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Complete the table showing the relationship between Total Cost, Total Variable Cost, Average Variable Cost, and Marginal Cost. Show all calculations.

Economics

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Step-by-step solution

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Here is the completed table with all calculations shown.

The formulas used are:

  • Total Fixed Cost (TFCTFC) = Total Cost (TCTC) when Quantity (QQ) = 0 (TFC is constant for all output levels)
  • Total Variable Cost (TVCTVC) = TC−TFCTC - TFC
  • Average Fixed Cost (AFCAFC) = TFCQ\frac{TFC}{Q}
  • Average Variable Cost (AVCAVC) = TVCQ\frac{TVC}{Q}
  • Average Total Cost (ATCATC) = TCQ\frac{TC}{Q} or ATC=AFC+AVCATC = AFC + AVC
  • Marginal Cost (MCMC) = ΔTCΔQ\frac{\Delta TC}{\Delta Q} or ΔTVCΔQ\frac{\Delta TVC}{\Delta Q}

Here is the completed table:

QTCTFCTVCAFCAVCATCMC060600−−−−1140608060801408022106015030751057032706021020709060432060260156580505380603201264766064206036010607040\begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Q} & \textbf{TC} & \textbf{TFC} & \textbf{TVC} & \textbf{AFC} & \textbf{AVC} & \textbf{ATC} & \textbf{MC} \\ \hline 0 & 60 & 60 & 0 & - & - & - & - \\ 1 & 140 & 60 & 80 & 60 & 80 & 140 & 80 \\ 2 & 210 & 60 & 150 & 30 & 75 & 105 & 70 \\ 3 & 270 & 60 & 210 & 20 & 70 & 90 & 60 \\ 4 & 320 & 60 & 260 & 15 & 65 & 80 & 50 \\ 5 & 380 & 60 & 320 & 12 & 64 & 76 & 60 \\ 6 & 420 & 60 & 360 & 10 & 60 & 70 & 40 \\ \hline \end{array}

Here are the step-by-step calculations for each row:

  1. Determine TFC.

    At Q=0Q=0, TC=60TC=60. Since TVC=0TVC=0 at Q=0Q=0, TC=TFCTC=TFC. Therefore, TFC=60TFC=60 for all output levels.

  2. Calculate for Q=0Q=0.

    • TC=60TC = 60 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=60−60=0TVC = TC - TFC = 60 - 60 = 0
    • AFC,AVC,ATC,MCAFC, AVC, ATC, MC are not applicable or undefined at Q=0Q=0.

  3. Calculate for Q=1Q=1.

    • TC=140TC = 140 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=140−60=80TVC = TC - TFC = 140 - 60 = 80
    • AFC=TFCQ=601=60AFC = \frac{TFC}{Q} = \frac{60}{1} = 60
    • AVC=TVCQ=801=80AVC = \frac{TVC}{Q} = \frac{80}{1} = 80
    • ATC=TCQ=1401=140ATC = \frac{TC}{Q} = \frac{140}{1} = 140
    • MC=ΔTCΔQ=140−601−0=801=80MC = \frac{\Delta TC}{\Delta Q} = \frac{140 - 60}{1 - 0} = \frac{80}{1} = 80

  4. Calculate for Q=2Q=2.

    • TC=210TC = 210 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=210−60=150TVC = TC - TFC = 210 - 60 = 150
    • AFC=TFCQ=602=30AFC = \frac{TFC}{Q} = \frac{60}{2} = 30
    • AVC=TVCQ=1502=75AVC = \frac{TVC}{Q} = \frac{150}{2} = 75
    • ATC=TCQ=2102=105ATC = \frac{TC}{Q} = \frac{210}{2} = 105
    • MC=ΔTCΔQ=210−1402−1=701=70MC = \frac{\Delta TC}{\Delta Q} = \frac{210 - 140}{2 - 1} = \frac{70}{1} = 70

  5. Calculate for Q=3Q=3.

    • TC=270TC = 270 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=270−60=210TVC = TC - TFC = 270 - 60 = 210
    • AFC=TFCQ=603=20AFC = \frac{TFC}{Q} = \frac{60}{3} = 20
    • AVC=TVCQ=2103=70AVC = \frac{TVC}{Q} = \frac{210}{3} = 70
    • ATC=TCQ=2703=90ATC = \frac{TC}{Q} = \frac{270}{3} = 90
    • MC=ΔTCΔQ=270−2103−2=601=60MC = \frac{\Delta TC}{\Delta Q} = \frac{270 - 210}{3 - 2} = \frac{60}{1} = 60

  6. Calculate for Q=4Q=4.

    • TC=320TC = 320 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=320−60=260TVC = TC - TFC = 320 - 60 = 260
    • AFC=TFCQ=604=15AFC = \frac{TFC}{Q} = \frac{60}{4} = 15
    • AVC=TVCQ=2604=65AVC = \frac{TVC}{Q} = \frac{260}{4} = 65
    • ATC=TCQ=3204=80ATC = \frac{TC}{Q} = \frac{320}{4} = 80
    • MC=ΔTCΔQ=320−2704−3=501=50MC = \frac{\Delta TC}{\Delta Q} = \frac{320 - 270}{4 - 3} = \frac{50}{1} = 50

  7. Calculate for Q=5Q=5.

    • TC=380TC = 380 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=380−60=320TVC = TC - TFC = 380 - 60 = 320
    • AFC=TFCQ=605=12AFC = \frac{TFC}{Q} = \frac{60}{5} = 12
    • AVC=TVCQ=3205=64AVC = \frac{TVC}{Q} = \frac{320}{5} = 64
    • ATC=TCQ=3805=76ATC = \frac{TC}{Q} = \frac{380}{5} = 76
    • MC=ΔTCΔQ=380−3205−4=601=60MC = \frac{\Delta TC}{\Delta Q} = \frac{380 - 320}{5 - 4} = \frac{60}{1} = 60

  8. Calculate for Q=6Q=6.

    • TC=420TC = 420 (given)
    • TFC=60TFC = 60
    • TVC=TC−TFC=420−60=360TVC = TC - TFC = 420 - 60 = 360
    • AFC=TFCQ=606=10AFC = \frac{TFC}{Q} = \frac{60}{6} = 10
    • AVC=TVCQ=3606=60AVC = \frac{TVC}{Q} = \frac{360}{6} = 60
    • ATC=TCQ=4206=70ATC = \frac{TC}{Q} = \frac{420}{6} = 70
    • $MC = \frac{\Delta TC}{\Delta Q} = \frac{420 - 380}{6 - 5} = \frac{40}{1} =
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