The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the TVC, TFC, AVC, AFC, SAC and SMC schedules of the firm for the corresponding values of output.
| TC | |
|---|---|
| 1 | 50 |
| 2 | 65 |
| 3 | 75 |
| 4 | 95 |
| 5 | 130 |
| 6 | 185 |
To find the various cost schedules, we first determine the Total Fixed Cost (TFC). It is given that Average Fixed Cost (AFC) at 4 units is Rs 5. Using the formula , we calculate . Since fixed costs remain constant irrespective of output, TFC is Rs 20 for all levels of output.
Next, we calculate the Total Variable Cost (TVC) for each output level using the relation . For example, at output 1, . We repeat this for all units. The AFC is calculated by dividing TFC by the quantity (), which falls as output increases. Average Variable Cost (AVC) is derived by dividing TVC by quantity ().
Short Run Average Cost (SAC) is calculated as (or ). Finally, Short Run Marginal Cost (SMC) is the change in total cost per unit change in output (). Assuming TC at zero output equals TFC (Rs 20), SMC for the first unit is .
The final schedules are presented in the table below:
| Q | TFC (Rs) | TVC (Rs) | TC (Rs) | AFC (Rs) | AVC (Rs) | SAC (Rs) | SMC (Rs) |
|---|---|---|---|---|---|---|---|
| 1 | 20 | 30 | 50 | 20.00 | 30.00 | 50.00 | 30 |
| 2 | 20 | 45 | 65 | 10.00 | 22.50 | 32.50 | 15 |
| 3 | 20 | 55 | 75 | 6.67 | 18.33 | 25.00 | 10 |
| 4 | 20 | 75 | 95 | 5.00 | 18.75 | 23.75 | 20 |
| 5 | 20 | 110 | 130 | 4.00 | 22.00 | 26.00 | 35 |
| 6 | 20 | 165 | 185 | 3.33 | 27.50 | 30.83 | 55 |
Explanation
The question requires calculating various cost concepts based on a given Total Cost (TC) schedule. The key to solving this is finding the Total Fixed Cost (TFC) first. The problem provides a specific data point: AFC at 4 units is Rs 5. Since AFC = TFC/Q, TFC can be easily derived. Once TFC is known, TVC is simply TC - TFC. The average concepts (AFC, AVC, SAC) are derived by dividing the respective total costs by quantity. SMC is derived from the difference in TC between consecutive units. The context provided in Table 3.3 and the formulas (3.7 to 3.11) clearly establish the relationships between these costs (e.g., SAC = AFC + AVC) and the method for calculating SMC.
Solution Steps
Step 1: Calculate Total Fixed Cost (TFC). Given AFC at Q=4 is Rs 5. TFC = AFC × Q = = Rs 20.
Step 2: Calculate Total Variable Cost (TVC) for each unit using TVC = TC - TFC. (e.g., at Q=1, TVC = 50 - 20 = 30).
Step 3: Calculate Average Fixed Cost (AFC) using AFC = TFC/Q. (e.g., at Q=1, AFC = 20/1 = 20).
Step 4: Calculate Average Variable Cost (AVC) using AVC = TVC/Q. (e.g., at Q=2, AVC = 45/2 = 22.5).
Step 5: Calculate Short Run Average Cost (SAC) using SAC = TC/Q. (e.g., at Q=3, SAC = 75/3 = 25).
Step 6: Calculate Short Run Marginal Cost (SMC) using SMC = ΔTC/ΔQ. Assuming TC at Q=0 is TFC (Rs 20), SMC at Q=1 is 50-20=30. Subsequent SMC is the difference in TC (e.g., at Q=2, SMC = 65-50=15).