A mixed duopoly input market: uniform pricing versus spatial price discrimination

We uniquely model an upstream mixed duopoly engaging in either uniform pricing or spatial price discrimination when facing a continuum of downstream firms. Uniform pricing generates higher welfare with a fully public firm. Uniform pricing generates greater optimal partial privatization except when the cost disadvantage of the public firm is large and downstream cost convexity is large. Similarly, welfare under optimal partial privatization is larger under uniform pricing except when the cost disadvantage of the public firm is relatively large and downstream cost convexity is large. Thus, the implications of the pricing scheme depend critically on the upstream and downstream cost structure and the ownership structure.