Show the relationship between total cost (TC), total fixed cost (TFC) and total variable cost (TVC) in short run.

In the short run, a firm’s total cost (TC) is the sum of its total fixed cost (TFC) and total variable cost (TVC). This relationship is expressed mathematically as:

$$TC=TFC+TVC$$

Key Relationships:

1. Total Cost (TC):

   • Represents the total expenditure incurred by a firm to produce a given level of output.
   • Includes both fixed and variable costs.

2. Total Fixed Cost (TFC):

   • Costs that do not change with the level of output in the short run.
   • Examples: Rent, salaries of permanent workers, insurance premiums, interest on loans.
   • Remains constant regardless of production volume.

3. Total Variable Cost (TVC):

   • Costs that vary directly with the level of output.
   • Examples: Raw materials, wages of temporary workers, electricity bills, transportation costs.
   • Increases as production rises and decreases as production falls.

Graphical Representation:

• The TFC curve is a horizontal line (parallel to the x-axis) because fixed costs do not change with output.
• The TVC curve starts from the origin (0,0) and slopes upward as output increases.
• The TC curve is obtained by vertically adding TFC and TVC at each level of output. It starts above the TVC curve by the amount of TFC and rises at the same slope as TVC.

Mathematical Explanation:

• If a firm produces 0 units of output, its TC = TFC (since TVC = 0).
• As production increases, TVC rises, and thus TC increases by the same amount.
• The slope of the TC curve is equal to the slope of the TVC curve because the change in TC is solely due to changes in TVC (TFC remains fixed).

Example:

Suppose a firm has:

• TFC = Rs. 50,000 (fixed costs like rent, salaries).
• TVC at 100 units = Rs. 30,000 (variable costs like raw materials).

Then, $$TC=TFC+TVC=50,000+30,000=\text{Rs. 80,000}$$

If production increases to 200 units and TVC rises to Rs. 50,000, then: $$TC=50,000+50,000=\text{Rs. 100,000}$$

This demonstrates that while TFC remains constant, TVC and TC change with output. The relationship TC = TFC + TVC holds true in all production scenarios in the short run.