Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Do Cost-Effectiveness Analyses Account for Drug Genericization? A Literature Review and Assessment of Implications

ObjectivesWe investigated how health technology assessment (HTA) organizations around the world have handled drug genericization (an allowance for future generic drug entry and subsequent drug price declines) in their guidelines for cost-effectiveness analyses (CEAs). We also analyzed a large sample of published CEAs to examine prevailing practices in the field.MethodsWe reviewed 43 HTA guidelines to determine whether and how they addressed drug genericization in their CEAs. We also selected a sample of 270 US-based CEAs from the Tufts Medical Center’s CEA Registry, restricting the sample to studies on pharmaceuticals published from 1991 to 2019 and to analyses taking a lifetime time horizon. We determined whether each CEA examined genericization (and if so, whether in base case or sensitivity analyses), and how inclusion of genericization influenced the estimated incremental cost-effectiveness ratios.ResultsFourteen (33%) of the 43 HTA guidelines mention genericization for CEAs and 4 (9%) recommend that base case analyses include assumptions about future drug price changes due to genericization. Most published CEAs (95%) do not include assumptions about future generic prices for intervention drugs. Only 2% include such assumptions about comparator drugs. Most studies (72%) conduct sensitivity analyses on drug prices unrelated to genericization.ConclusionsThe omission of assumptions about genericization means that CEAs may misrepresent the long run opportunity costs for drugs. The field needs clearer guidance for when CEAs should account for genericization, and for the inclusion of other price dynamics that might influence a drug’s cost-effectiveness.     

Provider networks and health plan premium variation

ObjectiveTo examine how plan premiums are associated with physician network breadth, hospital network breadth, and hospital network quality on the Affordable Care Act''s Health Insurance Marketplaces in all 50 states and the DC in 2016.Data SourcesData on plan premiums and characteristics came from 2016 Robert Wood Johnson Foundation Health Insurance Exchange (HIX) Compare. Provider network information was obtained from Vericred. Hospital characteristics were obtained from CMS Hospital Compare and the American Hospital Association (AHA) survey.Study DesignWe analyzed how plan premiums were associated with variations in physician network breadth, hospital network breadth, and hospital network quality using ordinary least square regressions with state‐rating area fixed effects and carrier fixed effects.Principal FindingsPlan premiums were positively associated with physician network breadth and hospital network breadth. We find the following statistically significant results: a one standard deviation increase in physician network breadth was linked to a premium increase of 2.8 percent or $101 per year; a one standard deviation increase in hospital network breadth was linked to a premium increase of 2.4 percent or $86 per year. There was no significant association between premiums and hospital network quality, as measured by hospital star ratings and the inclusion of teaching hospitals or the top‐20 hospitals nationwide.ConclusionsPhysician network breadth and hospital network breadth contributed positively to plan premiums. The roles of the two types of provider network breadth are quantitatively similar. Premiums appear to be insensitive to hospital network quality.     

Hospital Pricing Following Integration with Physician Practices

The past decade has witnessed a new wave of hospital-physician integration, with the fraction of hospitals owning any office-based physician practice increasing from 28% in 2009 to 53% in 2015 nationwide. We offer one of the first hospital-level longitudinal analyses in examining how hospital-physician integration affects hospital prices in the modern healthcare environment. We find a robust 3–5% increase in hospital prices following integration. There is little indication that hospital quality is commensurately higher or that patient mix has changed following integration. Our supplementary analyses point to stronger bargaining leverage and foreclosure of rival hospitals as potential mechanisms for the estimated price effects.     

Pricing and Reimbursement of Pharmaceuticals. A New Culture for the Community Pharmacist.

Pricing and reimbursement of pharmaceuticals are of concern for pharmacists. Different countries have different ways of organising their health care systems. The place for pharmaceuticals within these systems also differ. This article looks into the price and reimbursement systems for medicinal products in Germany, Sweden, the UK and Norway. Various ways of organising the pharmaceutical market emerge. Some existing measures have been in place for a long time while others have been introduced more recently. A common goal for the four countries seems to be the drive to cut costs, and attempts to do this can be directed through various reimbursement systems, by focusing on prices or by influencing the physicians' prescribing behaviour, either through the use of advice or through the use of budgets. It is important for the pharmacists to have indepth knowledge of the price and reimbursement system they have to work within in order to be of full service to their customers.     

