| In Chapter 1, we study a model of efficient risk sharing between two agents, A and B, who enjoy a private good and a common good. Only agent B can provide the common good. We consider self-enforcing equilibria in the absence of commitment. We characterize the Pareto frontier of the subgame perfect equilibrium payoffs. The consumption of the public good is at the socially optimal level in most cases. If the autarkic allocation displays risk sharing in a subset of states, so does the allocation in the optimal contract. If the incentive constraint of agent B binds when she is receiving transfers, then perfect risk sharing can again be implemented. Otherwise, agents' private consumptions covary positively with their income levels. The long-term equilibrium converges to the first best allocation if the latter is sustainable. If not, agents' utilities oscillate over a finite set of values.; Chapter 2 presents an application of the theoretical model in Chapter 1. We model the child support payments of a noncustodial father and the child expenditures of custodial mother as an optimal contract between parents where both parents can renege on their part of the contract at any time. The father aims to insure the mother through whom he insures the child. The optimal contract extends the insurance properties of the autarkic allocation. The child is insured not only in states where autarky dictates smoothing, but also in states where the mother is the recipient of transfers even though her incentive constraint is binding. A strict enforcement of child support payments as a fixed percentage of father's income is available to the mother as an outside option. Strict enforcement of payment guarantees that the mother and the child do not fall into destitution. However, it makes it more costly for the father to smooth out the child's consumption through transfers to the mother. Therefore, the child's consumption decreases compared to the contract where the autarky is defined as playing the static game every period. We also consider another policy where the parents can go to a judge who then builds an optimal contract for the parents.; Chapter 3 focuses on the remarkable structural transformation the U.S. went through between 1800 and 2000. A precipitous decline in the importance of agricultural goods in the economy was matched by the rapid ascent of a plethora of new non-agricultural goods and services. A competitive model is presented where consumption evolves along the extensive margin. This lessens the need to rely on satiation points, subsistence levels of consumption, and the like to explain agriculture's demise. The analysis suggests that between 1800 and 2000 economic welfare grew by at least 1.5 percent a year, and maybe as much as 10 percent annually, the exact number depending upon the metric preferred. |
