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Exercises · Q27
Q.

A firm's SMCSMC schedule is shown in the following table. The total fixed cost of the firm is Rs 100. Find the TVCTVC, TCTC, AVCAVC and SACSAC schedules of the firm.

QQSMCSMC (Rs)
1500
2300
3200
4300
5500
6800
Puducherry CbseNCERTSubjective· 5mImportance★★★★★
73% · 27/37 Questions
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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.

SMCn=TVCn−TVCn−1SMC_n = TVC_n - TVC_{n-1}

TVCn=∑i=1nSMCiTVC_n = \sum_{i=1}^{n} SMC_i

TCn=TVCn+TFCTC_n = TVC_n + TFC

AVCn=TVCnQnAVC_n = \frac{TVC_n}{Q_n}

SACn=TCnQnSAC_n = \frac{TC_n}{Q_n}

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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