Lecture 13 - Labour Supply

Question 1

What are some simplifying assumptions that we make when modelling labour supply?

Answer 1

• Individual has 7 days of 24 hours available (time endowment T=168)
• Individual takes the wage rate, w, as given and chooses the number of hours per week to work
• Time spent working generates labour income (no taxes or other expenses associated with work)
• All income (labour income+non-labour income) is used to finance consumption
• Individual has preferences over two ‘goods’ – leisure and consumption

Question 2

Imagine the following scenario about a consumer, Ant:
- Ant has T=168 hours available a week
- If Ant works for H hours he enjoys N=168-H hours of leisure
- Ant has non-labour income Y^u
- Ant can work at a wage of w (£/hr)
- H hrs of work generates labour income Y^e = wH
Given this data, what will Ant’s total income and consumption be?

Answer 2

Y = Y^u + Y^e = Y^u + wH

Question 3

What leisure and consumption does Ant get if he works H hours?

Answer 3

Leisure: N = 168 - H
Consumption: Y = Y^u + wH

Question 4

What is the general form and the gradient of Ant’s budget constraint?

Answer 4

General form: Y^u + wH ( Non-labour wage rate + labour wage rate)
Gradient: -w

Question 5

How does the budget constraint change if wage increases?

Answer 5

It rotates up (non-parallel). This means that the start point will be higher than at first but it will still end at the same point

Question 6

How does the budget constraint change if non-labour income changes?

Answer 6

If non-labour income changes then there will be a parallel shift in the budget constraint either upwards or downwards depending on whether non-labour income has increased or decreased

Question 7

What shape is the non-labour wage rate line (Y^u)?

Answer 7

On a diagram, non labour wage rate is a horizontal line

Question 8

On a diagram where is the optimal consumption-leisure point?

Answer 8

The optimal consumption-leisure point is where the indifference curve is tangent to the budget constraint

Question 9

How can we decompose the total change in the number of hours worked following a change in the wage rate?

Answer 9

Substitution effect: As wage increases, a person works more and substitutes leisure for work as the opportunity cost of leisure rises
Income effect: As wage increases, a person works less as his/her income has risen this allowing them to spend more time on leisure activities

Question 10

Explain how the income and substitution effects work when there is an increase in wage and how the income effect overpowers the substitution effect

Answer 10

If leisure is a normal good, the income and substitution effects work in opposite directions
- Increase in wage makes leisure more expensive relative to consumption and substitution effect means that the individual will choose more consumption and less leisure/more work
- An increase in wage will make the individual richer. If leisure is a normal good, income effect means that the individual will choose more leisure/less work

Question 11

How can we derive a consumer’s labour supply curve step by step?

Answer 11

1- To derive their labour supply curve we need to maximise their utility function subject to their budget constraint
2- Write the budget constraint in terms of N
3- Sub this into the utility function
4- Differentiate this with respect to N using the chain rule and make it equal to zero
5- Solve for N
6- Subtract this value of N from H to get the number of hours worked