Concept Architecture
Concept
Theoretically, Cross-Price Elasticity measures the responsiveness of the quantity demanded for one good to a change in the price of another good. It is a fundamental concept in microeconomic demand theory used to quantify the degree of substitution or complementarity between products. Cross-price elasticity exists to identify competitive relationships between goods and to understand how price changes in one market influence demand in another.
Mathematically, cross-price elasticity is represented as the ratio of the percentage change in the quantity demanded of one good to the percentage change in the price of another good. Positive values indicate substitute goods, negative values indicate complementary goods, and values close to zero indicate little or no economic relationship between the products. The mathematical framework provides a standardised measure of interdependence between demand functions.
In practice, cross-price elasticity is estimated using market data, econometric demand models, consumer choice models and regression analysis. In health economics, it is applied to evaluate substitution between pharmaceuticals, healthcare services, insurance products and preventive interventions, supporting pricing decisions, reimbursement policy, market competition analysis and health technology assessment.
Purpose
Used to quantify substitution and complementarity between healthcare goods and services, evaluate competitive market behaviour, estimate demand responses to price changes and inform pricing, reimbursement and health policy decisions.
Mathematical Formulae
Primary Formula
E?? = %?Q? � %?P?
Supporting Formulae
Arc cross-price elasticity:
E?? = ((Q?? ? Q??) / ((Q?? + Q??) � 2)) � ((P?? ? P??) / ((P?? + P??) � 2))
Interpretation:
- E?? > 0 : Substitute goods
- E?? < 0 : Complementary goods
- E?? � 0 : Unrelated goods
Related Mathematical Methods
- Demand function estimation
- Multiple regression analysis
- Almost Ideal Demand System (AIDS)
- Discrete choice modelling
- Consumer demand modelling
Example
A branded medicine increases in price by 10%. Demand for a generic equivalent increases from 1,000 to 1,150 prescriptions per month, representing a 15% increase.
E?? = 15% � 10% = 1.5
A cross-price elasticity of 1.5 indicates that the products are substitutes, with demand for the generic increasing as the branded medicine becomes more expensive.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| Percentage Change | =(B3-B2)/B2 | Calculate percentage change in quantity demanded or price. |
| Cross-Price Elasticity | =((B3-B2)/B2)/((C3-C2)/C2) | Estimate cross-price elasticity between competing healthcare products. |
| IF | =IF(D2>0,"Substitutes",IF(D2<0,"Complements","Unrelated")) | Classify the economic relationship between healthcare interventions. |
VBA (Optional)
Automate calculation of cross-price elasticities across multiple healthcare products and generate a substitution matrix for market analysis.
Sources
- 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.
- Varian HR. Intermediate Microeconomics: A Modern Approach. W.W. Norton.
- Nicholson W, Snyder C. Microeconomic Theory: Basic Principles and Extensions. Cengage Learning.
- ISPOR Good Practice Reports.
Related Concepts (2)
Library
Publications
1
The Economics of Health and Health Care — Folland, Goodman, Stano & Danagoulian, 9th Edition ed., 2024 (Routledge)
The market-leading general health economics textbook, giving comprehensive coverage of health economics through core economic themes and balancing theory, empirical evidence and public policy. The ninth edition adds chapters on health disparities and pandemic economics.
BookView source →
Frequently Asked Questions (6)
What is cross-price elasticity?
A measure of how the quantity demanded of one good responds to a price change in a different good, such as a substitute or complement.
Source: Varian 2014
How is cross-price elasticity calculated?
Cross-price elasticity is found by dividing the percentage change in the quantity demanded of one good by the percentage change in the price of another. Because both are expressed as proportional changes, the result is a pure number that does not depend on the units in which quantity or price are counted. A value of one half, for instance, means a rise of a tenth in the second good's price is associated with a rise of a twentieth in demand for the first. Varian (2014) sets out this calculation.
Source: Varian 2014
What does the sign of cross-price elasticity indicate?
The sign of cross-price elasticity indicates the relationship between the two goods. A positive value means the goods are substitutes: a rise in one good's price raises demand for the other, as buyers switch to it. A negative value means they are complements: a rise in one good's price reduces demand for the other, since they are used together. A value near zero means the goods are largely unrelated in demand, with the price of one barely affecting the other.
Source: Varian 2014
How does cross-price elasticity distinguish substitutes from complements?
Substitutes are goods that can replace each other in use, so a rise in one's price leads buyers to switch to the other, giving a positive cross-price elasticity. Complements are goods used together, so a rise in one's price reduces demand for both, giving a negative cross-price elasticity. The distinction reflects how the goods function for the consumer, and the cross-price elasticity measures the strength of the relationship, whichever kind it is, by how much demand for one responds to the other's price.
Source: Varian 2014
How is cross-price elasticity used in health care?
Cross-price elasticity is used in health care to gauge how the price of one service or product affects demand for another, informing pricing and policy. For example, it can indicate whether generic and branded drugs are substitutes, so that a rise in one's price shifts demand to the other, or whether a treatment and a follow-up service are complements. Understanding these relationships helps predict the wider effects of a price change, such as a co-payment, beyond the good directly affected.
Source: Varian 2014
What are the limitations of cross-price elasticity?
Cross-price elasticity describes the relationship between two goods over the range of prices observed, so it may not hold for large price changes or different conditions. It reflects the particular pair of goods and the buyers studied, and can change over time as alternatives and preferences shift. In health care, insurance and limited patient information complicate the response to price, so estimated elasticities may understate or distort the underlying relationship between the goods.
Source: Varian 2014
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 10 Sep 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EE-ME-013
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