L10 - Consumption-Leisure Model

Question 1

What does the Income-Leisure model look like?

Answer 1

• with Income per week on the y-axis and Hours of leisure per week on the x-axis
• draw a negative line which shows how An individual can divide their time between leisure and work (which earns income)
• On the x-axis the intercept is T and at hours of leisure per week is denote as L
• If an individual has L hours of leisure, then they work T – L hours
• Income is Y = w(T - L), where w is the wage rate and L is number of hours of leisure
• the y- intercept is wT

Question 2

How can you find the optimal choice between income and leisure?

Answer 2

• At the tangential point between the indifference curve and the budget constraint ( how may hours in a week)

Question 3

How does a change in wages affect the income-Leisure model?

Answer 3

• it increase/decrease the y-axis intercept cause the budget constraint to pivot
• The simply find the tangential point between the new budget constraint and its indifference curve to find the new optimal work hours and income
• as there is increase there is a decrease in leisure as someone can earn more for their work now

Question 4

How can we derive the Labour supply curve from the consumption-leisure model?

Answer 4

• Look at the consumption leisure model we can plot different budget constraints for different levels of wages
• we all plot there respective indifference curves to figure out the different about of leisure each person would have at each wage level
• Then by plot wage on the y-axis and Quantity Supplied (T-L) on the x-axis we can work out for each wage level then amount of work people want to do
• By plotting all these points and connecting them we get the Labour supply curve

Question 5

What is the Backward-bending labour supply curve?

Answer 5

• It can be created the same ways as the Labour supply curve
• Some times at high wages, people actually supply less labour as wage increase as they can already sustain their life comfortably and may not want to work more and instead want to spend more time with their family instead

Question 6

How does the Income and Substitution apply to the Consumption-Leisure model?

Answer 6

• So say there is an increase in wages and the new Budget constraint and indifference curve is plotted
• we can now find out if the change in hours of leisure were due to the substitution or income effect
• we therefore take the new budget constraint and move it parallel till it is tangential with the old indifference curve
• This tells us how a persons leisure time will change to get to gain the same satisfaction facing new prices
• The distance from the between the shifted leisure time and the original is the substitution effect
• the distance between the substitution leisure time and the new indifference curve leisure time is the income effect
• the income and substitution effect work in opposite direction and the income effect is larger than the substitution

Question 7

How does Income Tax Rates affect the Income-Leisure model?

Answer 7

• Suppose people start paying income tax when they earn Y{tax} –> which is below the current desired income and work level
• If tax is 20% out of every £1 over Y{tax}, then per hour they earn w – 0.2w = 0.8w
• This income tax changes the slope of the budget
  constraint for income over Y{tax} from -w to -0.8w
• this makes then budget constrain at Y{tax} become flatter from then point above
• this decreases their utility but people may still choice to work less then they did before

Question 8

What is the Income effect of a rise in the hourly wage rate?

Answer 8

• Positive income effect –> When higher wages cause people to want to work more hours in order to reach a target / desired income
• Negative income effect –> When a target income has been reached and people prefer spending more time on leisure rather than earning more income

Question 9

What is the Substitution effect of a rise in the hourly wage rate?

Answer 9

• A rise in the real wage increases the opportunity cost of leisure
• Therefore higher wages will always cause people to be incentivised to work longer hours via the substitution effect
• But the income effect may work in the opposite direction

Question 10

What would happen if the Income tax threshold was increased?

Answer 10

• as the slope only changes at Y’{tax} –> which occurs above the original desired income and work balance
• this would allow someone to raise their utility and a person may work more given their preferences

Question 11

How is the utility of those below the tax threshold effected?

Answer 11

• people below the first tax threshold do not change the leisure times which has given rise to whether they should be lowered in order to give people more of incentive to work

Question 12

How do Unemployment benefits affect a persons incentive to work?

Answer 12

• say if the government gave unemployment benefits up until at certain wage e.g. Y*
• With these benefited With benefits, the individual may choose to work 0 hours, earn less but actually get a higher utility from it
• this is an issue that keeps people in the poverty trap —> there is no incentive to actual start working if you can maintain a comfortable lifestyle on benefits
• to combat this people argue that you should lower the benefit income so that if people want to continue to maintain their lifestyle they have incentive to work