Answer to Question #172438 in Microeconomics for yaashi mehta

Question #172438

Output AC. AFC. AVC. MC

1. 100. 40

2. 36

3. 36

4. 36

5. 12. 41


1
Expert's answer
2021-03-22T11:01:25-0400

Let's first find the fixed cost (FC):


AFC1=FCQ1,AFC_1=\dfrac{FC}{Q_1},FC=AFC1Q1=$401=$40.FC=AFC_1Q_1=\$40\cdot1=\$40.

Then, we can find AFCAFC for the output from Q=2Q=2 to Q=5Q=5:


AFC2=FCQ2=$402=$20,AFC_2=\dfrac{FC}{Q_2}=\dfrac{\$40}{2}=\$20,AFC3=FCQ3=$403=$13.33,AFC_3=\dfrac{FC}{Q_3}=\dfrac{\$40}{3}=\$13.33,AFC4=FCQ4=$404=$10,AFC_4=\dfrac{FC}{Q_4}=\dfrac{\$40}{4}=\$10,AFC5=FCQ5=$405=$8.AFC_5=\dfrac{FC}{Q_5}=\dfrac{\$40}{5}=\$8.

Since, AC=AFC+AVCAC=AFC+AVC, we can find AVCAVC for each number of output:


AVC1=AC1AFC1=$100$40=$60,AVC_1=AC_1-AFC_1=\$100-\$40=\$60,AVC2=AC2AFC2=$36$20=$16,AVC_2=AC_2-AFC_2=\$36-\$20=\$16,AVC3=AC3AFC3=$36$13.33=$22.67,AVC_3=AC_3-AFC_3=\$36-\$13.33=\$22.67,AVC4=AC4AFC4=$36$10=$26,AVC_4=AC_4-AFC_4=\$36-\$10=\$26,AVC5=AC5AFC5=$12$8=$4.AVC_5=AC_5-AFC_5=\$12-\$8=\$4.

Let's find the TC. By the definition,


AC=TCQ,AC=\dfrac{TC}{Q},TC1=AC1Q1=$1001=$100,TC_1=AC_1\cdot Q_1=\$100\cdot1=\$100,TC2=AC2Q2=$362=$72,TC_2=AC_2\cdot Q_2=\$36\cdot2=\$72,TC3=AC3Q3=$363=$108,TC_3=AC_3\cdot Q_3=\$36\cdot3=\$108,TC4=AC4Q4=$364=$144,TC_4=AC_4\cdot Q_4=\$36\cdot4=\$144,TC5=AC5Q5=$125=$60.TC_5=AC_5\cdot Q_5=\$12\cdot5=\$60.

By the definition of MC we have:


MC1=TC2TC1Q2Q1=$72$10021=$28,MC_1=\dfrac{TC_2-TC_1}{Q_2-Q_1}=\dfrac{\$72-\$100}{2-1}=-\$28,MC2=TC3TC2Q3Q2=$108$7232=$36,MC_2=\dfrac{TC_3-TC_2}{Q_3-Q_2}=\dfrac{\$108-\$72}{3-2}=\$36,MC3=TC4TC3Q4Q3=$144$10843=$36,MC_3=\dfrac{TC_4-TC_3}{Q_4-Q_3}=\dfrac{\$144-\$108}{4-3}=\$36,MC4=TC5TC4Q5Q4=$60$14454=$84.MC_4=\dfrac{TC_5-TC_4}{Q_5-Q_4}=\dfrac{\$60-\$144}{5-4}=-\$84.

Finally, we get the following table:


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