Capacity choice and optimal privatization in a mixed duopoly

We examine a mixed duopoly where the degree of privatization of a public firm is set before firms choose their capacity scales and then choose their outputs. We find that the public firm chooses over-capacity for high degrees of privatization and under-capacity for low degrees of privatization, while the private firm always chooses over-capacity. We then find that the optimal degree of privatization of the public firm depends non-monotonically on its relative inefficiency: it is low for small or large levels of inefficiency and it is high for intermediate levels of inefficiency. We finally show that, given the optimal degree of privatization, the public firm may choose over-capacity or under-capacity, and that this choice also depends non-monotonically on its relative inefficiency.