Alternative Measures, analyze the labor market before, during, and after the financial crisis

For this box you will analyze the labor market before, during, and after the financial crisis.You will analyze the 2006-2016 period; these are the years that have the same unemployment rates at both end-points (4.7% in both January 2006 and December 2016).- Go to www.BLS.gov (Links to an external site.)Links to an external site. and look for 1) the Unemployment Rate; 2) Labor Force Participation Rate; and 3) hours of work (search: total private average weekly hours of all employees).The purpose of this box is to document and explain these three indicators during the Great Recession.The participation rate and hours correspond to the extensive and intensive margins, respectively. The extensive margin refers to whether to work or not, and the intensive margin refers to how many hours —once one has decided to work.
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ECON 562
Macroeconomic Analysis & Public Policy
Module 4: Households Labor-Leisure
Decision
Introduction
A One-Period Model of a Household
Optimal Allocation of Time
The Labor Supply
Taxes on Labor
Introduction
Every day we have to decide how
to allocate our time between labor
and leisure.
How can we model this
economic decision?
ECON 562
Macroeconomic Analysis & Public Policy
Module 4a: A One-Period Model
A One-Period Model
In this module, we develop a theory of households who live for just one
day.
So we model how a “representative” household chooses:
 How much to work and
 How long to stay home
The models predictions are consistent with the data.
A One-Period Model
In this one-period model what you earn, you consume, but you also like to
rest and/or socialize.
So lets suppose that household utility for consumption ? and leisure ? is
given by:
???? + ? – ? ???
And there is a time constraint
? + ? = ??,
and a budget constraint
? = ??.
There are 16 hours in a day that can be either spent working (?) or spent on
leisure (?).
Optimal Allocation of Time
Solving for ? in the time constraint and substituting ? and ? in the utility
function we get:
??? ? + ??? ? + ? – ? ?? – ?
To find the optimal choice of L, we take the derivative of this function with
respect to L and set it equal to 0,
? ?-?

=?
? ?? – ?
This yields
? = ???.
Hours of work are proportional to the weight on consumption (and
independent of ?!)
The Labor Supply
So, how could it be that the wage rate does not affect the
decision on hours?
Wages matter, of course, but there are two opposing forces
that make them disappear from the solution of the problem:
 If wages go up, your time endowment is worth more, and as you are richer
you want more ? and ?, that is, to work less (income effect).
 But, if wages go up, the (opportunity) cost of staying home rises, and you
want less leisure and work more (substitution effect).
Taxes on Labor
The solution is consistent with the data!
Hours worked per-capita are trendless over long-periods of time, even
though wages have been increasing over time with productivity.
This finding has fiscal implications.
Unlike the tax on capital, which reduces the capital stock, taxes on wages
dont appear to be distortionary (based on this model specification).

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