Cost Curves and Their Relationships

The per-unit cost curves and the way they relate to one another are the most heavily examined part of this chapter. All of it follows from three total-cost concepts — $TFC$, $TVC$ and $TC$ — and the four per-unit concepts derived from them.

The Total Cost Curves

• $TFC$ is a horizontal straight line — fixed cost is the same at every output, including zero.
• $TVC$ starts from the origin (zero at zero output) and rises as output rises, typically flattening first (when marginal cost is falling) and then getting steeper (when marginal cost is rising).
• $TC = TFC + TVC$, so the $TC$ curve has the same shape as $TVC$ but starts at the height of $TFC$ on the vertical axis (its value at zero output equals $TFC$). The vertical gap between $TC$ and $TVC$ is always exactly $TFC$.

The Four Per-Unit Cost Curves

Why AFC Falls Continuously

$AFC=\dfrac{TFC}{Q}$ is a fixed number divided by a rising output, so it falls continuously and gets closer and closer to the horizontal axis without ever touching it (a rectangular hyperbola). This is why the gap between the $AC$ and $AVC$ curves — which equals $AFC$ — narrows as output rises but never closes.

The Key MC-AC and MC-AVC Relationship

The single most important result of this chapter:

• The $MC$ curve cuts both the $AVC$ curve and the $AC$ curve exactly at their minimum points, and cuts them from below.
• When $MC < AC$, the $AC$ curve is falling; when $MC > AC$, the $AC$ curve is rising; when $MC = AC$, $AC$ is at its minimum. Exactly the same holds for $MC$ and $AVC$. …