Modern Cost Analysis

Concept

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Theoretically, Economies of Scale describe the reduction in average cost that occurs as the volume of production or service delivery increases. The concept originates from production theory and reflects the ability of organisations to spread fixed costs over greater output, improve operational efficiency, exploit specialisation and utilise resources more effectively. In health economics, economies of scale are fundamental to understanding the efficiency of hospitals, laboratories, screening programmes and other healthcare providers as activity levels increase.

Mathematically, economies of scale occur when average cost decreases as output expands. Within a cost function, this is characterised by a declining average cost curve over the relevant range of production. Economies of scale are commonly evaluated using estimated cost functions or measures of scale elasticity that compare the proportional change in costs with the proportional change in output.

In practice, economies of scale are investigated using provider-level expenditure and activity data. Econometric estimation of cost functions enables analysts to determine whether increasing patient volume reduces average treatment costs after adjusting for case mix and service complexity. Evidence of economies of scale informs decisions regarding service consolidation, provider configuration, hospital mergers and investment in high-volume specialist services.

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Purpose

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Used to determine whether increasing the scale of healthcare production reduces average costs, thereby informing decisions on service organisation, provider efficiency and optimal resource allocation.

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Mathematical Formulae

Primary Formula

AC(Q) = TC(Q) / Q

Economies of scale exist when:

dAC(Q) / dQ < 0

Supporting Formulae

Scale elasticity of cost:

SE = MC / AC

Economies of scale occur when:

SE < 1

where:

• MC = marginal cost
• AC = average cost

Related Mathematical Methods

• Cost Function
• Average Cost
• Marginal Cost
• Scale Elasticity
• Diseconomies of Scale
• Econometric Cost Function Estimation

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Example

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A diagnostic imaging centre increases annual scan volume from 20,000 to 40,000 examinations. Total operating costs increase from �6 million to �10 million.

Average Cost at 20,000 scans:

�6,000,000 � 20,000 = �300 per scan

Average Cost at 40,000 scans:

�10,000,000 � 40,000 = �250 per scan

Because average cost decreases as output increases, the imaging centre demonstrates economies of scale, indicating improved production efficiency through higher service volume.

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Excel Implementation

Function	Example Formula	Health Economics Application
SLOPE	=SLOPE(AverageCostRange,OutputRange)	Assesses whether average cost decreases as output increases.
LINEST	=LINEST(CostRange,OutputRange,TRUE,TRUE)	Estimates the underlying healthcare cost function.
SUM	=TotalCost/Output	Calculates average cost at different production volumes.
IF	=IF(CurrentAC<PreviousAC,"Economies","No Economies")	Identifies reductions in average cost as activity increases.
FORECAST.LINEAR	=FORECAST.LINEAR(NewOutput,CostRange,OutputRange)	Projects total costs for higher service volumes.

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VBA (Optional)

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VBA can automate estimation of provider cost functions and identify the output range over which economies of scale are achieved across healthcare organisations.

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Sources

• Varian HR. Intermediate Microeconomics: A Modern Approach. W.W. Norton.
• Nicholson W, Snyder C. Microeconomic Theory: Basic Principles and Extensions. Cengage Learning.
• Coelli TJ, Rao DSP, O'Donnell CJ, Battese GE. An Introduction to Efficiency and Productivity Analysis. Springer.
• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.