Quality and Welfare in a Mixed Duopoly with Regulated Prices: The Case of a Public and a Private Hospital

Abstract. Hospital markets are often characterized by price regulation and the existence of different ownership types. Using a Hotelling framework, this paper analyses the effect of heterogeneous objectives of hospitals on quality differentiation, profits and overall welfare in a price‐regulated duopoly with exogenous symmetric locations. In contrast to other studies on mixed duopolies, this paper shows that, in this framework, privatization of the public hospital may increase overall welfare. This holds if the public hospital is similar to the private hospital or less efficient and competition is low. The main driving force is the single‐regulated price which induces under‐provision (over‐provision) of quality of the more (less) efficient hospital compared with the first best. However, if the public hospital is sufficiently more efficient and competition is fierce, a mixed duopoly outperforms both a private and a public duopoly due to an equilibrium price below (above) the price of the private (public) duopoly. This medium price discourages over‐provision of quality of the less efficient hospital and – together with the non‐profit objective – encourages an increase in quality of the more efficient public hospital.     

Efficiency,access, and the mixed delivery of health care services

Universal health systems often rely on both pubic provision and contracting arrangements with private hospitals. This paper studies the optimal mix of public and private provision of health care services. We propose a model in which the regulator acts as athird-party payer, and aims to ensure universal access to treatment at minimal cost. Patients need one unit of medical services and differ in the severity of illness. A private and a public hospital are available. Under incomplete contracts, ownership affects the regulatory constraints and the power of managerial incentives. Only the private manager internalizes profits, and has incentives to reject costly patients and to exert effort in cost reduction. Contracting with the private hospital is optimal when managerial effort is relatively effective in reducing costs. By using the public hospital as a last resort provider, the regulator can ensure access, provide incentives to the private manager, and internalize part of the resulting cost savings. Imposing a no-dumping constraint on the private hospital reduces the power of incentives and is not always optimal.     

Equality of opportunity and optimal cash and in-kind policies

This paper examines the argument for public provision of certain private goods, like education and health, based on equality of opportunity by studying the utility possibility frontier of a society in which there is a concern for the distribution of these goods. A given quality of education or health services can be consumed for free in the public sector, but people can opt-out and purchase their desired quality levels in the private sector. Some of the conclusions are: (i) a pure cash transfer is optimal when the utility redistribution is either “sufficiently” small or large; (ii) if and only if both the equality-of-opportunity concern and the utility redistribution are large enough, can an in-kind program which attracts the whole population be justified; (iii) even when everybody chooses the in-kind program, it may be optimal to perform some additional utility redistribution by increasing the size of such program.     

VOLUNTARY CONTRIBUTIONS TO A PUBLIC GOOD: NON-NEUTRALITY RESULTS

Abstract.  We show that the well-known neutrality theorem (that a small redistribution of wealth does not affect the aggregate private provision of a public good) no longer holds if agents take into account the effect of their individual supply of the public good on the relative price of private goods.     

Saving the public from the private? Incentives and outcomes in dual practice

We consider a monopoly physician offering free public treatment and, if allowed, a private treatment for which patients have to pay out of pocket. While patients differ in the propensity to benefit from private treatment it always yields better health outcomes than public treatment but is also more costly in terms of money and time. We study the physician's supply of private care and allocation of time costs across public and private patients and contrast these with the first‐best allocation. To increase the willingness‐to‐pay for private treatment the physician shifts time costs to public patients. While this turns out to be socially optimal, the resulting positive network effect leads to an over‐provision of private care if time costs are sufficiently high. A second‐best allocation arises when the health authority sets public reimbursement but has no control over private provision. Depending on the welfare weight the health authority attaches to physician profits, a ban of dual practice may improve on the second‐best allocation. Notably, a ban benefits not only public patients but also private patients with a moderate propensity to benefit from private care.     

Pricing of Transport Networks,Redistribution, and Optimal Taxation

The author studies optimal pricing of roads and public transport in the presence of nonlinear income taxation. Individuals are heterogeneous in unobservable earning ability. Optimal transport tariffs depend on time costs of travel and work schedule adjustments (days and hours worked per day) as a response to commuting costs. The author finds that discounts for low‐income individuals are optimal only if the time cost of a trip is small enough. Lower travel time costs facilitate screening; therefore, redistribution provides an additional motive for congestion pricing. Finally, the study investigates the desirability of means‐testing of transport tariffs.     

Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

Is Fiscal Progressivity Enhanced by Redistribution in Kind?

This paper considers the redistributive effects of four mixed fiscal systems in which redistribution in cash is combined with redistribution in kind. A private good is offered by both the public and the private sector, at a non-zero price in both cases, so that the market is vertically segmented and the quality differences are used to select recipients on the basis of their income. This paper shows how an appropriate selection of recipients can add redistributive power to an already redistributive taxation system, while universal public provision never does. A numerical simulation gives some policy insights.     

Public–private mix of health expenditure: A political economy and quantitative analysis

This paper constructs a simple model to examine decisions on public and private health spending under majority voting. In the model, agents with heterogeneous incomes choose how much to consume and spend on health care and vote for public health expenditure. The health status of an agent is determined by a CES composite of public and private health expenditure. The existence and uniqueness of the voting equilibrium are established. A quantitative exercise reveals the importance of the relative effectiveness of public and private health expenditure and their substitutability in determining the public‐private mix of health expenditure and in accounting for the observed differences across a sample of 22 advanced democratic countries.     

