This dissertation considers optimal government policy when agents in the economy are privately informed about their various characteristics. The first chapter deals with optimal education policy. Raising children is an important productive activity for a society since children's outcomes depend on their parents' investments. This paper develops an intergenerational framework in which adult outcomes are determined by parental investment, analyzes Pareto efficient allocations, and derives implications for policy. There are two key frictions: first, parental altruism type is private information; second, it is impossible for society to monitor parental investment. The main characterization result is that in any ex post Pareto efficient allocation, in any generation, society should transfer extra resources to all poor parents. This implies all agents, including the poor, should live above a certain welfare level, independent of whether or not society cares about them. Regarding implementation, the paper considers a market structure in which parents cannot sign contracts binding their descendants. Under such a market structure, implementing any Pareto efficient allocation requires government intervention. A feature shared by all Pareto efficient income tax schedules is that income taxes of agents with currently low income are negative.

The second chapter analyzes efficient allocation of resources in an economy in which agents are initially heterogeneous with regard to their wealth levels and whether they have ideas or not. An agent with an idea can start a business that generates random returns. Agents have private information about (1) their initial types, (2) how they allocate their resources, and (3) the realized returns. The unobservability of returns creates a novel motive for subsidizing agents who have ideas but lack resources to invest in them. The unobservability of initial types and actions implies that the subsidy that poor agents with ideas receive is limited by incentive compatibility: the society should provide other agents with enough incentives so that they do not claim to be poor and have ideas. The paper then provides an implementation of the constrained-efficient allocation in an incomplete markets setup that is similar to the U.S. Small Business Administration's Business Loan Program.