We compare the welfare results of mixed duopoly model where a firm can be private, public or partial‐delegated‐public. We consider two types of partial‐delegated‐public firms. In partial‐delegated‐public with location delegation, the firm chooses location to maximize its profit while the social planner chooses price to maximize social surplus. Partial‐delegated‐public firm with price delegation is the opposite where the firm chooses price to maximize its profit. We find significant differences in equilibrium outcomes both between the two types of partial‐delegated‐public firms, and between the partial‐delegated‐public firms and the purely private/public firms. While equilibrium prices in the partial‐delegated‐public firm cases lie in between those in the pure cases (purely private or purely public), the private firm's profit may be higher when its rival is a partial‐delegated‐public firm rather than a purely private/public firm. We also find a ‘trade‐off’ within the two partial‐delegated‐public firm cases: social surplus is higher under location delegation, but consumer surplus and profit of the partial‐delegated‐public firm are higher under price delegation.