Supply

Supply in Health Care Markets

In economics, supply is a whole schedule, the amount that hospitals, laboratories, clinicians or drug manufacturers would provide at every possible price or payment rate, with costs, technology and capacity held fixed, as distinct from the number of services delivered last year. Health economists use it to predict how providers respond to tariffs, fees and input costs, and to work out how much of a rise in spending buys extra care and how much becomes provider income. Health care strains the idea, because payers set many prices, entry to the professions is licensed, many hospitals are not run for profit, and staff and equipment take years to expand. The buyer's side is on the demand page, and the two sides meet in market equilibrium.

The supply function and what shifts it

The OpenStax economics text describes supply as the amount of a good or service a producer is willing to produce or bring to market at each price. Supply is the relationship across a range of prices, while quantity supplied is one point on it. For a health service the relationship can be written as follows.

$$Q_s = S(P, w, T, K, N, g)$$

where $Q_s$ is the quantity supplied per period (tests, operations, bed days or packs of a medicine), $P$ is the price or payment the provider receives per unit, $w$ is the prices of inputs such as staff wages and consumables, $T$ is the technology of production, $K$ is fixed capacity such as beds, scanners and trained staff in post, $N$ is the number of suppliers, and $g$ collects government policy, including regulation, taxes, subsidies and licensing.

Varying $P$ with everything else fixed traces the supply curve. OpenStax calls the positive link between price and quantity supplied the law of supply and notes that it assumes all other influences on supply are held constant. A change in the product's own price is a movement along the curve, while a change in input costs, technology or government decisions shifts the whole curve. A rise in agency nursing rates shifts a hospital's supply of bed days to the left, and an automated analyser that cuts the cost per test shifts a laboratory's supply to the right.

Marginal cost as the source of the supply curve

For a firm that takes the market price as given, the supply curve comes from its costs. OpenStax states that, for a perfectly competitive firm, the marginal cost curve above the minimum point of the average variable cost curve becomes the firm's supply curve. Below that shutdown point the firm cannot cover its variable costs.

$$P = MC(q) \quad \text{for} \quad P \ge \min AVC$$

where $P$ is the price received, $MC(q)$ is the marginal cost of the $q$-th unit, and $\min AVC$ is the lowest point of average variable cost.

Read sideways, the curve gives the lowest price at which each unit would be offered, which OpenStax describes as the minimum price a firm will accept to produce a given quantity. The area between the price line and the curve is therefore producer surplus. Few health providers are price-taking competitive firms, but the derivation still shows that supply slopes upward only as steeply as marginal cost rises. A hospital or laboratory with spare staff and equipment has nearly flat marginal cost and can expand cheaply, while one at its capacity cannot expand at any price until the fixed inputs change. Hospital cost function studies estimate that shape.

Price elasticity of supply and the time horizon

The responsiveness of supply is measured by the price elasticity of supply, the percentage change in quantity supplied divided by the percentage change in price. OpenStax classes supply as elastic when the elasticity exceeds one and inelastic when it is below one. For a finite change the midpoint form is used.

$$\varepsilon_s = \frac{(Q_1 - Q_0)/\bar{Q}}{(P_1 - P_0)/\bar{P}}$$

where $\varepsilon_s$ is the arc price elasticity of supply, $Q_0$ and $Q_1$ are the quantities supplied before and after the change, $P_0$ and $P_1$ are the prices before and after, and $\bar{Q}$ and $\bar{P}$ are the averages of the two quantities and the two prices.

OpenStax notes that supply and demand are more elastic in the long run. In health care the short run is fixed by the staff in post, the beds and the theatres, and the long run by training places and building programmes, so the same price change can draw a small response in the first year and a larger one later. Unlike the price elasticity of demand, the supply elasticity is normally positive.

