Monopoly regulation in the presence of consumer demand-reduction

I study a monopoly regulation in the setting where consumers can engage in demand-reducing investments. I first show that, when the regulator ignores the consumers' investments, the excess investment occurs. Next, I analyze the case where the regulator takes consumers' investments into account and compare the optimal policy under asymmetric information with the first-best policy. Optimal policy results in higher average price, higher level of consumer investment, but lower prices for efficient firms, compared to the first-best.