Inelastic Demand

Inelastic Demand in Health Care and Medicines

Inelastic demand is the case in which buyers cut their purchases by a smaller percentage than the price rises, so the own-price elasticity is negative and smaller than one in absolute value. Most estimates for medical care as a whole fall in this range, which is why cost sharing trims the use of care without cutting it sharply and why patients' own spending usually rises when charges go up. The same property gives medicine makers pricing power when insurance shields patients from the list price, and it explains why tobacco taxes raise revenue more readily than they reduce smoking. The general measure is covered on the price elasticity of demand page and the opposite case on the elastic demand page.

Where inelastic demand sits on the elasticity scale

Elasticities are classified by size. The OpenStax microeconomics text by Shapiro, MacDonald and Greenlaw states that elasticities less than one indicate low responsiveness to price and correspond to inelastic demand, and that the elasticity is usually reported as an absolute value. A reported 0.2 and a signed minus 0.2 therefore describe the same response.

$$\varepsilon = \frac{\partial Q}{\partial P}\,\frac{P}{Q}$$

where $\varepsilon$ is the own-price elasticity, $Q$ is the quantity demanded, $P$ is the price the buyer faces, and $\partial Q / \partial P$ is the slope of the demand curve at that point. Demand is inelastic when $\varepsilon$ lies between minus one and zero, and perfectly inelastic at zero, an extreme that the OpenStax text says is approached by necessities with no close substitutes, such as life-saving drugs.

Spending moves in the same direction as price when demand is inelastic. For a small price change the proportional change in spending is approximately as follows.

$$\frac{\Delta E}{E} \approx (1 + \varepsilon)\,\frac{\Delta P}{P}$$

where $E = P \times Q$ is spending by the buyers who face price $P$, which is also revenue to the seller, and $\Delta$ marks a small change. With $\varepsilon$ between minus one and zero the bracket is positive, so a higher price raises spending. Elasticity also varies along a straight-line demand curve, where the OpenStax example finds 0.45 between one pair of points and 1.47 higher up.

Why demand for medical care is price inelastic

Ringel and colleagues, in a RAND review of the demand for health care, expect demand for health care services to be relatively inelastic, in large part because there are few close substitutes for medical services. The OpenStax text adds that elasticities are often lower in the short run than in the long run, and an acute illness leaves little time to adjust.

Insurance adds to this. Cover lowers the price paid at the point of use, and the review reports that studies consistently find lower levels of demand elasticity at lower levels of cost sharing. Money is only part of the price. The review notes that where the out-of-pocket cost is very low or zero, time prices can still ration the use of medical services, so the patient time cost of travel and waiting does some of the rationing that charges do elsewhere.

Some services respond more than others. The review finds preventive care and pharmacy among the more price-sensitive services, with elasticities around minus 0.30 against a centre of about minus 0.17 for health care in general. Among its reasons are the larger number of substitutes for preventive care and its often weaker insurance cover.

Evidence from the RAND experiment and drug cost-sharing studies

The central evidence comes from the RAND Health Insurance Experiment. Run between 1971 and 1982, it randomly assigned families to free care or to 25, 50 or 95 per cent coinsurance, among other plans. The RAND summary reports that participants with 25 per cent coinsurance spent 20 per cent less than those with free care, and those with 95 per cent coinsurance about 30 per cent less.

Aron-Dine, Einav and Finkelstein describe the famous RAND estimate that the elasticity of medical spending with respect to its out-of-pocket price is minus 0.2. The figure rests on modelling assumptions as well as the randomised data, and their own simple summaries give elasticities between minus 0.04 and minus 0.6. Ringel and colleagues find that much of the response comes through whether people use any care at all.

Every one of these estimates is inelastic, and none is zero. Aron-Dine and colleagues recall that at the time of the experiment medical care was argued to be determined by needs and therefore not sensitive to price, a view the experiment rejected. A JAMA review by Goldman, Joyce and Zheng of 132 studies found that each 10 per cent increase in cost sharing was associated with a fall of 2 to 6 per cent in prescription drug spending, depending on the drug class and the patient's condition. For Medicare Part D, Einav and Finkelstein report an elasticity of about minus 0.05 from one model of the same data and about minus 0.25 from another, so the estimate also depends on the model.

