Q.Explain, using the analogy of a cricketer's batting average, why the Marginal Cost curve must lie below the Average Cost curve whenever average cost is falling, and above it whenever average cost is rising.

A cricketer's average falls when her latest score is below her existing average, and rises when it is above — cost behaves identically, with MC as the "latest score."

A cricketer's batting average, at any point in her career, is the average of all her innings scores SO FAR. Whenever she plays a new innings, two things can happen: if her score in that new innings is BELOW her existing average, including this new score in the average must pull the average DOWN — because a below-average number was just added to the pool. Conversely, if her new score is ABOVE her existing average, it pulls the average UP. Only when her new score exactly EQUALS her existing average does the average stay exactly unchanged.

Marginal Cost and Average Cost relate to each other in EXACTLY the same arithmetic way. Marginal Cost is the cost of the "newest" unit of output — analogous to the batter's latest innings score — while Average Cost is the average cost of ALL units produced so far. So:

• Whenever $MC < AC$: the newest unit costs less than the existing average, so including it pulls the average DOWN — Average Cost is falling.
• Whenever $MC > AC$: the newest unit costs more than the existing average, so including it pulls the average UP — Average Cost is rising.
• Only when $MC = AC$ does adding the newest unit leave the average exactly unchanged — this is precisely the average's minimum (or turning) point. …

Students sometimes think this relationship applies only to Average VARIABLE Cost — in fact it applies equally to Average Total Cost, and indeed to ANY marginal-average pair in economics or elsewhere (marginal product and average produ …