This paper analyses the interconnections between underreported earnings and redistribution. Two generations overlap: the young and the old. The young earn, contribute to the pension system, pay taxes, and if they can, save. The old receive pensions and dissave. Public expenditures are financed from wage taxes. We derive the reported earnings and savings from individual utility maximization, assuming over-discounting of the future, partial satisfaction from reporting earnings, and possible free riding in the use of public services. The government maximizes a social welfare function formed from paternalistic objective utility functions, yielding the parameter values of the socially optimal tax and pension system. For a utilitarian social welfare function and logarithmic utility functions, the optimal proportional (contributional) pension system provides higher welfare than any system containing a flat (basic) component in a dark grey economy, and lower welfare in a light grey economy. But the superiority of the proportional system can probably be re-established if an appropriate means-tested pension is added.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.