What cost sharing cuts when demand is inelastic

A small elasticity says how much use falls when the price rises. It does not say which care is given up. The RAND summary reports that cost sharing reduced the use of both highly effective and less effective services in roughly equal proportions.

For the average participant the reduction in use had no adverse effect on health. The exceptions fell on the poorest and sickest 6 per cent, who had better outcomes under free care for 4 of the 30 conditions measured, including the control of high blood pressure. Goldman and colleagues found that higher drug cost sharing was associated with lower rates of treatment, worse medication adherence and more frequent discontinuation, and, for some chronic conditions such as congestive heart failure and diabetes, with greater use of medical services. An inelastic average can hide a clinically important response.

Inelastic demand and moral hazard in health insurance

In the insurance literature the price response of demand has its own name. Einav and Finkelstein describe moral hazard in health insurance as the responsiveness of demand for care to the price the patient pays, conditional on underlying health status, and note that the view that care is determined by need amounts to saying demand is completely inelastic with respect to its price.

The elasticity matters because of an argument they trace to Pauly. If use responds to price and health status cannot be written into the contract, full insurance costs more than people may be willing to pay, and they cite Holmstrom for the result that optimal contracts are then incomplete. The closer demand is to perfectly inelastic, the less extra use full health insurance induces, and the weaker the case on these grounds for charges at the point of use. An elasticity of minus 0.2 is far from perfectly inelastic, and Cutler and Zeckhauser, quoted by Aron-Dine and colleagues, read the RAND elasticities as showing moderate moral hazard in demand.

Pricing power when insured demand is inelastic

The revenue rule matters for sellers who set their own prices. Marginal revenue can be written in terms of the elasticity.

$$MR = P\left(1 + \frac{1}{\varepsilon}\right)$$

where $MR$ is the change in total revenue from selling one more unit, $P$ is the price and $\varepsilon$ is the own-price elasticity at that price. When $\varepsilon$ lies between minus one and zero the bracket is negative, so a seller with pricing power and positive marginal cost gains from raising the price until demand at the chosen price becomes elastic.

The demand a manufacturer faces depends on what patients pay. Danzon, Towse and Mestre-Ferrandiz write that insurance undermines patients' price sensitivity, potentially leading to prices above second-best efficient levels. For countries with universal insurance they describe a remedy in which each payer sets an incremental cost-effectiveness ratio threshold based on its citizens' willingness to pay for health, manufacturers price to it, and payers limit reimbursement to patients for whom the drug is cost-effective at that price. A cost-effectiveness threshold used this way supplies the price limit that inelastic patient demand does not, the logic behind value-based pricing.

Taxes on products with inelastic demand

The OpenStax text cites research suggesting that a 10 per cent rise in cigarette prices reduces adult smoking by about 3 per cent, and concludes that higher cigarette taxes raise revenue without much affecting the quantity smoked, with the burden falling on the more inelastic side of the market. For a Pigouvian tax meant to reduce consumption, inelastic demand means a smaller health effect for each pound of tax and a larger tax take.

Worked example with a prescription charge rise

All numbers in this example are illustrative. A payer covers a medicine with a list price of GBP 40 per item. Patients pay a fixed copayment of GBP 10 and the payer pays GBP 30. Patients collect 100,000 items a year, and the copayment rises to GBP 12, an increase of 20 per cent.

1. Choose the demand form. The analysis assumes a constant elasticity of minus 0.3 with respect to the copayment, inside the range implied by the drug review. The constant-elasticity form is used because a 20 per cent change is too large for the linear approximation.

$$Q_1 = Q_0 \left(\frac{c_1}{c_0}\right)^{\varepsilon}$$

where $Q_0$ and $Q_1$ are items dispensed before and after the change, $c_0$ and $c_1$ are the copayments before and after, and $\varepsilon$ is the constant elasticity with respect to the copayment.

2. Forecast use. The ratio is 12 / 10 = 1.2, and 1.2 raised to the power minus 0.3 is 0.946772. Items fall to 100,000 × 0.946772 = 94,677, a fall of 5,323 items or 5.3 per cent.

3. Patient spending. Patients paid 10 × 100,000 = GBP 1,000,000 and now pay 12 × 94,677 = GBP 1,136,124, a rise of 13.6 per cent, as the revenue rule predicts.

