This paper develops a welfare accounting decomposition that identifies and quantifies the origins of welfare gains and losses in general economies with heterogeneous individuals and disaggregated production. The decomposition — exclusively based on preferences and technologies — first separates efficiency from redistribution considerations. Efficiency comprises i) exchange efficiency, which captures allocative efficiency gains due to reallocating consumption and factor supply across individuals, and ii) production efficiency, which captures allocative efficiency gains due to adjusting intermediate inputs and factors, as well as technical efficiency gains from primitive changes in technologies, good endowments, and factor endowments. Leveraging the decomposition, we provide a new characterization of efficiency conditions in disaggregated production economies with heterogeneous individuals that carefully accounts for non-interior solutions, extending classic efficiency results in Lange (1942) or Mas-Colell et al. (1995). In competitive economies, prices (and wedges) are directly informative about the welfare-relevant statistics that shape the welfare accounting decomposition, which allows us to characterize a generalized Hulten’s theorem and a new converse Hulten’s theorem. We present several minimal examples and four applications to workhorse models in macroeconomics: i) the Armington model, ii) the Diamond-Mortensen-Pissarides model, iii) the Hsieh-Klenow model, and iv) the New Keynesian model.
This paper shows that it is possible to define an unambiguous notion of the direct effect of a parameter perturbation on the value of an optimization problem’s objective away from an optimum for problems with linearly homogeneous constraints. This notion of the direct effect relies on reformulating the optimization problem using shares as choice variables, and has the interpretation of holding choice variables — when formulated as shares — fixed. This short paper contains one formal “non-envelope” theorem and four applications to i) consumer demand, ii) cost minimization, iii) planning in exchange economies, and iv) planning in production economies.