6.2 Unit Costing, Service Delivery & Economies of Scale

6.2 Unit Costing, Service Delivery & Economies of Scale

Unit-cost calculations compare resources used with services delivered. The hypothetical models here use stated fixed overheads, constant per-transaction variable costs and a common time horizon. Real costs may be stepped, mixed or non-linear; do not extend a simplified formula beyond its relevant range or treat the lowest modelled cost as a complete procurement decision.

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Cost Behaviour in Public Administration

To analyze public service delivery, operational expenditure must be segmented into distinct behavioural cost categories:

1. Fixed Costs (FC)

Fixed costs are expenditures that remain constant within the specified time period and relevant activity range, despite changes in the volume of services or transactions delivered. These expenses reflect the underlying capacity and administrative infrastructure of an agency:

• Property Leases & Facilities: Annual rent and rates for departmental head offices and regional public counters.
• Core ICT Infrastructure: Enterprise software licensing, cloud data centre hosting, and core network maintenance.
• Permanent Management Salaries: Remuneration for permanent administrative leadership and governance personnel.
• Depreciation: Allocation of an asset’s depreciable cost over its useful life; distinguish this accounting charge from the cash purchase price.

2. Variable Costs (VC)

In this linear model, total variable costs change in direct proportion to changes in operational activity or transaction volume. If zero services are provided, variable costs are zero:

• Transactional Consumables: Plastic smart-cards, biometric passport booklets, and specialized secure stationery.
• Secure Postage & Delivery: Postal rates for delivering driving licences, medical cards, and legal notices to citizens.
• Per-Transaction ICT Fees: Automated SMS verification alerts and payment gateway transaction fees.
• External Caseworker Fees: Contracted medical assessments, specialized legal reviews, or translation services paid per claimant.

3. Semi-Variable & Stepped Fixed Costs

Many public services feature hybrid costs:

• Semi-Variable Costs: Contain a baseline fixed fee plus a usage rate (e.g., fleet utility contracts with standing charges and per-kilometer fuel costs).
• Stepped Fixed Costs: Costs that remain fixed within a defined operational band but jump discontinuously once capacity is breached. For example, a single civil service supervisory team can oversee up to 50,000 welfare claims annually; reaching 50,001 claims requires hiring an additional Executive Officer and acquiring additional workstation licenses.

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Formulations for Total Cost and Unit Cost

Within the stipulated linear model, total cost is:

$\text{Total Cost (TC)} = \text{Fixed Costs (FC)} + [\text{Variable Cost per Unit (VC)} \times Q]$

Average cost requires $Q>0$. Here $Q$ represents the total volume of transactions, citizens served, or cases processed. The Average Unit Cost (AC)—frequently termed the unit cost per case—is obtained by dividing total cost by output:

$\text{Average Unit Cost (AC)} = \frac{\text{TC}}{Q} = \frac{\text{FC}}{Q} + \text{VC}$

The Dynamics of Spreading Overhead

With positive fixed costs and constant variable cost per unit, as $Q$ increases within the model, the term $\frac{\text{FC}}{Q}$ (Average Fixed Cost) asymptotically approaches zero. Consequently, the average unit cost declines steadily and converges toward the marginal variable cost $\text{VC}$.

Average Unit Cost
       ^
       |
  High | \ 
       |  \ 
       |   \_ 
   Low |     \___________________  Asymptotic limit = Variable Cost (VC)
       +------------------------->
       0           Volume (Q)

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Break-Even & Indifference Analysis in Service Delivery

Public service managers frequently evaluate whether to retain a decentralized delivery model or invest capital in a centralized, automated facility. This decision centers on finding the Cost Indifference Point (or operational break-even volume $Q^*$):

• Model 1 (Decentralized / Manual): Lower initial fixed overheads ($\text{FC}_1$), but higher manual variable costs per claim ($\text{VC}_1$).
• Model 2 (Centralized / Automated): High capital investment and fixed infrastructure ($\text{FC}_2$), but significantly lower automated variable costs per claim ($\text{VC}_2$).

At the indifference point, the total operational cost of both models is identical:

$\text{FC}_1 + (\text{VC}_1 \times Q^*) = \text{FC}_2 + (\text{VC}_2 \times Q^*)$

For different variable-cost rates, rearrange to solve for $Q^*$. A useful positive crossing must lie within both models’ capacity ranges:

$Q^* = \frac{\text{FC}_2 - \text{FC}_1}{\text{VC}_1 - \text{VC}_2}$

Cost-Only Decision Rule for the Stated Models

For the stated ordering $\text{FC}_2>\text{FC}_1$ and $\text{VC}_2<\text{VC}_1$:

• If projected annual transaction volume $Q < Q^*$, choose Model 1 (the lower fixed cost model).
• If projected annual transaction volume $Q > Q^*$, choose Model 2 (the lower total-cost model above the crossing). Quality, capacity and transition costs must also match the exercise assumptions.

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Life-Cycle Costing in Public Procurement

A procurement decision follows its applicable rules and published award criteria. Life-cycle costing is a cost-effectiveness approach, not a universal mandatory method for every public purchase. Article 67 of Directive 2014/24/EU recognises price or cost approaches, including life-cycle costing and price-quality criteria. Do not infer that the cheapest initial bid must always win, or that it can never win.

Life-cycle costing evaluates the Total Cost of Ownership (TCO) over a stated common horizon. For the undiscounted examples here, use:

$\text{TCO} = \text{Capital Purchase Price} + \sum_{t=1}^n \text{Operating Costs}_t + \sum_{t=1}^n \text{Maintenance Costs}_t + \text{Disposal Costs} - \text{Residual Value}$

Check whether the task includes energy, maintenance, licensing, overhauls and end-of-life values. If a discount rate is supplied, convert future amounts to the required present-value basis rather than simply adding them. Avoid counting the purchase price and its depreciation twice.

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Worked Administrative Example: Regional Hubs vs. Centralized Processing

The Department of Social Protection is evaluating the administration of a national scheme processing 400,000 annual claims. Two structural delivery options are under consideration:

• Option A (Decentralized Regional Offices): Five regional centres with combined annual fixed costs of €1,200,000 and variable processing costs of €8.50 per claim.
• Option B (Centralized Automated Facility): A single national facility with annual fixed overheads of €2,400,000 and automated variable processing costs of €3.50 per claim.

1. Determining the Cost Indifference Volume

$Q^* = \frac{2{,}400{,}000 - 1{,}200{,}000}{8.50 - 3.50} = \frac{1{,}200{,}000}{5.00} = 240{,}000 \text{ claims}$

2. Comprehensive Volume Comparison Table

At the example’s stipulated operating volume of 400,000 claims, Option B reduces average unit cost from €11.50 to €9.50, delivering an annual taxpayer saving of €800,000.