This utility, given the real wage (W) the

This condition is related to the income that an
individual needs to purchase goods and services in the marketplace. The
individual’s income are the sum of his/her the wage rate (W*H) and non-labor
incomes (V).  This equation implies that
the individual consumption expenditures is equal to the total income. We can
rewrite equations (2) and (3) as follows:

W(T-L) + V = C                                                                                 (4)

The individual’s utility maximization problem
becomes:

Max U (C, L) subject to C = W (T-L) + V                                         (5)

The first order conditions solution yield the
following equations:

MaxUC=

                                                                                            (6)

MaxUL=

W                                                                                        (7)

Hence, the following principle was derived:

W= MRS (UL for UC)                                                                         (8)

In order to maximize utility, given the real wage
(W) the individual should select to work that number of hours for which the
marginal rate of substitution of leisure for consumption is equal to real wage (Nicholson,
2005) .

Moreover, based on consumer theory, Ackah et al
(2009)1
argue that, if an individual maximizes his/her utility (U) function for
consumption of items (C) and leisure (L), the model can be expressed as

1   This study would like to assess the
determinants of socio-economic and demographic factors of the labor force
participation, thus,  we will adopt the
extension of utility maximization theory in which Ackah et al (2009) included
the  variable
X which represents individual characteristics  such as age, marital status etc.

For
more details on the derivation of utility optimization, see Ackah et al (2009).