Clemens and Gottlieb used a change in Medicare's physician fees to estimate the response. In 1997 Medicare consolidated the geographic regions across which it adjusts physician payments, which created price shocks that differed by area. On average a 2% rise in payment rates led to a 3% rise in care provided, an implied elasticity of 3/2 = 1.5, and elective procedures such as cataract surgery responded much more strongly than less discretionary services. Evidence on the labour supply of nurses is less settled. A review of American and British econometric studies by Antonazzo and colleagues found considerable variation in results depending on the methods used, particularly in the effect of wages, and only one study using UK data.

Supply conditions that set health care apart

Kenneth Arrow, in his 1963 paper on the welfare economics of medical care, noted that in competitive theory supply is governed by the net return from production compared with the return from using the same resources elsewhere, and that medical care departs from this in several ways. Entry to the profession was restricted by licensing, which restricts supply, raises the cost of care and is defended as guaranteeing a minimum of quality. American medical education was costly but borne only to a minor extent by the student, a subsidy that should lower the price of medical services but was offset by rationing places in medical schools. Arrow also pointed to the overwhelming predominance of non-profit over proprietary hospitals, which he read as a preference, among donors or patients, against the profit motive in the supply of hospital services.

These departures change how supply should be read. A provider that does not maximise profit may answer a higher payment with more staff or higher quality rather than more volume, so the slope of its supply curve depends on its objectives as well as its costs. Where a payer sets the price through a tariff or fee schedule, as described on the provider payment and fee-for-service pages, the supply curve shows the volume offered at that tariff, and a tariff below the clearing level shows up as waiting lists rather than a price rise, as the equilibrium page explains. Under a block budget or capitation the payment for one more unit of care is close to zero, so the price that matters for supply is the marginal payment and not the average one. Where clinicians can shape what patients ask for, a payment rise can move demand as well as supply, the case covered under supplier-induced demand.

Medicines show the same logic at the bottom of the price range. The FDA, for the inter-agency Drug Shortages Task Force it led, analysed 163 drugs that went into shortage between 2013 and 2017. Of these, 63% were sterile injectables, 67% had a generic version on the market, and the median time since first approval was almost 35 years. Its report states that these shortages do not appear to resolve in the textbook way, with prices rising and suppliers increasing production, and names as the first root cause a lack of incentives to produce less profitable drugs, which weakens firms' motivation to stay in or enter the market and to invest in quality and redundant capacity. A recalculation in February 2020 found that 42% of the shortage drugs had a significant production increase and 30% had their quantity fully restored to pre-shortage levels.

Worked example with a laboratory tariff and a capacity limit

All figures are illustrative. A pathology laboratory sells blood tests to a commissioner at a tariff per test, and its marginal cost rises with monthly volume as overtime and agency staff are used.

$$MC(Q) = 5 + \frac{Q}{200}$$

where $MC(Q)$ is the marginal cost in GBP of the $Q$-th test in a month and $Q$ is the number of tests per month.

1. Supply curve. Setting the tariff equal to marginal cost gives $Q_s = 200(P - 5) = 200P - 1000$ for tariffs of GBP 5 or more, where $P$ is the tariff in GBP. Average variable cost, $AVC = 5 + Q/400$, is lowest at GBP 5, so the whole curve lies above the shutdown point.

2. Quantity at two tariffs. At GBP 30 the laboratory supplies 200 × 30 − 1,000 = 5,000 tests and at GBP 36 it supplies 200 × 36 − 1,000 = 6,200 tests.

3. Elasticity. With midpoints of 5,600 tests and GBP 33, the proportional changes are 1,200 / 5,600 = 0.214 in quantity and 6 / 33 = 0.182 in price, so the arc elasticity is 0.214 / 0.182 = 1.18, which is elastic.

4. Where the extra spending goes. Spending rises from 30 × 5,000 = GBP 150,000 to 36 × 6,200 = GBP 223,200, an increase of GBP 73,200. The resource cost of the 1,200 extra tests is the area under marginal cost, 1,200 × (30 + 36) / 2 = GBP 39,600. The other GBP 33,600 is a gain in producer surplus, made up of 6 × 5,000 = GBP 30,000 extra on the tests already supplied and 0.5 × 6 × 1,200 = GBP 3,600 on the new ones. About 54% of the extra spending buys resources.

