2.4 Labour supply elasticities
The structural basis of the discrete model means that there is no explicit labour supply function which depends on wage and other characteristics of the individual. This contrasts with the continuous hours approach where a supply function arises from utility maximisation subject to the budget constraint.[11] The estimated parameters are parameters of the utility function, which determine labour supply in terms of a distribution of hours worked. This raises the question of how the concept of the wage elasticity of labour supply can be applied in the discrete hours context.
An elasticity measure may be based on expected hours worked rather than a standard supply curve. Consider an individual with known characteristics, including the hourly wage and the net incomes associated with each hours point, from which the probabilities of being at each of the discrete hours points can be calculated.[12] Using these probabilities the expected value of labour supply can be computed. Next, the individual’s gross wage is increased by a small amount, keeping all other characteristics the same, and the new expected labour supply is calculated. An elasticity can be produced by dividing the percentage change in expected labour supply by the imposed percentage change in the wage. Such elasticities will in general vary according to the initial wage rate and the individual’s characteristics, as well as the net incomes at the hours points, which are determined by the tax and benefit system.
In some models with more complex error specifications (as discussed in section 7), it is not possible to determine the probabilities analytically. However, a simulation approach can be taken. Values from the relevant error distributions are drawn for all labour supply points, after which the optimal choice of labour supply can be determined by finding the highest 
. If this process is repeated several times the distribution of labour supply for a particular individual can be determined by counting the number of times each discrete point is the optimal point. Given the probabilities at each of the discrete hours points the expected value of labour supply can be calculated and the process of deriving wage elasticities is then the same as described above.
