Labor Supply Garrison Schlauch - CLAS
Maximizing utility in the context of labor supply is IDENTICAL to what you’ve been doing thus
far, just with a different budget constraint. Apropos, let’s see how the budget constraint for labor
supply is derived. Understand and you won’t need to memorize.
Budget Constraint
You might see different variables used, but here are the ones I like. Let
T= Total Hours, Le= Hours of Leisure, La= Hours of Labor, C = Consumption,
p= Price of Consumption, Y = Total Income, Yn= Non-wage Income, w = Hourly Wage Rate.
You may be asking, “what’s the difference between consumption and income?”. Think of consumption
as real income and income as nominal income. Recall that real income is our purchasing power, i.e.
how many units of stuff we can buy. So
C=Y
p.
However, don’t stress this too much. In this class, we ALWAYS set p= 1, so consumption always
equals income.
To get the budget constraint, we need two relatively straight-forward equations:
T=Le+La(Why?)
and
Y=Yn+wLa⇐⇒ Total Income = Non-wage income + wage income.
Then
Y=Yn+wLa=Yn+w(T−Le).
Rearranging terms, we have that
Y+wLe=Yn+wT ⇐= BUDGET CONSTRAINT EQUATION
Technically, it should be
pC +wLe=Yn+wT ,
but at p= 1 consumption equals total income.
Graphically,
Yn+wLa
Slope = −w
T
Yn
Le
C