Price–quality competition in a mixed duopoly

We examine competition between a private and a public provider in markets for merit goods, such as education, healthcare, housing, recreation, or culture. The private firm provides a high‐price/high‐quality variety of the good and serves richer individuals, whereas the public firm provides a low‐price/low‐quality variety and serves poorer individuals. We first characterize the private competitor’s best response to changes in the public firm’s price and quality. This enables us to examine the distributional effects of policies that affect the price or quality of the public firm’s product. We then numerically characterize the public firm’s optimal provision policy, taking the private response into consideration. Our results have implications for the financing of publicly provided goods, and for whether additional resources, if available, should be spent on reducing the price or enhancing the quality of these goods.     

Optimal price‐level drift under commitment in the canonical New Keynesian model

Abstract In both the canonical and many extended versions of the New Keynesian model, optimal monetary policy under commitment implies price‐level stationarity as long as expectations are rational. We show that this is no longer the case if the central bank and private agents make decisions before observing current shocks. The optimal amount of price‐level drift in response to unexpected innovations to inflation is quantitatively important. This result has important implications for monetary policy, including the design of the optimal loss function for the central bank if it cannot commit to its future policies.     

State versus private provision: How does China’s market‐oriented reform affect healthcare delivery?

The role of the government in health care provision remains a contested issue worldwide. Public hospitals dominate China’s health care industry. However, in the early 2000s, the eastern China city of Suqian privatized all its hospitals and relaxed entry barriers for private hospitals. We assess the impact of the pro‐market reform on hospital performance using a differences‐in‐differences approach. We find that the pro‐market reform decreased medical price and expenditure, improved self‐reported health outcomes, and reduced search time and cost for patients. We show that after the reform, Suqian residents had greater trust in doctors than did residents from other cities.     

Price Discrimination in Public Healthcare

Could a public healthcare system use price discrimination—paying medical service providers different fees, depending on the service provider's quality—lead to improvements in social welfare? We show that differentiating medical fees by quality increases social welfare relative to uniform pricing (i.e. quality‐invariant fee schedules) whenever hospitals and doctors have private information about their own ability. We also show that by moving from uniform to differentiated medical fees, the public healthcare system can effectively incentivise good doctors and hospitals (i.e. low‐cost‐types) to provide even higher levels of quality than they would under complete information. In the socially optimal quality‐differentiated medical fee system, low‐cost‐type medical‐service providers enjoy a rent due to their informational advantage. Informational rent is socially beneficial because it gives service providers a strong incentive to invest in the extra training required to deliver high‐quality services at low cost, providing yet another efficiency gain from quality‐differentiated medical fees.     

A Discriminatory Mechanism to Reduce Urban Congestion

In this article, we propose an optimal mechanism to reduce congestion when information is asymmetric. Each car driver receives a quantity of traffic rights such that his adjusted marginal benefit is equal to the marginal cost of congestion and payments are based on willingness to pay. We show that the level of congestion achieved is lower and each car user can receive more or fewer rights than under complete information. With symmetric beliefs, the payment rule results from a second‐degree price discrimination. When beliefs are asymmetric, it results simultaneously from a second‐degree price discrimination and from a third‐degree price discrimination and high willingness‐to‐pay car users are discriminated against. The revenue raised can be used to reduce distortionary taxes, thereby gaining public acceptability.     

Public Investment, Congestion, and Private Capital Accumulation

This paper analyses the impact of public investment on the dynamics of private capital formation in an intertemporal optimising market-clearing framework. The key feature characterising the analysis is that the public good is treated as a durable capital good, subject to congestion. We show how in the presence of congestion the effect of government investment on private capital formation involves a tradeoff between the degree of substitution between private and public capital in production and the degree of congestion. Both lump-sum and distortionary tax financing are considered, with this tradeoff being tightened in the latter case     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

COLLUSION,FLUCTUATING DEMAND,AND PRICE RIGIDITY*

We study an infinitely repeated Bertrand game in which an i.i.d. demand shock occurs in each period. Each firm receives a private signal about the demand shock at the beginning of each period. At the end of each period, all information but the private signals becomes public. We consider the optimal symmetric perfect public equilibrium (SPPE) mainly for patient firms. We show that price rigidity arises in the optimal SPPE if the accuracy of the private signals is low. We also study the implications of more firms and firms' impatience on collusive pricing.     

Profiling hospital utilization in a mixed public–private system

While there is an extensive body of literature on the demand for hospital services, little is known about the interaction between public and private hospitals in a mixed system. In this article, we (1) apply latent class analysis to identify distinct subgroups of patients who use the hospital market differently, (2) characterize each patient type by their personal characteristics and (3) link the patient type to future hospital admissions. We apply our analysis to individual-level longitudinal patient data from Australia, focusing on three popular procedures that are performed in both public and private hospitals. We find 4–5 patient types. The most common types use either a public or a private hospital almost exclusively and absorb a moderate level of hospital resources. The severe types represent 13–17% of patients. The type which uses both sectors makes up 10–20% and tends to have private health insurance coverage. The patient types are predictive of prospective utilizations as we find that patients tend to be admitted to the sector they have used in the past. By revealing how patients use coexisting public and private hospitals, our results have direct implications on health resource financing and allocations.