Subsidy design: wealth versus benefits

A government would like to subsidize an indivisible good. Consumers' valuations of the good vary according to their wealth and benefits from the good. A subsidy scheme may be based on consumers' wealth or benefit information. We translate a wealth-based policy to a benefit-based policy, and vice versa, and give a necessary and sufficient condition for the pair of policies to implement the same assignment: consumers choose to purchase the good under the wealth-based policy if and only if they choose to do so under the translated benefit-based policy. General taxation allows equivalent policies to require the same budget.