1. EC202: Worked Example #3.10 Frank Cowell April 2006
This presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments
To start the presentation select Slideshow\View Show or click on icon below left.
Mouse click or [Enter] to advance through slide show

2. WX3.10: Labour supply
Part 1: Check out the utility function

3. WX3.10: CES, special cases x1
s  0 x2 x1
s = 1 x2 x2 x1
s  

4. WX3.10: Labour supply
Part 2: derive individual’s behavioural responses

5. WX3.8: Set up optimisation problem
Budget constraint
Transform utility function
Substitute in budget constraint

6. WX3.8: Solve optimisation problem
FOC for an interior maximum
Rearrange this:
Get the labour supply function

7. WX3.8: Check labour supply function
From the FOC
This must be less than 1
But if M were too large expression would be negative
So we have constraint on w for positive h
Individual chooses not to work if
Where h is positive:

8. WX3.10: Labour supply
Part 3: Characterise behaviour for people of different types

9. WX3.8: Comparative statics for w
Differentiate h with respect to the wage
Evaluate this
Rearrange
Work may decrease with the wage rate if s < 1 and M is small.

10. WX3.8: Effect on consumption
From labour-supply function and the budget constraint:
Differentiate this with respect to the wage

11. WX3.8: Consumption for different types
Consumption (disposable income) is higher for higher w
Consumption is higher for workers than non workers
Only low ability people choose not to work
Higher ability people enjoy higher consumption

12. WX3.10: Labour supply
Part 4: Apply results to tax system

13. WX3.10: Use comparative statics
Given restriction on s…
…lower w means lower h
But tax lowers wage from w to [1t]w
Also benefit B raises consumption of leisure and other goods
So tax-transfer system causes people to work less