ECON6009 Economics of the Labour Market
Problem Set 2: Individual Labour Supply
Semester 1, 2024
Problems for week 3
Problems with *: solution (or ideas for a solution) to be prepared/presented by problem set group 3; ** by PS group 4 (see Canvas) .
Advice: always draw diagrams to work towards the answer and to avoid inconsistencies in your thinking!
0. Describe the static model of individual labour supply: what are the assumptions, basic story and predic- tions? Give one example of a trend in the labour market that this model can help us understand. Explain.
1. A person who receives time-and-a-half wage (150%) for working more than 8 hours per day will have a(n) which is beyond 8 hours of labour.
(a) indifference curve; flatter
(b) indifference curve; steeper
(c) budget constraint; steeper
(d) budget constraint; flatter
2*. Suppose the hourly wage rate falls but an individual’s other source of income rises to make the original optimal combination of (C,L) just affordable. In this case, desired hours of work will:
(a) decrease
(b) increase
(c) remain the same
(d) change ambiguously
3. Studies of the hours of work of older men have found that the substitution effect dominates the income
effect. This suggests that, other things the same,
(a) that an increase in the tax rate on income will cause older men to work longer hours.
(b) that older men will retire earlier in those careers where wages fall more as they get older.
(c) that an increase in non-work expenses will cause older men to work shorter hours.
(d) show that tax changes have no effect on their labour supply.
4*. Suppose daycare centres charge working parents for each hour their children spend at the centre. Hence there is an hourly cost of care and no fixed cost of care per day (thus no fixed cost associated with working).
i) Which part of the labour-leisure choice diagram is affected by the childcare cost? To illustrate this, draw a diagram for daily labour supply representing the situation of someone without children and someone with children making use of childcare.
ii) A newly introduced subsidy to pay for a portion of childcare costs will cause mothers who are participating in the labour force to work hours.
(a) fewer
(b) the same number
(c) more
(d) at least as many
(e) we cannot tell with the info provided.
(Note: Suppose you were told that working mothers have a labour supply elasticity of +0.2. Which answer is correct in this case?)
iii) How will the newly introduced subsidy affect participation decisions of mothers?
5*. Suppose daycare centres instead charge working parents daily fees, for care up to 10 hours per day. This is an example of a fixed cost of work.
(a) Draw the budget constraint representing this situation (for daily labour supply).
(b) Discuss the impact of this fixed cost of work on both hours and participation.
(c) Discuss intuitively the impact of this daily fixed cost of work on weekly labour supply (or the organization of labour supply throughout a week).
(d) Are there any other examples of a fixed cost of work?
6**. Jian needs to decide how much to work this month. He has T = 480 hours and earns w = $20per hour. He also has $600 of non-labour income that he will spend this month. (The price level p = 1). Jian’s utility .
(a) Is Jian willing to work? How many hours does he optimally work?
(b) If his boss pays him a 20% higher wage/hr for every hour above 200 hrs (overtime pay – per month). Draw the budget constraint. Does this affect his desired hours of work? Explain.
7. Consider the budget constraint for a worker in the Australian income tax system. Assume maximum annual hours worked is 5840hrs (16hrs × 365 days), and a real wage of $20/hr. See the income tax schedule in the table below.
(a) What are the marginal tax rates in each income bracket?
(b) The budget constraints are drawn in the figure below: without (in pencil) and with income tax (in red). Why does the after-tax budget constraint have this shape? Briefly explain.
(c) Indicate and describe the effects this income tax has on hours worked and participation – by comparing this to the situation without income tax.
Note: Suppose you were told that working mothers have a labour supply elasticity of +0.2, while working men have LS elasticity of -0.1. What is the impact on hours worked for each group?
8**. Suppose Tom has preferences for leisure and income that can be represented as follows: U(C, L) = C2/1 L2/1. If the wage w = $14/hr, Tom’s unearned income YN = $50 (and the price level is normalized to p = 1). Tom needs to decide how to allocate his time (T = 16hrs).
(a) What is Tom’s reservation wage? Explain what this means, and will he participate in the labour market? (b) How much time would he optimally spend working, h* ? What is his consumption of the composite commodity C* (or total income) and his utility level?
(c) What if Tom’s non-labour income increased to YN = $100 ?
(d) How would his time allocation change if his wage was to rise to $18/hr? (with YN = $50)
9. Suppose your labour supply curve is reflected in the following: h = −20 + 3w, where h = hours of work and w = hourly wage. Write down an expression for the (wage) elasticity of your labour supply. What is the elasticity at a wage of $10 per hour? Explain.
10. Suppose a government is considering several options to ensure that legal services are provided to the poor. Discuss the likely effects of each option on the hours of work among lawyers. (Note: it helps to draw the constraints created by each option.)
❼ Option A: all lawyers would be required to devote 5% of their work time to the poor, free of charge.
❼ Option B: Lawyers would be required to provide 100 hours of work, free of charge, to the poor.
❼ Option C: Lawyers who earn over ✩100,000 in a given year would have to donate $5000 to a fund that the government would use to help the poor.