Topology of utility possibility frontiers of economies with Ramsey taxation

We explore the scope of employing standard assumptions and replicating standard (KuhnTucker-type) techniques that are used to study the first-best Pareto frontier to the study of Pareto frontiers of second-best economies. In the context of a simple second-best situation created by the inability of the government to implement personalized lump-sum transfers and where the government takes recourse to linear (Ramsey) commodity taxes as alternative redistributive devices, we identify at least three potential problems that second-best situations create for obtaining well-behaved Pareto frontiers. We show that additional conditions are required to ensure that the second-best Pareto frontier of an economy with H consumers will have the expected structure of a H −1-dimensional manifold. Second-best Pareto optima, as is well-known, are characterized by consumption and/ or production inefficiencies. In a class of private-ownership economies with Ramsey taxation, we show that, generically, while the jointly production and consumption inefficient component of the second-best Pareto manifold is a submanifold that also has a dimension equal to H − 1, the production efficient but consumption inefficient, consumption effi- cient but production inefficient, and the first-best components are lower dimensional, and hence negligible in size, submanifolds. Thus, we formally demonstrate that, generically, in second-best economies, joint production and consumption inefficiencies are prevalent and, hence, neither producer nor consumer prices reveal the true social shadow prices of resources. The recovery of unobservable shadow prices from observable data is crucial for cost-benefit analysis of competing public sector projects. Our results demonstrate the important need for further research for recovering the true social shadow prices from observable data in second-best economies.