An Analysis on Danish Micro Data - School of Economics and ...

H > 0 or a corner solution, H = 0 . In the case of an interior solution the first-order conditions for
utility maximization result in the following condition
w
= −m
,
p
( C,
H;
V Z )
∂U
∂H
= −
∂U
∂C
which says that the real wage equals the negative of the marginal rate of substitution of working
hours for consumption of commodities.
Evaluating the expression for the marginal rate of substitution at H = 0 gives an expression for the
real reservation wage, w * , which is the lowest compensation the individual will accept for
participating in the labour market. 25 The reservation wage represents the individual’s implicit value
of his time. If the offered market wage is greater than the reservation wage, the individual will
participate in the labour market by working H > 0 hours. On the other hand, if the offered market
wage is less than or equal to the reservation wage, the individual will supply H = 0 hours of work,
and use his entire endowment of time for the consumption of leisure, L = L0
.
The conditions of participation in the labour market are established through the reservation wage,
and therefore it is an important concept. The reservation wage depends on the properties of the
utility function at the point of zero labour supply and also on the value of the non-wage income, I. 26
Assuming the individual’s preferences do not change, that is, the properties of the utility function
do not change, the only factor influencing the reservation wage is the non-wage income. The
reservation wage depends positively on the non-wage income, which means that an increase in nonwage
income will increase the reservation wage, and therefore lower the probability of participation
in the labour market. This conclusion is only valid though, if it is assumed that leisure is a normal
good.
<strong>An</strong> important concept that can be applied directly from consumer demand theory to labour supply
theory is the effect of a price change on the quantities demanded, which is measured by the
substitution and income effect. 27 In the following the demand effects are explained when the price
decreases, but the effects are the same when the price increases, only with an opposite sign. A price
decrease will have at total effect on a good’s demand that can be decomposed into two effects. The
first effect is the substitution effect, which states that a good becomes relatively cheaper after a
price decrease and therefore the consumer will purchase more of it. The second effect is the income
effect, which states that after a price decrease the consumer’s purchasing power is increased, and
25 Pencavel (1986) and Cahuc and Zylberberg (2004)
26 Cahuc & Zylberberg (2004)
27 Jehle and Reny (2001)
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