This paper analyzes the optimal regulatory policy for a monopolist whose costs are unknown to the regulator. The regulator aims to maximize a linear social welfare function that combines consumer surplus and the firm's profit. The optimal policy involves setting prices and subsidies based on the firm's cost report, ensuring the firm has no incentive to misreport its costs and maintains non-negative profit. The regulator must balance the firm's incentives with social welfare, considering the asymmetry of information between the regulator and the firm. The paper begins by discussing the classical problem of regulating a monopolist with known costs, where the optimal solution involves setting prices equal to marginal cost and subsidizing the firm to cover fixed costs. However, when costs are unknown, the regulator must design a policy that accounts for the firm's potential to misreport costs. The paper introduces the concept of incentive-compatible regulation, where the firm has no incentive to misreport its costs, and derives the optimal regulatory policy under such conditions. The optimal policy is characterized by a set of outcome functions (r, p, q, s) that determine the firm's probability of being allowed to operate, its regulated price, quantity of output, and the subsidy it receives. The policy is derived under the assumption that the regulator has a prior probability distribution over the firm's unknown cost parameter. The regulator's objective is to maximize a weighted sum of consumer surplus and the firm's profit, with the weight (α) reflecting the relative importance of the firm's profit in the social welfare function. The paper shows that the optimal regulatory policy involves adjusting the firm's cost parameter to account for the regulator's uncertainty. This adjustment leads to a non-decreasing regulated price and a non-increasing quantity of output. The optimal policy also ensures that the firm's expected profit is non-negative and that the regulator's social welfare is maximized. The paper concludes by discussing the implications of the optimal policy, including how the regulator's weight (α) on the firm's profit affects the regulated price and the firm's incentives. The results show that as the weight on the firm's profit increases, the regulated price decreases, and the firm's incentives to misreport costs are mitigated. The optimal policy balances the firm's incentives with social welfare, ensuring that the firm operates efficiently while maximizing overall social welfare.This paper analyzes the optimal regulatory policy for a monopolist whose costs are unknown to the regulator. The regulator aims to maximize a linear social welfare function that combines consumer surplus and the firm's profit. The optimal policy involves setting prices and subsidies based on the firm's cost report, ensuring the firm has no incentive to misreport its costs and maintains non-negative profit. The regulator must balance the firm's incentives with social welfare, considering the asymmetry of information between the regulator and the firm. The paper begins by discussing the classical problem of regulating a monopolist with known costs, where the optimal solution involves setting prices equal to marginal cost and subsidizing the firm to cover fixed costs. However, when costs are unknown, the regulator must design a policy that accounts for the firm's potential to misreport costs. The paper introduces the concept of incentive-compatible regulation, where the firm has no incentive to misreport its costs, and derives the optimal regulatory policy under such conditions. The optimal policy is characterized by a set of outcome functions (r, p, q, s) that determine the firm's probability of being allowed to operate, its regulated price, quantity of output, and the subsidy it receives. The policy is derived under the assumption that the regulator has a prior probability distribution over the firm's unknown cost parameter. The regulator's objective is to maximize a weighted sum of consumer surplus and the firm's profit, with the weight (α) reflecting the relative importance of the firm's profit in the social welfare function. The paper shows that the optimal regulatory policy involves adjusting the firm's cost parameter to account for the regulator's uncertainty. This adjustment leads to a non-decreasing regulated price and a non-increasing quantity of output. The optimal policy also ensures that the firm's expected profit is non-negative and that the regulator's social welfare is maximized. The paper concludes by discussing the implications of the optimal policy, including how the regulator's weight (α) on the firm's profit affects the regulated price and the firm's incentives. The results show that as the weight on the firm's profit increases, the regulated price decreases, and the firm's incentives to misreport costs are mitigated. The optimal policy balances the firm's incentives with social welfare, ensuring that the firm operates efficiently while maximizing overall social welfare.