Elasticity of Labor Supply and Fiscal Policy. (40 points).
Consider the static
(i.e., one-period) consumption-leisure framework.
In quantitative and policy applications
that use this framework, a commonly-used utility function is
( , )
denotes the number of hours (in a week) spent in leisure,
(the Greek letters “psi” and “theta,” respectively) are
though we will not assign any numerical value to them) in the utility function.
representative individual has no control over either
, and both
is measured as
= 168 –
is denoted by
, and the labor-income tax
rate is denoted by
(the fraction of labor income that an individual
keeps) can thus be defined as
Finally, expressed in real terms, the representative
individual’s budget constraint is
Thus, this is
the consumption-leisure framework studied in Chapter 2, with now a
particular functional form for
For the given utility function, set up the consumption-leisure optimality
condition, and then solve it for
expressing the solution in terms of (among other
(that is, your final expression here should be of the form
and on the right-hand side the take-home rate
should appear, but the tax rate
need to set up a Lagrangian in order to analyze this
problem; you may go straight to the consumption-leisure optimality condition.
careful in deriving the result, because the rest of the analysis is based on this.)