A revised version of this item is available at www.econmodel.com/classic/ucost1.htm
Why MC is above, below, and equal to AC
Answer 1: Numerical Example. The first approach looks at what
happens when the average cost changes from 10 to 9, 10, or 11 as the quantity
increases from 100 to 101. These changes in average cost are exaggerated
for a 1% increase in quantity, but the numbers for the three cases illustrate
the character of the changes.
| Q · AC | |||||||
| Decreasing AC | Constant AC | Increasing AC | |||||
| Q = 100 | 100 · 10 = 1000 | 100 · 10 = 1000 | 100 · 10 = 1000 | ||||
| Q = 101 | 101 · 9 = 909 | 101 · 10 = 1010 | 101 · 11 = 1111 | ||||
| MC | -91 | 10 | 111 | ||||
| MC < AC | MC = AC | MC > AC | |||||
Answer 2: Algebra. Let ACn denote the average cost for a quantity of n. Look at what happens when the average cost changes from AC100 to AC101 as Q changes from 100 to 101.
MC = 101 · AC101 - 100 · AC100
MC= AC101 + 100 · (AC101 - AC100)
If AC is increasing ( AC101 - AC100 > 0 ), then MC > AC101. If AC is decreasing ( AC101 - AC100 < 0 ), then MC < AC101. If AC is constant ( AC101 - AC100 = 0 ), then MC = AC101.
Answer 3: Calculus. The first equality is the definition of MC. The second equality is the definition of AC.
MC = dTC / dQ = d(Q · AC) / dQ
Apply freshman calculus.
MC = AC + Q · dAC / dQ
If dAC / dQ > 0, then MC > AC. If dAC / dQ < 0, then MC < AC. If dAC / dQ = 0, then MC = AC.
Posted by bparke at January 11, 2003 03:35 PM