To analyze a firms profit maximizing
behavior, we need three measures of cost.

Total Cost TC(Q) is the total
dollar cost of production when the firm is producing Q units of output. It is
measured in dollars.

Average Cost AC (Q) - is the
average dollar cost of production per unit when the firm is producing Q units
of output. It is measured in dollars/unit. Mathematically, AC (Q) = TC(Q)/Q

Marginal Cost MC(Q) - is the
cost per unit of producing one additional unit of output when the firm is
already producing Q units of output. It is measured in dollars/unit.
Mathematically, we can think of MC(Q) as the slope of the total cost curve
i.e. the change in total cost when one more unit is produced. In calculus
terms, MC(Q) = dTC(Q)/dQ the first derivative of the total cost curve.

The standard model of the firm shows costs
moving through three phases as output rises.

In the first phase, expansion of output
permits adoption of more efficient techniques for example, moving from hand
assembly to an assembly line. The increased efficiency is reflected in falling
Marginal Cost because each unit costs less to produce then the previous
one. In this phase, Marginal Cost lies below Average Cost each new unit costs
less than the average to this point and so Average Cost is also falling. Total
Cost is rising at a diminishing rate that is, doubling the output
less than doubles the cost.

In the second phase of expansion, the firm
begins to run into bottlenecks for example, coordination problems and so Marginal
Cost begins to rise. Since Marginal Cost is the slope of the Total Cost
Curve, Total Cost now rises at an increasing rate. But because Marginal
Cost still lies below Average Cost, Average Cost continues to fall.

In the third and final phase of expansion,
Marginal Cost now exceeds Average Cost so that Average Cost is now rising. Marginal
Cost continues to rise and Total Cost continues to rise at an increasing rate.

In the graph below, check the evolution
of the three phases of expansion.

Question: Why does Marginal Cost cut Average Cost at
the point of minimum average cost? Explain why this emerges from the
relationship between the two cost measures.