Mobile Edition
Print
Get the Mag
Weekly UpdatesIntroduction
The paper investigates the impact of government support of a potential entrant in an industry given a monopoly firm producing a pharmaceutical drug for the treatment of a communicable disease in the presence of externalities and heterogeneous agents. The paper is motivated by the prevalence of communicable diseases such as malaria, tuberculosis and HIV/AIDS in developing countries, that often involves a monopoly firm in providing of pharmaceutical drug and government concern about the welfare of individuals in the population. The fixed cost of production often serves as a barrier to the entry of new firms, causing a monopolistic industry.
The economic literature on communicable diseases has been developing since the early of 1990's. Brito et al. (1991) analyzes externalities associated with vaccination in a static framework with heterogeneous agents and argues that it may not be correct for the government to compel all individuals to get vaccinated. Francis (1997) examines externalities in the market for vaccinations in a static and a dynamic environment respectively. Gersovitz and Hammer (2004) provide a general framework for the economics of infection and associated infection externality and prevention externality. The study reveals that in the SIS (susceptible-infected-susceptible) model, the optimal government subsidies should equally weight both preventive and therapeutic activities. However, these studies relate to market power-free framework. In contrast, Geoffard and Philipson (1997) first point out that a vaccine monopolist faces a non-standard dynamic incentive to keep the disease and thus to increase its profit. Their results show that a steady-state of infection may be compatible with a constant price. Recently, Mechoulan (2007) proposes a new theoretical framework for the dynamic problem of treatment under different market structures where externalities and heterogeneous agents are present. The main results are the price and prevalence paths of a drug monopolist converge to a non-zero steady state, while the social planner generally eradicates the disease, or subsidizes treatments when eradication is impossible or too costly.
This study extends the work of Mechoulan (2007) by introducing the government's choice into the model and investigating the impact of government funding aimed at reducing fixed entry cost of a potential entrant on market prices for treatment, the prevalence of the disease and thus on the total social welfare in a dynamic environment.
The specific questions addressed by this study are as follows: First, how does the government funding influence the market prices for treatment and the prevalence of the disease? Second, under what conditions does the government offer the subsidy fund to the potential entrant to reduce its fixed cost of entry? Third, how is the level of government funding to the potential entrant affected by parameters in the model? These questions will be addressed through the development of an economic model, involving the government's choice in a dynamic environment given the prevalence path of the disease. The economy is represented by a sequential game involving: At stage 1, the government chooses whether or not to offer a grant to the potential entrant firm 2. If the government decides to do so, the optimal value of the grant is determined at stage 2. At stage 3, observing the value of government funding (grant), the incumbent monopolist firm 1 commits the price for treatment in the first period to deter the entry of firm 2 in the second period. It is assumed that the fixed cost is sufficiently high that firm 2 does not enter without government funding (grant). As a result, the incumbent monopolist firm 1 determines the prices for treatment starting at stage 2. The key findings of the study are as follows: First, the government offers a fund to the potential entrant when the number of sick in the population reaches a sufficiently large value and the fixed cost of entry is sufficiently low. Second, the government's offer to fund the potential entrant induces the incumbent monopoly firm to lower its prices for treatment to deter the entry of a new firm and, correspondingly, the prevalence of the disease is reduced. Third, the optimal value of government's expected funding is increasing in the fixed cost of entry and the prevalence of the disease when the proportion of sick in the population exceeds a sufficiently large threshold value. The policy implications of the results of the study are as follows: The establishment of a credible policy towards the funding of potential new entrants into an industry can be effective at reducing the market prices for pharmaceutical drugs aimed at treating communicable diseases. International aid agencies' and local governments' action to establish funding policies that provide a credible threat and sufficiently high probability of new entrants can reduce the prevalence of communicable diseases and be welfare improving.
The paper proceeds as follows: The theoretical model is present in The Model section of the paper. Additionally, government funding choices are also discussed in The Model section. In the Conclusion section, the conclusion of the study is outlined.
