ABSTRACT
This paper will analyze the market of refractive surgery and considervarious factors. First, we will consider the existence of a single service provider (monopoly) and the problem of optimal control in continuous case where the optimum production of refractive surgery will be sought and the production of substitute goods will be considered(control variables). Next, we will introduce a state owned medical service which provides maximization of the social welfare. At last, we will raise a problem of oligopoly in which we consider the presence of n service providers who seek optimal production that maximizes their profits in a period time. We do this in order to prove or disapprove the hypothesis that the price is higher in oligopoly and monopoly, which is subject to the restriction in the flow of replacement demand. And at last, we compare the obtained results with that a public company would be interested in maximizing social welfare. The paper is organized as follows. After introduction we present some theoretical antecedents and frameworks of our models. Next, we work out three mathematical
models: Monopoly, Social Welfare and Oligopoly Competition. Conclusions, Acknowledges and Reference List will be the last part of this paper. Due to the volume restrictions, we omit certain too lengthy as well as preliminary proofs, which will appear elsewhere.
