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Exercises · Q26
Q.

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 TVCTVC, TFCTFC, AVCAVC, AFCAFC, SACSAC and SMCSMC schedules of the firm for the corresponding values of output.

QQTCTC (Rs)
150
265
375
495
5130
6185
Sikkim CbseNCERTSubjective· 5mImportance★★★★★
70% · 26/37 Questions
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Given total cost and one piece of information about average fixed cost, we can recover the entire cost structure: fixed cost remains constant at all output levels, variable cost is the residual, and the per-unit averages and marginal cost follow by division and differencing.

The logic of cost decomposition

Total cost splits into two components: the part that does not change with output (fixed cost, like rent or a manager's salary) and the part that does (variable cost, like raw materials and hourly wages). Mathematically,

TC=TFC+TVC.TC = TFC + TVC.

Fixed cost is the same whether you produce one unit or six; variable cost starts at zero when output is zero and rises as production expands. Once we know TFCTFC, everything else falls into place: TVCTVC is simply TC−TFCTC - TFC, average fixed cost is AFC=TFCQAFC = \frac{TFC}{Q}, average variable cost is AVC=TVCQAVC = \frac{TVC}{Q}, short-run average cost (also called ACAC or SACSAC) is TCQ\frac{TC}{Q}, and short-run marginal cost is the increment in total cost when output rises by one unit, SMC=ΔTC/ΔQ=TCn−TCn−1SMC = \Delta TC / \Delta Q = TC_n - TC_{n-1}.

The question hands us a single anchor: at Q=4Q=4, average fixed cost is Rs 5. That tells us

AFC4=TFC4=5  ⟹  TFC=20.AFC_4 = \frac{TFC}{4} = 5 \implies TFC = 20.

Because fixed cost never changes, TFC=20TFC = 20 at every level of output. Now we can fill in the rest.

TVC=TC−TFC,AVC=TVCQ,AFC=TFCQ,SAC=TCQ,SMC=TCn−TCn−1.TVC = TC - TFC, \quad AVC = \frac{TVC}{Q}, \quad AFC = \frac{TFC}{Q}, \quad SAC = \frac{TC}{Q}, \quad SMC = TC_n - TC_{n-1}.

Step-by-step construction of the schedules

For Q=1Q=1:

TVC=50−20=30TVC = 50 - 20 = 30

AFC=201=20AFC = \frac{20}{1} = 20

AVC=301=30AVC = \frac{30}{1} = 30

SAC=501=50SAC = \frac{50}{1} = 50

SMCSMC: not defined for the first unit in this table (no prior output to compare), though one could interpret it as the change from zero output; we'll compute it from Q=2Q=2 onward.

For Q=2Q=2:

TVC=65−20=45TVC = 65 - 20 = 45

AFC=202=10AFC = \frac{20}{2} = 10

AVC=452=22.5AVC = \frac{45}{2} = 22.5

SAC=652=32.5SAC = \frac{65}{2} = 32.5

SMC=65−50=15SMC = 65 - 50 = 15

For Q=3Q=3:

TVC=75−20=55TVC = 75 - 20 = 55

AFC=203≈6.67AFC = \frac{20}{3} \approx 6.67

AVC=553≈18.33AVC = \frac{55}{3} \approx 18.33

SAC=753=25SAC = \frac{75}{3} = 25

SMC=75−65=10SMC = 75 - 65 = 10

For Q=4Q=4:

TVC=95−20=75TVC = 95 - 20 = 75

AFC=204=5AFC = \frac{20}{4} = 5 (matches the given information)

AVC=754=18.75AVC = \frac{75}{4} = 18.75

SAC=954=23.75SAC = \frac{95}{4} = 23.75

SMC=95−75=20SMC = 95 - 75 = 20

For Q=5Q=5:

TVC=130−20=110TVC = 130 - 20 = 110

AFC=205=4AFC = \frac{20}{5} = 4

AVC=1105=22AVC = \frac{110}{5} = 22

SAC=1305=26SAC = \frac{130}{5} = 26

SMC=130−95=35SMC = 130 - 95 = 35

For Q=6Q=6:

TVC=185−20=165TVC = 185 - 20 = 165

AFC=206≈3.33AFC = \frac{20}{6} \approx 3.33

AVC=1656=27.5AVC = \frac{165}{6} = 27.5

SAC=1856≈30.83SAC = \frac{185}{6} \approx 30.83

SMC=185−130=55SMC = 185 - 130 = 55

Note

Notice that AFCAFC falls continuously as output rises—fixed cost is being spread over more units. Meanwhile SMCSMC first falls (from 15 to 10), then rises sharply, a pattern consistent with diminishing marginal returns in the short run.

The complete cost schedules …

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