Nonlinear relationships can be more complex than the ones we've seen so far. To the right we show a positive, nonlinear relationship that starts out increasing at a decreasing rate, but at higher levels of Q the curvature changes and the relationship becomes one that is increasing at an increasing rate.

   This is a Total Cost curve showing that cost increases as output, Q, increases but that the rate of increase depends on the amount of output. When Q is very low the slope is 3 but falling. The declining slope shows that cost is increasing at a decreasing rate. Toward the middle of the graph the curve "flattens out" and the slope becomes quite small, though never negative.⁹ As we move farther to the right the direction of curvature changes and the slope begins increasing again, showing that as Q continues to rise cost is increasing at an increasing rate.

⁹ Relationships where the slope changes sign are common, but the relationship shown to the right is not one of these.

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