The Questionable Economic Case for Value-Based Drug Pricing in Market Health Systems

This article investigates the economic theory and interpretation of the concept of “value-based pricing” for new breakthrough drugs with no close substitutes in a context (such as the United States) in which a drug firm with market power sells its product to various buyers. The interpretation is different from that in a country that evaluates medicines for a single public health insurance plan or a set of heavily regulated plans. It is shown that there will not ordinarily be a single value-based price but rather a schedule of prices with different volumes of buyers at each price. Hence, it is incorrect to term a particular price the value-based price, or to argue that the profit-maximizing monopoly price is too high relative to some hypothesized value-based price. When effectiveness of treatment or value of health is heterogeneous, the profit-maximizing price can be higher than that associated with assumed values of quality-adjusted life-years. If the firm sets a price higher than the value-based price for a set of potential buyers, the optimal strategy of the buyers is to decline to purchase that drug. The profit-maximizing price will come closer to a unique value-based price if demand is less heterogeneous.     

Alcohol taxation policy in Thailand: implications for other low- to middle-income countries

Aim Prevention of drinking initiation is a significant challenge in low‐ and middle‐income countries that have a high prevalence of abstainers, including life‐time abstainers. This paper aims to encourage a debate on an alternative alcohol taxation approach used currently in Thailand, which aims specifically to prevent drinking initiation in addition to reduce alcohol‐attributable harms. Methods Theoretical evaluation, simulation and empirical analysis. Result The taxation method of Thailand, ‘Two‐Chosen‐One’ (2C1) combines specific taxation (as a function of the alcohol content) and ad valorem taxation (as a function of the price), resulting in an effective tax rate that puts a higher tax both on beverages which are preferred by heavy drinkers and on beverages which are preferred by potential alcohol consumption neophytes, compared to either taxation system alone. As a result of these unique properties of the 2C1 taxation system, our simulations indicate that 2C1 taxation leads to a lower overall consumption than ad valorem or specific taxation alone. In addition, it puts a relatively high tax on beverages attractive to young people, the majority of whom are currently abstaining. Currently, the abstention rates in Thailand are higher than expected based on its economic wealth, which could be taken as an indication that the taxation strategy is successful. Conclusion ‘Two‐chosen‐one’ (2C1) taxation has the potential to simultaneously reduce alcohol consumption and prevent drinking initiation among youth; however, additional empirical evidence is needed to assess its effectiveness in terms of the public health impact in low‐ and middle‐income countries.     

Sharing Risk between Payer and Provider by Leasing Health Technologies: An Affordable and Effective Reimbursement Strategy for Innovative Technologies?

The challenge of implementing high-cost innovative technologies in health care systems operating under significant budgetary pressure has led to a radical shift in the health technology reimbursement landscape. New reimbursement strategies attempt to reduce the risk of making the wrong decision, that is, paying for a technology that is not good value for the health care system, while promoting the adoption of innovative technologies into clinical practice. The remaining risk, however, is not shared between the manufacturer and the health care payer at the individual purchase level; it continues to be passed from the manufacturer to the payer at the time of purchase. In this article, we propose a health technology payment strategy—technology leasing reimbursement scheme—that allows the sharing of risk between the manufacturer and the payer: the replacing of up-front payments with a stream of payments spread over the expected duration of benefit from the technology, subject to the technology delivering the claimed health benefit. Using trastuzumab (Herceptin) in early breast cancer as an exemplar technology, we show how a technology leasing reimbursement scheme not only reduces the total budgetary impact of the innovative technology but also truly shares risk between the manufacturer and the health care system, while reducing the value of further research and thus promoting the rapid adoption of innovative technologies into clinical practice.