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Average Cost = Cost / quantity

C. 1. 20. 20/1 = 20. 35. 2. 22. 22/2 = 11. C. q. AC = C/q. 3. 23. 23/3 = 7.67. 24. 23. 4. 24. 24/4 = 6. 22. 5. 35. 35/5 = 7. 20. q. 1. 2. 3. 4. 5. Average Cost = Cost / quantity. AC = C / q. C. 1. 20. AC = m = 7. 35. 2. 22. C. q. AC = C/q. AC = m = 7.67.

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Average Cost = Cost / quantity

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  1. C 1 20 20/1 = 20 35 2 22 22/2 = 11 C q AC = C/q 3 23 23/3 = 7.67 24 23 4 24 24/4 = 6 22 5 35 35/5 = 7 20 q 1 2 3 4 5 Average Cost = Cost / quantity AC = C / q

  2. C 1 20 AC = m = 7 35 2 22 C q AC = C/q AC = m = 7.67 3 23 24 23 4 24 22 5 35 20 AC = m = 6Least slope, Least AC q 1 2 3 4 5 Average Cost AC = Cost / quantity = Slope of the line from the origin m = 20/1 = 20 m = 22/2 = 11 m = 23/3 = 7.67 m = 24/4 =6 m = 35/5 = 7

  3. Average Cost AC = Cost / quantity =Slope of the line from the origin • Marginal Cost MC = Cost of producing the next item =Slope of the Tangent line C q MC > AC MC < AC MC < AC MC = AC MC < AC Minimum Average Cost when:MC = ACSlope of the tangent line = Slope of the line from the origin

  4. C MC > AC MC < AC MC < AC MC < AC q MC = ACMinimum Average Cost MC < ACMarginal Cost is less than Average Cost By increasing production, the average cost is reduced • MC > ACMarginal Cost is greater than Average costBy increasing production, the average cost is increased. As long as marginal Cost MC is less than Average Cost AC, the Average Cost AC continues to get smaller. Once Marginal Cost MC is more than Average Cost AC, the Average Cost AC starts to go up.

  5. 2q2 - 6q + 7 = 6q2 - 12q + 7 Example: If the cost function is C = 2q3 - 6q2 + 7q a) Find the marginal cost MC: MC = C ' = 6q2 - 12q + 7 b) Find the average cost AC: AC = C / q = (2q3 - 6q2 + 7q )/q = 2q2 - 6q + 7 c) Find the point where AC is minimum: AC = MC 0= 4q2 - 6q 0= 2(2q - 3) q = 0 (not a solution) or q = 3/2 = 1.5 units

  6. q C = 2q3 - 6q2 + 7q MC = 6q2 - 12q + 7 AC = 2q2 - 6q + 7 2.5 Dollars/unit 4.5 Dollars/unit 0.5 2.25 Dollars 1 Dollar/unit 3 Dollar/unit 1 3 Dollars 2.5 Dollars/unit 2.5 Dollars/unit 1.5 3.74 Dollars 7 Dollars/unit 3 Dollars/unit 2 6 Dollars 14.5 Dollars/unit 4.5 Dollars/unit 2.5 11.25 Dollars 25 Dollars/unit 7 Dollars/unit 3 21 Dollars d) Find the cost (C) of producing 0.5, 1, 1.5 , 2 , 2.5 and 3 units. e) Find the Marginal Cost (MC) of producing 0.5th, 1st, 1.5th , 2nd , 2.5th and 3rd unit. f) Find the Average Cost (AC) of producing 0.5, 1, 1.5 , 2 , 2.5 and 3 units. MC = AC

  7. Marginal CostMC CostC Average CostAC Lowest point for AC or Minimum AC AC = MC

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