Diamond and Mirrlees (American Economic Review, 1971, 61, 8-27 and 261
-278) showed that the first-order conditions for the Ramsey tax proble
m do not necessarily characterize tax optima. Researchers have since b
ecome cautious in using the first-order conditions. This paper establi
shes the validity of a version of the first-order conditions, using th
em to determine when uniform taxation is optimal. We show Deaton's (Re
view of Economic Studies, 1979, 46, 391-405) conditions to be sufficie
nt, but not necessary, for our problem. We also give a necessary and s
ufficient condition for uniform taxation to be optimal in terms of the
wage-compensated supply of labor and a closed-form representation for
preferences.