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.     

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.