Health Economics Metrics

Topic 5 of 76 · Economic reasoning foundations

Marginal vs Average Cost

Average cost is total cost divided by units produced. Marginal cost is the cost of producing one additional unit. Decisions should be made on marginal cost — but published unit costs are almost always averages.

Why it matters

The single most common error in digital health business cases is valuing a saved resource at its average cost when the real saving is the marginal cost. A hospital bed day has an average (fully absorbed) cost of £400+, but freeing one bed day does not save £400 — the building, heating, and most staffing costs continue. The cash actually released may be £50–£150 unless enough beds are freed to close a ward.

The math

Average cost:  AC = TC / Q
Marginal cost: MC = dTC/dQ   (cost of one more/one fewer unit)

TC = total cost, Q = quantity

Fixed costs make MC < AC for capacity reductions, and MC can approach zero when spare capacity exists. Savings claims should use:

True saving = ΔQ × MC          (small changes)
True saving = step change in TC (large changes that cross a capacity threshold, e.g. closing a ward)

Worked example

Your software reduces average length of stay, freeing 1,000 bed days/year at a trust.

  • Naive claim: 1,000 × £400 average cost = £400,000 saved. Wrong.
  • Marginal claim: variable cost per bed day (food, laundry, consumables, some nursing flex) ≈ £120. Saving = 1,000 × £120 = £120,000, plus the freed capacity's value if beds are refilled with waiting elective patients (income under activity-based payment, or waiting-list reduction).
  • Step-change claim: if the trust frees 7,300 bed days/year (a 20-bed ward) it can actually close the ward: staffing + running ≈ £1.5 million/year of real cash. Now the average-cost math is closer to true.

Same intervention, three defensible numbers, depending on whether the change crosses a capacity step.

Software engineering connection

Cloud economics is native marginal-cost territory:

  • The marginal cost of one more CI run on already-reserved capacity is ≈ £0, while the average cost per run (total platform spend ÷ runs) may be pounds. Chargeback systems that bill average cost drive teams to under-use shared capacity that is actually free at the margin.
  • Conversely, "we saved 30% of compute" only releases cash if instances are actually terminated or reservations reduced — the software version of the bed-day trap. See cash-releasing vs non-cash-releasing savings.

Pitfalls

  • Valuing capacity at average cost and presenting it as cash (the classic).
  • Assuming marginal cost is constant. It steps at capacity boundaries (ward closures, license tiers, reserved-instance commitments).
  • Using marginal cost for expansion decisions but average for contraction in the same case — pick per the actual decision.

Sources