Assignment

1. Assume that an individual has unearned income of $V and can select how many hours she works per week at a wage of $w per hour. Suppose that she has a total of 110 hours of time to allocate between work and leisure (i.e., Hmax = 110).  Her utility depends on leisure (H) and accessible consumption (Y).

a. Draw a diagram representing her budget illustrating and constraint her optimal option of leisure and consumption. Ensure she chooses to supply a strictly positive amount of labour.

b. Suppose that her employer relocates to a new establishment that is some distance from her residence.  As a result, if she works she should spend 5 hours per week commuting to job, regardless of the number of hours she chooses to work.  Commuting time doesn’t change her utility but it does decrease the time accessible for work and leisure.  Draw a diagram which shows how this time cost of working alters her budget constraint.  Describe how it will affect her optimal choice.

c. Assume that her employer had not relocated, but instead needed her to rent a uniform and renting that uniform cost $R per week, regardless of how many hours she works.  Demonstrate how this would affect her budget constraint.  What happens to her optimal choice?

2. An individual is currently working 40 hours per week, earning $10 per hour.  He loses his job and successfully applies for unemployment insurance.  The insurance plan works as follows:

- He gets a weekly benefit equal to 50 percent of his earnings prior to losing his job (that is, the benefit level is $200 per week).
- He is allowed to earn income while receiving unemployment benefits.  If he earns an amount up to ¼ of pre-unemployment earnings, his benefit is unaffected.  If he earns more than ¼ but less than ½ of pre-un-employment earnings, his weekly benefit is cut in ½, to $100.  If he earns more than ½ of pre-unemployment earnings, he no longer receives a benefit.

a. Demonstrate this individual’s budget constraint in a carefully labelled graph.  For simplicity, assume that he is able to earn a wage of $10 per hour while on unemployment and that there is no unearned income except for unemployment insurance benefits.

b. Show that it would be economically irrational for unemployment insurance recipients to desire to work more than 10 hours per week.  Show that this program may persuade individuals to leave full-time jobs in order to receive unemployment insurance benefits.

3.  Much of the supply-side, fiscally conservative economic policies of Margaret Thatcher, Ronald Reagan, and even Mike Harris in Ontario were predicated on the belief that high income tax rates discourage work.  Cutting income tax rates would, it was argued, stimulate incentives to work and thereby increase economic growth.  Demonstrate an income tax cut leading to greater labour supply in a labour-leisure trade-off model.  What does this outcome assume about the relative sizes of the income and substitution effects?

4.  Consider a worker who earns $8.00 per hour and has no other source of income.  Compare the following two transfer policies:

i. A negative income tax that sets the tax (per day) at T = 0.2Y – 15
ii. An earned income tax credit that subsidizes the worker at 40 cents for each dollar earned, up to a maximum daily subsidy of $15, maintains the subsidy at $15 until the worker’s labour earnings equal $45 per day, and then phases out at a rate of 20 cents per dollar of earnings.

Illustrate the budget constraints generated by these programs, showing both in the same diagram.

5. Consider two individuals with endowments of 60 hours per week of leisure, nonlabour income of $Y per week, and a wage of $7.50.  At this wage assume that workers are constrained by their employers to work exactly 40 hours per week or not at all.

a. On separate diagrams, show the equilibrium of a worker (A) for whom 40 hours is the optimum labour supply, and a worker (B) who would prefer to work 20 hours per week, but still prefers the 40 hour week to not working at all.  Compare the marginal rates of substitution for these individuals at 40 hours per week.

b. Show that the employer can make both itself and worker B better off by instituting lower wages for part time workers and letting them work less (assuming that the firm can hire more part time workers at that lower wage).