Question

 

Assume that an individual wins a lottery. Assume also that the individual was working before the lottery win and had no other nonlabor income before the lottery win.

a) Using the basic static model of individual labour supply, discuss both graphically and explain in your own words how the lottery win will affect the individual’s level of hours worked. Discuss all relevant effects.

b) Is it possible that the individual decides to stop working following the lottery win? In your answer discuss the concept of reservation wages and add the individual’s reservation wage before and after the lottery win to your graph.

Answer 1

Q.1) a. There are two effects evolving around individual labor supply curve. Those are i. Substitution effect, ii. Income effect. Labor supply curve is aunique shaped backward bending curve which states r elation between wage rate and working hours.

A typical labor supply curve shows that labor supply increases with the increase in wage but after a certain point as shown in the above diagram an increase in wage decreases labor supply. There are two main effects which are responsible for this behavior of labor supply curve Substitution effect and income effect.

Substitution effect deals with work and leisure. It states that a higher wage makes work more attractive than leisure.Hence with the increase in wage, labor supply also increases as work becomes more remunerative.

According to income effect a higher income means workers can achieve a target income by working fewer hours. Hence a swage increases it becomes easier for workers to reach to a targeted wage at by working few hours. There may be some exogenous income factors too whoich can increase weightage of income effect. Winning a lottery is an appropriate example of this.

Labor supply curve moves from left to right as long as substitution effect overshoots income effect. From the time income effect becomes higher than substitution effect, labor supply curve start moving from right to left i.e. it becomes backward bending.

In this situation winning a lottery is nothing but an exogenous income shock for the individual. Income of the individual rises to a large extent after winning a lottery. Though this increase in income is one time increase, but it has a long term effect on the behavior of the person. The exogenous shock increases income effect and it overshoots substitution effect and the individual prefer to work less hours and labor supply curve for the individual becomes backward bending.

b.Now we are going to discuss whether it is possible that the individual completely stop working after the lottery win. This depend on the following things:

1. The amount of money the individual has won in the lottery. If the amount of money the individual has won is huge in number, the individual might chose to stop working as the amount of increase in income effect might totlly overshoot substitution effect and the labor supply curve may hit the vertical axis. This is shown in the following diagram

In the above diagram point B shows the point when the labor demand curve meet the vertical axis. At that point income effect fully nullifies substitution effect and the individual refuses to work any more. Although in research it is seen that in most of the cases individuals donot stop working after winning a lottery. Usualy they decrease their working hour.

2. The individual may have a low target of weath income throughout his life. If the individual have a low target, that can be easily met by the amount he wins in the lottery. This may induce him to leave the job.

3. There might be some psychological reason too. Suppose the individual does a job in which he is not satisfied and he is an aged peron whodoesnot have courage to start some business of his like. This may induce the person to leave the job when he wins a lottery. The individual may feel contented by the amount he wins though that may not be large in amount.

According to labor economics a treservation wage is the lowest amount of wage in which a labor is willing to accept a particular job given the other factors like work condition, work culture etc remain unchanged.

In the above diagram the reservation wage for the individual is at W0 where the labor supply of the individual starts from and reservation wage for the individual after winning the lottery is at any point above W1 where income effect overshoots substitution effect. After winning the lottery the reservation wage for the individual nust increse as the individual possesses a large amount of exogenous income.