5. A capacity limit. Suppose two analysers cap output at 5,800 tests a month until a third can be bought. At GBP 36 the laboratory then supplies 5,800 tests, and marginal cost at the cap is 5 + 5,800 / 200 = GBP 34, below the tariff. The proportional change in quantity is 800 / 5,400 = 0.148, so the arc elasticity falls to 0.148 / 0.182 = 0.81. Spending rises by 36 × 5,800 − 150,000 = GBP 58,800, of which the resource cost of the extra 800 tests is 800 × (30 + 34) / 2 = GBP 25,600 and the gain in producer surplus GBP 33,200. Only about 44% of the extra spending now buys extra tests.

6. Interpretation. The same tariff rise draws 1,200 extra tests when capacity can expand and only 800 while it cannot, and in that case more of the money becomes provider income. A commissioner forecasting volume from a long-run elasticity would overstate the short-run response, and an appraisal that costs the extra tests at the tariff of GBP 36 would overstate the resource cost of each one.

Supply in economic evaluation and budget planning

Supply enters economic evaluation mostly through assumptions that are seldom stated. A model that values every unit of a resource at one fixed unit cost treats the supply of that input as perfectly elastic at that cost. That is reasonable for a small programme but not for one large enough to draw on scarce staff or equipment, which is why the capacity page discusses resource constraints in economic evaluation. In the example, the commissioner's cost is the tariff while the cost to society is marginal cost, and the gap between them is producer surplus that a welfare account treats as a transfer. Forecasts of uptake in budget impact analysis also depend on supply, because a new service cannot grow faster than the trained staff and equipment needed to deliver it.

The cost-effectiveness threshold also rests on what the health system produces at the margin. Claxton and colleagues describe the threshold as the additional cost the system must bear to forgo one QALY of health through displacement, and their central estimate for the English NHS was GBP 12,936 per QALY, based on 2008 expenditure. This figure reflects the health the system produces with its marginal spending, a different quantity from the value individuals place on health.

Supply beside neighbouring terms

Several nearby terms describe parts of the supply side. The table sets out what each describes.

Common misreadings of supply in health care

Several errors recur. Treating activity data as a supply curve ignores that each observed point is an intersection with demand, often under rationing, so estimating supply needs price changes that come from outside the market, such as the Medicare consolidation used by Clemens and Gottlieb. Assuming that a tariff rise buys proportionately more care ignores capacity, which in the example turned most of the extra spending into provider income. Reading low prices as a pure gain for payers ignores the exit and shortages that the FDA task force traced to unprofitable older medicines.

Sources

• Antonazzo E, Scott A, Skatun D, Elliott RF. The labour market for nursing: a review of the labour supply literature. Health Economics. 2003;12(6):465-478. doi:10.1002/hec.737. https://pubmed.ncbi.nlm.nih.gov/12759916/
• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973. https://www.aeaweb.org/aer/top20/53.5.941-973.pdf
• Claxton K, Martin S, Soares M, Rice N, Spackman E, Hinde S, et al. Methods for the estimation of the National Institute for Health and Care Excellence cost-effectiveness threshold. Health Technology Assessment. 2015;19(14):1-503. doi:10.3310/hta19140
• Clemens J, Gottlieb JD. Do physicians' financial incentives affect medical treatment and patient health? American Economic Review. 2014;104(4):1320-1349. doi:10.1257/aer.104.4.1320. https://pmc.ncbi.nlm.nih.gov/articles/PMC4144420/
• Food and Drug Administration, Drug Shortages Task Force. Drug Shortages: Root Causes and Potential Solutions. October 2019, updated February 2020. https://www.fda.gov/drugs/drug-shortages/report-drug-shortages-root-causes-and-potential-solutions
• Greenlaw SA, Shapiro D, MacDonald D. Principles of Economics 3e. Houston, TX: OpenStax; 2022. Sections 3.1, 3.2, 5.1, 5.3 and 8.2. https://openstax.org/books/principles-economics-3e/pages/3-1-demand-supply-and-equilibrium-in-markets-for-goods-and-services