Marginal Cost Formula
Reference for MC = ΔTC / ΔQ.
Covers average cost relationship, fixed vs variable costs, and profit-maximizing output where MC equals marginal revenue.
The Formula
MC = ΔTC / ΔQ
Marginal cost is the additional cost incurred by producing one more unit of output. It helps businesses determine the optimal level of production for maximum profit.
Variables
| Symbol | Meaning |
|---|---|
| MC | Marginal cost (cost per additional unit) |
| ΔTC | Change in total cost |
| ΔQ | Change in quantity produced |
Example 1
Total cost rises from $10,000 to $10,800 when production increases from 100 to 110 units
ΔTC = $10,800 - $10,000 = $800
ΔQ = 110 - 100 = 10
MC = 800 / 10
MC = $80 per unit
Example 2
A bakery's cost goes from $2,500 to $2,540 when making 1 more cake
ΔTC = $2,540 - $2,500 = $40
ΔQ = 1
MC = $40 (the cost of producing one more cake)
When to Use It
Use the marginal cost formula when:
- Deciding whether to increase production
- Setting prices that cover the cost of additional output
- Finding the profit-maximizing quantity (where MC = marginal revenue)
- Analyzing economies or diseconomies of scale
Key Notes
- MC typically falls first (economies of scale as capacity is used efficiently) then rises (diminishing returns as inputs are stretched), producing the classic U-shaped MC curve
- The profit-maximizing rule: keep producing as long as MC < marginal revenue (MR); stop at MC = MR — any unit beyond that costs more to produce than it earns
- Marginal cost is based only on variable costs (materials, labor, energy) — fixed costs (rent, equipment) do not change with output and are excluded from MC
Key Notes
- Formula: MC = ΔTC/ΔQ = dTC/dQ: The change in total cost from producing one additional unit. For a continuous cost function, MC is the derivative of total cost with respect to quantity. Fixed costs do not affect MC — only variable costs matter.
- Profit maximization: produce where MC = MR: A firm maximizes profit by producing up to the point where marginal cost equals marginal revenue. Producing one more unit beyond this point adds more cost than revenue; producing less foregoes profitable units.
- The U-shaped MC curve: MC typically falls initially (specialization, economies of scale within a plant) then rises (diminishing marginal returns as capacity is approached). The minimum of MC corresponds to the most efficient production rate.
- MC is the supply curve: In competitive markets, a firm's supply curve is its marginal cost curve above average variable cost. The market supply curve is the horizontal sum of all firms' MC curves. Price signals from demand directly control quantity through this MC relationship.
- Applications: Marginal cost analysis guides production volume decisions, pricing strategy (price = MC under perfect competition; price > MC under monopoly), make-vs-buy decisions, airline seat pricing (near-zero MC for the last seat), and utility rate regulation.