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Producer Behavior – Cost

To analyze a firm’s 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. 

 

Created by Frank Levy and Myounggu Kang
Last Updated on September 26, 2003