Product differentiation, privatization commitment and profitability comparisons

This paper analytically compares the Cournot and Bertrand games with and without the privatization commitment in a differentiated mixed duopoly. It intuitively examines the interactions of welfare maximization, output substitution and diminishing returns to scale effects and exhibits the reversal results found in the literature. Under diminishing returns, the rankings of optimal outcomes in all cases are relevant to the level of product substitutability and the magnitude of marginal cost. At optimal levels, the government will partially privatize a public firm in Cournot and fully nationalize it in Bertrand. In Cournot, the (non)monotonic property carries over to the relationship between goods substitutability and the optimal privatization level if the parameter of marginal cost is sufficiently high (low). A comparison of numerical simulations in the Cournot and Bertrand games reveals that privatization generates the largest profits in Cournot under high substitutability, while nationalization generates the largest profits in Bertrand under low substitutability. Furthermore, a privatization commitment in Cournot increases producer surplus but decreases consumer surplus. Essentially, nationalization in Bertrand competition yields higher welfare than any policy reform in Cournot competition regardless of goods substitutability.