Short-Run Costs

Core Idea

In the short run, some inputs (typically capital) are fixed and others (typically labor) are variable. Total cost equals fixed cost (FC) plus variable cost (VC). Average total cost (ATC = TC/Q), average variable cost (AVC = VC/Q), and marginal cost (MC = dTC/dQ) are the key per-unit measures. The MC curve intersects both ATC and AVC at their minimum points, a consequence of the mathematical relationship between marginal and average values. The U-shaped cost curves arise directly from diminishing marginal returns to the variable input.

How It's Best Learned

Build the cost curves numerically from a production table and then graph them, explicitly linking the MC-ATC intersection to the algebra. Identifying the efficient scale (minimum ATC) is a key applied exercise.

Common Misconceptions

• Fixed costs do not affect marginal cost — students often add FC into MC calculations.
• The MC curve intersects ATC at the *minimum* of ATC, not at any arbitrary point; this is a mathematical necessity, not a coincidence.

Explainer

Short-run cost analysis is the direct translation of what you already know about production into the language of money. From your study of the production function, you know that adding more of a variable input (labor) to a fixed input (capital) eventually produces diminishing marginal returns — each additional worker adds less to output than the one before. Cost curves are just this physical production story rephrased in dollars.

Fixed costs (FC) are unavoidable in the short run — the factory lease, equipment depreciation, insurance. They do not change with output. Variable costs (VC) rise as you produce more, because you must hire more labor and buy more raw materials. Total cost (TC = FC + VC) combines both. The key insight is asymmetry: since FC is constant, *all* of the short-run changes in total cost come from variable cost. This means marginal cost — the cost of producing one more unit — is entirely driven by what happens to variable inputs. Fixed costs are irrelevant to marginal cost, because they don't change at all.

The U-shape of the marginal cost (MC) curve traces directly back to production. When you add early workers to a fixed capital stock, they divide tasks, specialize, and output rises fast relative to cost — MC falls. But as the plant fills up, diminishing returns set in: each additional worker adds less output than the last, so you need more and more labor to produce one more unit, and MC rises. The same physical law that shaped the production function shapes the MC curve, just viewed from the cost side.

The relationship between MC and the average cost curves follows from pure arithmetic. Whenever marginal cost is below average total cost, the average must be falling — the new unit is cheaper than the average so it pulls the average down. Whenever MC exceeds ATC, the average is rising. MC must therefore cross ATC exactly at its minimum — this is not an empirical coincidence but a mathematical law, like how your test average falls whenever a new score is below your current average. The same logic applies to AVC. The efficient scale — the output level at which ATC is minimized — is where a firm produces most cheaply per unit. For a competitive firm, that minimum ATC is the long-run benchmark that determines the market price in equilibrium.