Average Cost Cost quantity AC C q C

Average Cost = Cost / quantity AC = C / q C q 35 24 23 22 20 1 2 3 4 5 C AC = C/q 1 20 20/1 = 20 2 22 22/2 = 11 3 23 23/3 = 7. 67 4 24 24/4 = 6 5 35 35/5 = 7 q

Average Cost AC = Cost / quantity = Slope of the line from the origin C q AC = m = 7 35 AC = m = 7. 67 24 23 22 20 C AC = C/q 1 20 m = 20/1 = 20 2 22 m = 22/2 = 11 3 23 m = 23/3 = 7. 67 4 24 m = 24/4 = 6 5 35 m = 35/5 = 7 AC = m = 6 Least slope, Least AC 1 2 3 4 5 q

• 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 MC > AC MC < AC MC = AC MC < AC Minimum Average Cost when: MC = AC Slope of the tangent line = Slope of the line from the origin q

C MC > AC MC < AC MC = AC Minimum Average Cost q MC < AC MC > AC Marginal Cost is less than Average Cost By increasing production, the average cost is reduced Marginal Cost is greater than Average cost By 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.

Example: If the cost function is C = 2 q 3 - 6 q 2 + 7 q a) Find the marginal cost MC: MC = C ' = 6 q 2 - 12 q + 7 b) Find the average cost AC: AC = C / q = (2 q 3 - 6 q 2 + 7 q )/q = 2 q 2 - 6 q + 7 c) Find the point where AC is minimum: AC = MC 2 q 2 - 6 q + 7 = 6 q 2 - 12 q + 7 0 = 4 q 2 - 6 q 0 = 2(2 q - 3) q = 0 (not a solution) or q = 3/2 = 1. 5 units

d) Find the cost (C) of producing 0. 5, 1, 1. 5 , 2. 5 and 3 units. e) Find the Marginal Cost (MC) of producing 0. 5 th, 1 st, 1. 5 th , 2 nd , 2. 5 th and 3 rd unit. f) Find the Average Cost (AC) of producing q C = 2 q 3 - 6 q 2 + 7 q 0. 5, 1, 1. 5 , 2. 5 and 3 units. MC = 6 q 2 - 12 q + 7 AC = 2 q 2 - 6 q + 7 0. 5 2. 25 Dollars 2. 5 Dollars/unit 4. 5 Dollars/unit 1 3 Dollars 1 Dollar/unit 3 Dollar/unit 1. 5 3. 74 Dollars 2. 5 Dollars/unit 6 Dollars 7 Dollars/unit 3 Dollars/unit 11. 25 Dollars 14. 5 Dollars/unit 25 Dollars/unit 7 Dollars/unit 2 2. 5 3 21 Dollars MC = AC

Marginal Cost MC Cost C Average Cost AC Lowest point for AC or Minimum AC AC = MC