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Given a table with Output (Q), Price (P), Total Cost (TC), and Marginal Cost (MC), calculate Total Revenue (TR) and Marginal Revenue (MR) for each output level.

Economics

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To complete the table, we will use the following formulas:

  • Total Revenue (TR) = Price (P) ×\times Output (Q)
  • Marginal Revenue (MR) = TRn−TRn−1\text{TR}_n - \text{TR}_{n-1} (Change in Total Revenue from the previous unit)
  • Marginal Cost (MC) = TCn−TCn−1\text{TC}_n - \text{TC}_{n-1} (Change in Total Cost from the previous unit)

Note: There appears to be a typo in the original table for Total Revenue (TR) at Output (Q) = 2. Based on the formula TR = P ×\times Q, the TR for Q=2 should be 15×2=3015 \times 2 = 30, not 36. We will use the corrected value of 30 for our calculations.

Step 1: Calculate Total Revenue (TR) for each output level.

TR0=17×0=0TR1=16×1=16TR2=15×2=30TR3=14×3=42TR4=13×4=52TR5=12×5=60TR6=11×6=66TR7=10×7=70TR8=9×8=72TR9=8×9=72TR10=7×10=70\begin{align*} \text{TR}_0 &= 17 \times 0 = 0 \\ \text{TR}_1 &= 16 \times 1 = 16 \\ \text{TR}_2 &= 15 \times 2 = 30 \\ \text{TR}_3 &= 14 \times 3 = 42 \\ \text{TR}_4 &= 13 \times 4 = 52 \\ \text{TR}_5 &= 12 \times 5 = 60 \\ \text{TR}_6 &= 11 \times 6 = 66 \\ \text{TR}_7 &= 10 \times 7 = 70 \\ \text{TR}_8 &= 9 \times 8 = 72 \\ \text{TR}_9 &= 8 \times 9 = 72 \\ \text{TR}_{10} &= 7 \times 10 = 70 \end{align*}

Step 2: Calculate Marginal Revenue (MR) for each output level using the corrected TR values.

MR1=TR1−TR0=16−0=16MR2=TR2−TR1=30−16=14MR3=TR3−TR2=42−30=12MR4=TR4−TR3=52−42=10MR5=TR5−TR4=60−52=8MR6=TR6−TR5=66−60=6MR7=TR7−TR6=70−66=4MR8=TR8−TR7=72−70=2MR9=TR9−TR8=72−72=0MR10=TR10−TR9=70−72=−2\begin{align*} \text{MR}_1 &= \text{TR}_1 - \text{TR}_0 = 16 - 0 = 16 \\ \text{MR}_2 &= \text{TR}_2 - \text{TR}_1 = 30 - 16 = 14 \\ \text{MR}_3 &= \text{TR}_3 - \text{TR}_2 = 42 - 30 = 12 \\ \text{MR}_4 &= \text{TR}_4 - \text{TR}_3 = 52 - 42 = 10 \\ \text{MR}_5 &= \text{TR}_5 - \text{TR}_4 = 60 - 52 = 8 \\ \text{MR}_6 &= \text{TR}_6 - \text{TR}_5 = 66 - 60 = 6 \\ \text{MR}_7 &= \text{TR}_7 - \text{TR}_6 = 70 - 66 = 4 \\ \text{MR}_8 &= \text{TR}_8 - \text{TR}_7 = 72 - 70 = 2 \\ \text{MR}_9 &= \text{TR}_9 - \text{TR}_8 = 72 - 72 = 0 \\ \text{MR}_{10} &= \text{TR}_{10} - \text{TR}_9 = 70 - 72 = -2 \end{align*}

Step 3: Calculate Marginal Cost (MC) for each output level.

MC1=TC1−TC0=18−10=8MC2=TC2−TC1=23−18=5MC3=TC3−TC2=25−23=2MC4=TC4−TC3=27−25=2MC5=TC5−TC4=28−27=1MC6=TC6−TC5=32−28=4MC7=TC7−TC6=40−32=8MC8=TC8−TC7=50−40=10MC9=TC9−TC8=64−50=14MC10=TC10−TC9=80−64=16\begin{align*} \text{MC}_1 &= \text{TC}_1 - \text{TC}_0 = 18 - 10 = 8 \\ \text{MC}_2 &= \text{TC}_2 - \text{TC}_1 = 23 - 18 = 5 \\ \text{MC}_3 &= \text{TC}_3 - \text{TC}_2 = 25 - 23 = 2 \\ \text{MC}_4 &= \text{TC}_4 - \text{TC}_3 = 27 - 25 = 2 \\ \text{MC}_5 &= \text{TC}_5 - \text{TC}_4 = 28 - 27 = 1 \\ \text{MC}_6 &= \text{TC}_6 - \text{TC}_5 = 32 - 28 = 4 \\ \text{MC}_7 &= \text{TC}_7 - \text{TC}_6 = 40 - 32 = 8 \\ \text{MC}_8 &= \text{TC}_8 - \text{TC}_7 = 50 - 40 = 10 \\ \text{MC}_9 &= \text{TC}_9 - \text{TC}_8 = 64 - 50 = 14 \\ \text{MC}_{10} &= \text{TC}_{10} - \text{TC}_9 = 80 - 64 = 16 \end{align*}

Step 4: Present the completed table.

The completed table is shown below:

\begin{array}{|c|c|c|c|c|c|} \hline Output (Q) & Price (P) & Total Revenue (TR) & Marginal Revenue (MR) & Total Cost (TC) & Marginal Cost (MC) \\ \hline 0 & 17 & 0 & - & 10 & - \\ \hline 1 & 16 & 16 & 16 & 18 & 8 \\ \hline 2 & 15 & 30 & 14 & 23 & 5 \\ \hline
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