Horizontal mergers between public and private firms in vertically-differentiated markets

This paper studies the impact of mergers between public and private firms in vertically-differentiated markets on product repositioning, profits, consumer surplus, and social welfare. We analyze a game-theoretical model with a public firm and two private firms in which the public firm’s objective is to maximize social welfare while both the private firms’ objectives are to maximize profits. Before the merger, we show that the public firm should produce the highest-quality product among three firms to achieve the largest social welfare and consumer surplus. However, (i) when both private firms merge into a new private firm to compete with the public firm, if the new private firm’s cost reduction of producing one product is salient, the public firm should produce a lower-quality product than the new private firm who should produce a single product; If the cost reduction is low, the public firm should produce a middle-quality product and the new private firm should produce two products. This merger can benefit the new private firm, and the benefit always destroys consumer surplus but might extend to the public firm and improve social welfare; (ii) when the public firm and one private firm merge into a new public firm to compete with the other private firm, if the new public firm’s cost reduction of producing one product is salient, the new public firm should produce a higher-quality product than the other private firm; If the cost reduction is low, the public firm should produce two products with the highest-quality and lowest-quality levels. Unlike the merger between both private firms, this merger between the public firm and one private firm can induce a win-win-win outcome, in which the private firm without being merged, customers, and social welfare are all better off if the cost reduction is salient.