push in the same direction and it is reasonable to expect the two policies to coexist.
Our results show that this affinity between wage subsidies and workfare disappears when
labor is supplied along the extensive margin. Thus, when assessing the compatibility of
workfare with other elements of welfare policy, it is important to distinguish between
average wage subsidies and marginal wage subsidies.
The remainder of the article is organized as follows. In the next section, we introduce
and analyze our basic model, which is a straightforward extension of the Diamond (1980)
model of optimal taxation. We offer some extensions and qualifications to our analysis
in Section 3. Concluding remarks are found in Section 4. The proofs of our results are
contained in an appendix.
2 The Basic Model
All individuals in the economy are capable of working in the market. They can choose
to work, but not the number of hours they work. Those who enter the market produce n
units of a composite consumption good c. Individuals differ in their market productivity
along some interval [n,n]. The labor market is perfectly competitive, so that n also
measures the before-tax income of the individual.
The government can observe a worker’s before-tax income and implement a tax
schedule t(n). A worker’s consumption is equal to after-tax income and is given by
c(n) = n - t(n).2 Negative taxes are interpreted as subsidies. In addition to the tax
schedule, the government provides a welfare benefit of b units of the consumption good.
Receipt of this benefit is conditional on the individual engaging in some required activity,
denoted r.
Individuals’ utilities are increasing in consumption and decreasing in an index of
the onerousness of labor. For market work, this onerousness is measured by a variable
tax system might feature either marginal wage taxes or marginal wage subsidies.
2This set of informational assumptions is consistent with Diamond (1980). Chone and Laroque (2011)
allow workers to generate income less than their productivity n should it be in their interest to do so in
a model of extensive labor supply choice. They characterize optimal tax schedules without workfare.