A firm’s SMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVC, TC, AVC and SMC schedules of the firm.
| TC | |
|---|---|
| 0 | - |
| 1 | 500 |
| 2 | 300 |
| 3 | 200 |
| 4 | 300 |
| 5 | 500 |
| 6 | 800 |
Given: TFC = Rs 100, and the table shows SMC schedule.
Step 1: Calculate TC Schedule At Q=0, TC = TFC = Rs 100 (since TVC = 0 at zero output) TC at each level = TC at previous level + SMC
TC at Q=1 = 100 + 500 = Rs 600 TC at Q=2 = 600 + 300 = Rs 900 TC at Q=3 = 900 + 200 = Rs 1100 TC at Q=4 = 1100 + 300 = Rs 1400 TC at Q=5 = 1400 + 500 = Rs 1900 TC at Q=6 = 1900 + 800 = Rs 2700
Step 2: Calculate TVC Schedule TVC = TC – TFC
TVC at Q=0 = 100 – 100 = Rs 0 TVC at Q=1 = 600 – 100 = Rs 500 TVC at Q=2 = 900 – 100 = Rs 800 TVC at Q=3 = 1100 – 100 = Rs 1000 TVC at Q=4 = 1400 – 100 = Rs 1300 TVC at Q=5 = 1900 – 100 = Rs 1800 TVC at Q=6 = 2700 – 100 = Rs 2600
Step 3: Calculate AVC Schedule AVC = TVC ÷ Q
AVC at Q=1 = 500 ÷ 1 = Rs 500 AVC at Q=2 = 800 ÷ 2 = Rs 400 AVC at Q=3 = 1000 ÷ 3 = Rs 333.33 AVC at Q=4 = 1300 ÷ 4 = Rs 325 AVC at Q=5 = 1800 ÷ 5 = Rs 360 AVC at Q=6 = 2600 ÷ 6 = Rs 433.33
Complete Schedule Table:
| Q | SMC (Rs) | TC (Rs) | TVC (Rs) | AVC (Rs) |
|---|---|---|---|---|
| 0 | – | 100 | 0 | – |
| 1 | 500 | 600 | 500 | 500 |
| 2 | 300 | 900 | 800 | 400 |
| 3 | 200 | 1100 | 1000 | 333.33 |
| 4 | 300 | 1400 | 1300 | 325 |
| 5 | 500 | 1900 | 1800 | 360 |
| 6 | 800 | 2700 | 2600 | 433.33 |
Explanation
The question provides the SMC schedule (though labeled as TC in the table header, the question text clarifies it shows SMC). Using the relationship SMC = ΔTC/Δq, we can derive TC by cumulatively adding SMC to the previous TC. Starting from Q=0 where TC equals TFC (Rs 100), each subsequent TC is calculated. TVC is derived using TVC = TC – TFC, and AVC using AVC = TVC/q. The AVC first falls (from Rs 500 to Rs 325 at Q=4) and then rises, showing the typical U-shaped AVC curve.
Solution Steps
Step 1: Identify that the table shows SMC values, and at Q=0, TC = TFC = Rs 100
Step 2: Calculate TC at each output level using TC(n) = TC(n-1) + SMC(n)
Step 3: Calculate TVC at each level using TVC = TC – TFC
Step 4: Calculate AVC at each level using AVC = TVC ÷ Q
Step 5: Present all schedules in a complete table format