2  The Economic Model

2.1  Utility Maximisation

In the model chosen in this paper, the household is assumed to be the decision-making unit on labour supply and consumption. Thus, we use a household utility function or a unitary utility function, which does not explicitly take into account individual consumption or utility, but assumes there is one common utility function for the whole household. Although alternative models are available, which incorporate perhaps more realistic assumptions on utility maximization in the household or allow for home production to enter the model independently, these models would introduce additional complications[2]. To estimate a model where all household members have their own utility functions, information is needed on the private consumption of individuals or on the amount of income allocated to them. No data set combines all necessary information on consumption or home production, income sources, and labour supply. Therefore strong assumptions are often needed on how income is shared to allow estimation of collective utility models or on the value and amount of home produced goods to estimate models that explicitly allow for home production, rather than implicitly as in the unitary utility models. To deal with these additional complications other parts of the model need to be simplified and as a result retaining the complexity of the tax and transfer system would be very difficult.

The literature that studies the effect of policy changes in taxation or social security systems mostly favours the neoclassical approach for its suitability to incorporate detailed budget constraints. Given the aim of incorporating the details of the tax and transfer system in the labour supply model, this literature is followed.

By setting up the model in the familiar neoclassical way, starting from utility maximization under a budget constraint, a logical and consistent framework can be built to analyse labour supply (see for example Deaton and Muellbauer, 1980; or Killingsworth, 1983). For example, take a two-adult household (with or without dependent children), where the adults choose their labour supply to optimise the households utility. Their utility depends on household consumption (which is assumed to be equal to net household income x[3]), on the amount of leisure time of adult 1, and the amount of leisure time of adult 2.

In this paper, the term ‘leisure’ is used to indicate both pure leisure time and home production time. The combination of leisure and income that delivers the highest utility to the household is regarded as the optimal choice.

The choice of labour supply is simultaneously determined for both adult members of the household. Depending on the utility function chosen, this approach allows for direct interdependencies between the two adults’ labour supply or one adult’s labour supply and household income. This utility is maximized conditional on the restricted total amount of time available to each adult and the restricted amount of total household income. It is expected that utility increases with an increase in leisure and income. Usually more income means less leisure time for one of the adults, except when more income is obtained through social security benefits[4]. In short, maximizing a household’s utility involves balancing the amount of leisure and income.

With regard to the assumption of free choice underlying this economic model; it is often not known whether the observed labour supply is the optimal labour supply or, alternatively, whether people are restricted in their labour supply choice by demand side factors[5]. It would be interesting to analyse desired hours of work rather than actual hours of work or to allow for the restrictions in actual hours caused by the demand for labour (see for example Euwals and Van Soest (1999) or Euwals (2001)). However, the information necessary to do this is not available in the data.

A simple utility maximizing model would look as follows:

(1)     max U(x,l₁,l₂)

subject to:

T= l₁ + h₁= l₂ + h₂

where:

U( ) is the utility function of a two-adult household,

l₁ and l­₂ indicate the aggregate of leisure time and home production time per week of the husband and wife (married or de facto) respectively,

x indicates net income per week,

T is the total available time for each person in the household,

h₁ and h₂ are the hours of work of husband and wife,

g(h₁,h₂) is the net income of husband and wife at the different hours of work h₁ and h₂ taking into account taxation and withdrawal of benefits,

y₁ and y₂ are the non-labour incomes of husband and wife,

c is household composition,

B(c) is the amount of benefit households are eligible for, given their household composition c,

n( ) is the amount of income after the deduction of taxes.

The first two restrictions are time restrictions for the two adults. The third restriction, the budget constraint, denotes the level of available income in the household. If the first two restrictions are substituted in the third equation, the budget constraint may be written:

(2)    

For households with only one adult, the model can be simplified by leaving out everything relating to the second adult:

(3)     max U(x,l₁)

subject to:

T= l₁ + h₁

Or combining the two restrictions:

(4)