Topic 2.2a - Basic Labour Supply Model
Professor H.J. Schuetze
Economics 370
Income-Leisure Choice Theory
One of the most important decisions made by
an individual is how to allocate time between
market and non-market activities.
Activities in the market yield money, but
perhaps also some intrinsic satisfaction.
Activities outside the market also produce
satisfaction
Professor Schuetze - Econ 370
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Basic Income-Leisure Model
However, time is scarce so how do we allocate
our time between these two activities?
Leisure:
„ used here to describe all non-labour market
activities
Š
Š
We will model the decision between 2 goods,
leisure (l) and income (Y)
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Budget Constraint
Income constraint:
„ all the combinations of leisure and income
that are attainable by the household given
income and prices (wage).
T = the maximum amount of leisure available
„
„
„
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Budget Constraint
Y = w·h
slope = ratio - Pn = - w
($)
PY
slope = - w
T
l (leisure)
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Budget Constraint
Non-labour Income (YN):
„
Many individuals earn money outside of the labour
market.
How might we add this to our graph?
Y ($)
w•T
T
l (leisure)
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Indifference Curves
All the combinations of income and leisure
that yield the same total utility.
Y ($)
Downward Sloping
Convex
U1
U0
leisure
There is a whole “family” of indifference curves.
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Utility Maximizing Combination of Income and Leisure
Put together the individuals indifference map and
income constraint to obtain the optimal choice
The individual will try to
maximize his/her utility subject
to the income constraint.
Y ($)
MU
slope = - MU h
= - MRS
Y
U1
A
U0
T
l
Tangency Condition Implies?
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Analytical Example
Suppose the individual’s preferences can be
represented by the following utility function:
U=A⋅lα⋅Yβ
The budget constraint is given by:
Y=w⋅T + YN - w⋅l
To solve use the tangency condition
mul =
muY =
Slope of indifference curve -mul / muY=
Slope of budget constraint =
Professor Schuetze - Econ 370
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Income and Substitution Effects
What happens to labour supply (leisure demand) if we
increase the wage holding everything else constant?
1. Might work more (demand less leisure)
„
„
Substitution effect:
2. Might work less (demand more leisure)
„
Income effect:
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Income and Substitution Effects Graphically
T • w1
Y ($)
Initially at E0 with Y0
income, l0 leisure and
T – l0 hours of work.
suppose w0 goes up to w1
T • w0
Y0
E0
We can decompose
this overall change
into its components.
U0
l0
T
l
IE
SE
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Income and Substitution Effects
Income Effect:
Hold the prices fixed and allow income to
increase.
Choose more or less leisure?
Substitution Effect:
Hold utility fixed and allow prices to change
„
Note: In this example an increase in the wage leads to
an increase in hours. This doesn’t have to be the case.
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Deriving the Labour Supply Curve
Labour Supply: the
amount of labour that
will be offered at various
wages.
“Backward Bending
labour Supply”
$
T•w’’’
T•w’’
T•w’
w
wage
l
T
w’’’
w’’
w’
h
l
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Testing the Theory
A number of researchers have tested the
predictions of the Basic Model.
Most studies involved married women
„
In a sample of married women, regress
hours of work on wages and non-wage
income (includes husbands income).
Now check to see if women who receive
higher wages actually work more.
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Testing the Theory Continued
h = a + b • w + c • YN + d • kids + ...
Typically researchers find:
1.
2.
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Labour Supply Elasticity
There are also a number of studies estimating the
elasticity of labour supply for men
There is large variation in the estimates
„
„
The consensus estimate is -0.1
i.e.
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Labour Supply Elasticity
A number of recent papers use unique labour
markets to estimate labour supply responses
e.g.
-
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