The Model
Consider an economy with communicable diseases. The consumers have heterogeneous preferences over being healthy. The taste parameter for being healthy, [beta], is assumed to be uniformly distributed in the interval [0, 1]. The choice of patients is between paying for a treatment or not. The value of being sick and untreated is normalized to zero. Formally, as in Mechoulan (2007), let U denote the utility function of consumers at time period t:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [beta] [member of] [0, 1]. Clearly, the individuals who are healthy do not buy the treatment and therefore receive higher expected utilities than those who are sick. Patients choose to be treated if and only if they are sick at time period t and have positive payoff by purchasing the treatment, denoted by [beta]>[p.sub.t]. A simple transmission mechanism of the disease from one period to the next is proposed as in Mechoulan (2007). It is assumed that the disease strikes through person-to-person contacts. The individual with the disease who is untreated recovers naturally within the period t. The individual may be reinfected immediately after recovery so that neither treatment nor natural recovery confers temporary immunity. Therefore, there is always a positive demand for treatment for any positive prevalence of the disease. However, a patient who has bought the treatment at time t can not transmit the disease to others at time t + 1. In other words, anyone may become sick in any period, regardless of the past, but prevalence at time t + 1 is still a function of the proportion of those sick who did not buy treatment in time period t. The size of the total population is normalized to one. Formally, let the proportion of sick at time t be [r.sub.t], where [r.sub.t] [member of] [0, 1], and let T([r.sub.t]) be an endogenous transmission function. It is assumed that T'([r.sub.t]) < 0 which can be interpreted as the spread of the disease, given by T([r.sub.t]), is decreasing in the proportion of sick in the population at time t. Consistent with Mechoulan (2007), an indifferent patient is defined as having preferences such that [[beta].sup.*]=[p.sub.t] x [[beta].sup.*] represents the proportion of [r.sub.t] sick patients who do not get treated at time period t. Consequently, the prevalence in the next period is defined as: [r.sub.t+1] = T([r.sub.t])[r.sub.t][p.sub.t]. For simplicity, we assume that T([r.sub.t]) = a(1 - [r.sub.t]), where: [alpha] is a positive parameter. The change rate of [r.sub.t] over time can thus be approximated by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Therefore, [r'.sub.t] = [r.sub.t][[alpha](1 - [r.sub.t])[p.sub.t] - 1 which is denoted by g([r.sub.t], [p.sub.t])in the sequel. It is obviously that [partial derivative]g([r.sub.t], [p.sub.t])/[partial derivative][p.sub.t]) = [alpha][[r.sub.t](1 - [r.sub.t])] > 0 for any [r.sub.t] [member of] (0, 1). Intuitively, this can be interpreted as the rate of growth in the infection of the disease is increasing in the price of the treatment. In addition, [partial derivative]g([r.sub.t], [p.sub.t])/[partial derivative][r.sub.t] = [alpha][p.sub.t](1 - 2[r.sub.t]) - 1 which is positive when [r.sub.t] < [[alpha][p.sub.t] - 1/2[[alpha][p.sub.1].
Suppose there is a drug monopolist in the market, firm 1, producing treatment with marginal cost c with a uniform distribution on [[c.bar], [bar.c]]. A potential entrant, firm 2, producing at the same marginal cost c , faces a fixed entry cost, [k.sub.1]. The government faces a choice of whether or not to provide a grant G to the potential entrant aimed at reducing its fixed cost of entry. It is assumed that with the government funding, firm 2 may choose to enter the market at time t[greater than or equal to][T.sub.1] with ex-post cost of entry K=[K.sub.1] - G, where 0 < [T.sub.1] < [T.sup.1]. If firm 2 does not enter, firm 1 remains to be the monopolist in the market up to time T at which the competitive price applies.
The economy is represented by a sequential game in a dynamic environment. The sequence of the game is as follows: At stage 1, the government chooses whether or not to offer a grant to the potential entrant to reduce its fixed cost of entry. If the government decides to offer the grant, the optimal level of the fund is determined at stage 2. It is assumed that observing the level of government fund G>0, at stage 3, the incumbent monopolist in the market (firm 1), chooses to set the prices for treatment at the limit-output price levels in the first period for t [member of] [0, [T.sub.1]) to block the entry of firm 2 at time t[greater than or equal to][T.sub.1] (2). It is assumed that the Stackelberg game applies. Hence, at stage 4, firm 2 decides not to enter the market in the second period (i.e. for time t [member of] [[T.sub.1], T)) given the limit-output prices charged by firm 1 in the first period. In contrast, if the government decides not to provide the fund to firm 2 in the first stage, firm 2 could not enter the market given [k.sub.1]. It follows that starting at stage 2, the incumbent monopolist in the market, firm 1, chooses dynamic prices for treatment by maximizing the present value of its aggregate profit for t [member of] [0, T).
FEED