A firm's schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the , , and schedules of the firm.
| (Rs) | |
|---|---|
| 1 | 500 |
| 2 | 300 |
| 3 | 200 |
| 4 | 300 |
| 5 | 500 |
| 6 | 800 |
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Start your 14-day free trial to unlock the full solution →The short-run marginal cost (SMC) is the cost of producing one more unit. By cumulatively summing SMC, we get TVC; adding TFC gives TC; dividing by Q gives AVC and SAC.
We start with the fundamental relationship: Marginal cost is the change in total variable cost when output increases by one unit. In the short run, fixed cost does not change, so SMC is also the change in total cost. Therefore, to go from SMC to TVC, we simply add up the marginal costs of each successive unit.
Given that TFC = Rs 100, we can build the schedules step by step.
Step 1: Find TVC
For Q = 1, TVC₁ = SMC₁ = Rs 500.
For Q = 2, TVC₂ = TVC₁ + SMC₂ = 500 + 300 = Rs 800.
For Q = 3, TVC₃ = 800 + 200 = Rs 1000.
For Q = 4, TVC₄ = 1000 + 300 = Rs 1300.
For Q = 5, TVC₅ = 1300 + 500 = Rs 1800.
For Q = 6, TVC₆ = 1800 + 800 = Rs 2600.
Step 2: Find TC
TC = TVC + TFC. Since TFC is constant at Rs 100:
TC₁ = 500 + 100 = 600
TC₂ = 800 + 100 = 900
TC₃ = 1000 + 100 = 1100
TC₄ = 1300 + 100 = 1400
TC₅ = 1800 + 100 = 1900
TC₆ = 2600 + 100 = 2700
Step 3: Find AVC and SAC
AVC = TVC / Q, SAC = TC / Q.
For Q = 1: AVC = 500/1 = 500; SAC = 600/1 = 600
For Q = 2: AVC = 800/2 = 400; SAC = 900/2 = 450
For Q = 3: AVC = 1000/3 ≈ 333.33; SAC = 1100/3 ≈ 366.67
For Q = 4: AVC = 1300/4 = 325; SAC = 1400/4 = 350
For Q = 5: AVC = 1800/5 = 360; SAC = 1900/5 = 380
For Q = 6: AVC = 2600/6 ≈ 433.33; SAC = 2700/6 = 450 …
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