Two additions to Lucas's 'inflation and welfare'

• Autor(a) principal: Cysne, Rubens Penha
• Data de Publicação: 2004
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional do FGV (FGV Repositório Digital)
• Texto Completo: http://hdl.handle.net/10438/963
• topic: Arrow's theorem; Optimal control; Economia; Economia; Inflação; Bem-estar econômico

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.