Domestic and Foreign Ownership of Private Sector in Mixed Duopoly

This paper considers a quantity-setting mixed market model in which a public firm competes with a private firm. The paper examines the welfare effects of domestic and foreign ownership of the private firm. The paper shows that social welfare is maximized by fu ll domestic ownership o f the private firm, while consumer surplus is maximized by fu ll foreign ownership of the private firm.


Introduction
As is very well known, mixed o ligopolies are co mmon in developed and developing countries as well as in former communist countries. Public firms co mpete with domestic and/or foreign private firms in many industries, such as the airline, banking, broadcasting, education, electricity, health care, ho me loans, life insurance, overnight delivery, rail, shipbuilding, teleco mmunications, and tobacco. For example, in the tobacco industries of France, Italy, Russia, Spain, Austria, Turkey, China, Japan, etc., we can find real-world examp les in which public firms compete or competed against each other and other private firms such as Philip Morris and R. J. Reynolds. In the Norwegian o il industry, the state-owned Statoil co mpetes against two mu ltinational corporations Esso Norge and Norske Shell (see [1]). Furthermore, Krugman and Obstfeld [2] describe foreign ownership as "In U.S. statistics, a U.S. co mpany is considered foreign-controlled, and therefore a subsidiary of a foreign-based multinational, if 10 persent or more of stock is held by a foreign company; the idea is that 10 persent is enough to convey effective control." The pioneering theoretical work on a welfare-maximizing public firm was done by [3]. Since then, the analysis of mixed market models that incorporate welfare-maximizing public firms has received increasing attention and has been widely performed by many researchers (see [4][5][6][7][8] for excellent surveys). Most studies are mixed models with domestic private firms (see, fo r examp le, ).
Some resent studies include foreign private firms (see, for examp le, [31][32][33][34][35][36][37][38]. These studies does not consider part ial foreign ownership of private firms. Fjell and Pal [1] suggest that a fraction of the foreign firm's profits can be included in the domestic social welfare function. Fernández-Ruiz [39] investigates firms' decisions to hire managers in a duopoly where a public firm co mpetes with a foreign private firm. He then considers a situation in wh ich a fraction of the foreign private firm's profits can be included in the domestic social welfare function.
We consider a quantity-setting mixed market model in which a public firm with social welfare ob jectives competes with a private firm with profit objectives. We examine the welfare effects of domestic and foreign ownership of the private firm. We show that social welfare is maximized by full do mestic ownership of the private firm, wh ile consumer surplus is maximized by full foreign ownership o f the p rivate firm. As a result of these, we find that neither consumer surplus nor social welfare is maximized by partial fo reign ownership of the private firm.
The remainder of this paper is organized as follows. In Section 2, we describe a mixed duopoly model with a public firm and a private firm. Section 3 examines the welfare effect of domestic and foreign o wnership of the private firm in the model. Finally, Section 4 concludes the paper.

The Model
Let us consider a mixed duopoly model with one public firm and one private firm. In the remainder of this paper, subscripts 0 and 1 denote the public firm and the private firm, respectively. There is no possibility of entry or exit. The duopolists produce perfectly subsitutable commodities. The inverse demand function is g iven by 10 P Q = − , where P is the market price, and Q is the total quantity of output in the market.
Each firm's profit i π is given by where i q represents firm i 's output, and i m is firm i 's constant marg inal cost. We assume that the public firm is less efficient than the private firm, i.e. 1 0 0 m m < < . 1 For simp licity, we normalize 0 m to one and 1 m to zero. The private firm aims to maximize its own profit.
Do mestic social welfare W is the sum of consumer surplus and producer surplus, and is given by firm is foreign owned and its profit is excluded from domestic social welfare. The public firm aims to maximize domestic social welfare. In this paper, we analy ze the Nash equilibriu m of the quantity-setting mixed duopoly model.

Results
We first present the equilib riu m values of outputs and the price, obtained by maximizing (1) and (2) simultaneously: π is a strictly increasing function of λ .
Third, we consider domestic consumer surplus, which can be expressed as follows: studying mixed markets. See, for instance, [15,18,19,22,23,27,33,37,39]. Let us assume that the public firm is equally or more effici ent than the private firm. In this case, since the public firm, which is interested in social welfare, has a higher incentive to underbid an opponent's price than the private firm would have, the public firm chooses 0 q such that price equals marginal cost. Therefore, the private fi rm has no incentive to operat e in the market, and the public firm supplies the entire market, resulting in a wel fare-maximizing public monopoly. This assumption is made to eliminate such a trivial solution. Fourth, domestic social welfare can be expressed as follows: The maximizat ion of W with respect to λ is derived fro m dW dλ . That is, we have  We can now state the following proposition. Proposition 1. In the mixed ma rket model with one public firm and one private firm, (i) consumer surplus is maximized by full foreign ownership of the private firm, and (ii) social welfare is maximized by full do mestic ownership of the private firm.
This proposition indicates that neither consumer surplus nor social welfare is maximized by partial do mestic ownership of the private firm.

Conclusions
We have considered a quantity-setting mixed ma rket model in which a welfare-ma ximizing public firm co mpetes with a profit-maximizing private firm. We have examined the welfare effects of domestic and foreign ownership of the private firm. We have then demonstrated that social welfare is maximized by full do mestic ownership of the private firm, while consumer surplus is maximized by full fo reign ownership of the private firm.