates the changing rate of cost as production levels increase. This curve provides valuable insights into the cost structure of a firm and its decision-making process.

Explanation

1. Relationship between quantity produced and total variable cost
The TVC curve shows how the total variable cost varies with the quantity produced. As the quantity produced increases, the total variable cost also increases. This is because producing more output requires more variable inputs, such as labor and raw materials, which incur additional costs.

2. Law of Diminishing Marginal Returns
The inverted S-shape of the TVC curve is primarily influenced by the Law of Diminishing Marginal Returns. According to this law, as more units of a variable input are added to a fixed input, the marginal product of the variable input initially increases, reaches a maximum, and then starts to decline. This leads to changes in the rate of cost increase.

3. Initial stage of increasing returns
At the beginning of production, the TVC curve exhibits an upward slope but at a decreasing rate. This is because the firm experiences increasing returns to scale, where each additional unit of the variable input contributes more to output than the previous one. This results in a lower increase in total variable cost.

4. Middle stage of diminishing returns
As the firm continues to increase production, it eventually reaches a point where the marginal product of the variable input starts to decline. This is known as the stage of diminishing returns. The TVC curve becomes steeper during this stage, indicating a faster rate of cost increase. The increasing cost is primarily driven by the diminishing marginal product, which requires more variable inputs to produce each additional unit of output.

5. Final stage of negative returns
In the final stage, the TVC curve still increases but at a decreasing rate. This is due to the negative returns or dis-economies of scale, where the marginal product becomes negative. This means that additional units of the variable input lead to a decrease in output. As a result, the total variable cost continues to rise, but at a slower pace.

Conclusion
The inverted S-shape of the TVC curve reflects the changing rate of cost increase as a firm produces more output. It demonstrates the initial stage of increasing returns, followed by diminishing returns, and finally negative returns. Understanding the TVC curve helps firms make informed decisions regarding production levels and cost management.