4. Payer spending. The payer's spending drops from 30 × 100,000 = GBP 3,000,000 to 28 × 94,677 = GBP 2,650,956, a saving of GBP 349,044. Of this, 2 × 94,677 = GBP 189,354 is shifted to patients on items still dispensed, and 30 × 5,323 = GBP 159,690 comes from items no longer dispensed.

5. Perfectly inelastic case. With an elasticity of zero all 100,000 items are still dispensed and the payer saves 2 × 100,000 = GBP 200,000, all of it a transfer to patients.

6. Interpretation. The charge raises patients' spending, lowers the payer's and cuts use only modestly. Whether the 5,323 forgone items were low-value prescriptions or doses that kept a chronic condition under control is a separate question that the elasticity cannot answer.

Using inelastic estimates in budget impact and economic evaluation

An elasticity enters budget impact analysis as a forecast of use after a change in charges. The revenue rule applies only to the buyers who face the price, so the payer's spending has to be calculated separately from the change in use and its own share of the price.

The choice of price is the hardest step. Insurance contracts with deductibles and caps have no single price, and Aron-Dine and colleagues show that the choice of summary price for one RAND plan can change a predicted spending reduction by a factor of two. Because elasticities tend to be lower at low levels of cost sharing, an estimate from one range of charges may not hold for a much larger change. The uncertainty belongs in sensitivity analysis, and effects on health, such as lost adherence leading to later admissions, have to be modelled separately.

Common misreadings of inelastic demand in health

Errors with the term usually come from treating a low elasticity as no elasticity. Others come from carrying one figure into a setting where it does not apply.

1. Reading inelastic as unresponsive. An elasticity of minus 0.2 still means a 10 per cent price rise cuts spending on care by about 2 per cent.
2. Assuming that only low-value care is lost. In the RAND experiment cost sharing reduced highly effective and less effective care in roughly equal proportions.
3. Using one elasticity for all care. Preventive care and medicines respond more than care in general, and because substitutes drive elasticity, demand for one brand among close substitutes is more elastic than demand for the class, which the cross-price elasticity captures.
4. Applying the revenue rule to the wrong budget. A charge that raises patients' spending can lower the payer's spending at the same time.

Sources

• Aron-Dine A, Einav L, Finkelstein A. The RAND Health Insurance Experiment, three decades later. Journal of Economic Perspectives. 2013;27(1):197-222. doi:10.1257/jep.27.1.197. https://pmc.ncbi.nlm.nih.gov/articles/PMC3943162/
• Brook RH, Keeler EB, Lohr KN, Newhouse JP, Ware JE, Rogers WH, et al. The Health Insurance Experiment: a classic RAND study speaks to the current health care reform debate. RAND Research Brief RB-9174-HHS. Santa Monica, CA: RAND Corporation; 2006. https://www.rand.org/pubs/research_briefs/RB9174.html
• Danzon PM, Towse AK, Mestre-Ferrandiz J. Value-based differential pricing: efficient prices for drugs in a global context. NBER Working Paper 18593. Cambridge, MA: National Bureau of Economic Research; 2012. doi:10.3386/w18593. https://www.nber.org/papers/w18593
• Einav L, Finkelstein A. Moral hazard in health insurance: what we know and how we know it. Journal of the European Economic Association. 2018;16(4):957-982. doi:10.1093/jeea/jvy017. https://pmc.ncbi.nlm.nih.gov/articles/PMC6128379/
• Goldman DP, Joyce GF, Zheng Y. Prescription drug cost sharing: associations with medication and medical utilization and spending and health. JAMA. 2007;298(1):61-69. doi:10.1001/jama.298.1.61. https://pmc.ncbi.nlm.nih.gov/articles/PMC6375697/
• Ringel JS, Hosek SD, Vollaard BA, Mahnovski S. The Elasticity of Demand for Health Care: A Review of the Literature and Its Application to the Military Health System. MR-1355-OSD. Santa Monica, CA: RAND Corporation; 2002. https://www.rand.org/pubs/monograph_reports/MR1355.html
• Shapiro D, MacDonald D, Greenlaw SA. Principles of Microeconomics. 3rd ed. Houston: OpenStax; 2022. Chapter 5, sections 5.1 to 5.3. https://openstax.org/books/principles-microeconomics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply