1 = Labour Supply - ICs and BC

Question 1

What is the objective function and equality constraint for utility and labour?

Answer 1

Maximising utility indifference curve subject to budget constraint - Max C and L

• utility function
  subject to
• c + wL = wLo + R

Question 2

What is labour supply?

Answer 2

Workers decision - how many hours they are willing/able to supply at a given wage rate

Question 3

Labour market - what is the good and price?

Answer 3

Good = labour services (hours worked)
price = wage paid

Question 4

What are the assumptions made in neoclassical model of labour market?

Answer 4

1. wage rate is constant irrespective of hours worked
2. worker free to work as many hours as they want

Question 5

What are the features of neoclassical labour market?
3

Answer 5

• no frictions in the market = everything clears and works competitively
• workers choose how many hours to work
• unemployment is voluntary
  = workers make all the choices

Question 6

What is the consumption - leisure IC?

Answer 6

The locus of L and C which provides equal utility for the worker
- utility increases with more leisure and more consumption

Question 7

What is MRS - marginal rate of substitution?

Answer 7

The maximum amount of one good that a worker will sacrifice to obtain one more unit of another good = how willing they are to trade

Question 8

What is MUL - marginal utility of labour ?

Answer 8

The benefit gained from consuming one more unit of L

Question 9

How do you find the slope of IC = MRS

Answer 9

• MUL / MUC (always the x axis first)

Question 10

What are the properties of ICs?

Answer 10

1. convex
2. dont intersect
3. higher utility in NW
4. slope = MRS

Question 11

What is a budget constraint?

Answer 11

The market of exchange between C and L = wage rate

Question 12

What are the 2 BC’s that we have to maximise utility subject to?

Answer 12

1. Fixed time endowment
2. Income constraint

Question 13

What is the fixed time endowment?

Answer 13

Lo = h + L
24 = hours worked + leisure time

Question 14

What is the income constraint?
What is the price of consumption and price of leisure?

Answer 14

There is a limit on how much they can consume subject to their income

c = wh + r

• Price of C = 1
• Price of Labour = w*h
• R = non income wage

Question 15

How do we find the bundle of C and L that maximises a workers utility subject to workers time and income constraint?

Answer 15

1. graph
2. substitution
3. lagrangian

Question 16

What is the difference between interior and corner solution?

Answer 16

interior = optimal bundle - uses C and L
corner = only use 1 good

Question 17

What is the slope of BC?

Answer 17

• w

Question 18

How do you find optimal bundle - graph?

Answer 18

MRS = -MUL/MUC = -w

Question 19

When do you find corner solutions?

Answer 19

possible corner solution when IC hits axis
- works for perfect substitues / quasilinear

• MRS does not equal slope of BC
• MRS > w = steeper = wants more leisure x
• MRS < w = shallower = wants more consumption y = will work more hours

Question 20

How can you tell if an individual will work or choose to only do leisure?

Answer 20

They will work when:
w > MRS at reservation wage
which means they prefer to have more consumption = you can increase utility by increasing hours worked

Question 21

When MRS steeper than wage rate

Answer 21

preference for leisure
has to be compensated with a lot of C to lose 1 L
laid back

Question 22

When MRS is shallower than wage rate

Answer 22

prefers consumption
will work
workaholic
will sacrifice a lot of L for more C

Question 23

What happens graphically when wage increases?

Answer 23

• slope increases
• Y intercept higher
• pivots around Lo
• you are more rewarded for every hour you work

Question 24

What are the 2 effects from increasing wage?

• explain income (increases L) and substitution effects (decreases L)

Answer 24

1. income effect
   - how does demand change when income changes
   - I am richer now so can afford to leisure more
2. substitution
   - how does demand change when relative prices change
   - It is more expensive to do leisure so will reduce leisure
   - greater opportunity cost of not working

Question 25

How to find income and sub effect on graph

new IC to the left = income < sub = work more

Answer 25

1. new BC2
2. push old BC1 out to new IC2
3. new e on IC2 = income effect
4. go along IC2 until get to BC2 = substitution effect

Question 26

How do preferences change when non labour income R increases

Answer 26

• only income effect
• no relative prices change
• like winning lottery
• parallel shift up of BC by amount

= less work - more leisure

Question 27

Effects of increasing wage and one off payments non labour

Answer 27

wage = could increase/decrease hours worked - depends on size of income and substitution effect

lottery = less labour more leisure

Question 28

What is a convex set?
- how many equilibriums

BCs are either convex or nonconvex

Answer 28

2 dimensional set is convex if a line between any 2 points in the set stays contained in the set
- the line connects without leaving

• unique equilibrium

Question 29

What are the possible equilibria in convex linear BCs

• examples of convex BC’s
• linear BC
• progressive tax

Answer 29

• interior solution
• corner solution

Question 30

What are the possible equilibria in convex progressive tax BCs

Answer 30

• interior solution
• corner solution
• kink solutions (compute by working out utility of kinks and seeing if they are high)

Question 31

What are the possible equilibria in a non-convex BC

• e.g. part time and full time job

Answer 31

• interior
• corner
• kink
• multiplicity = 2 points they are indifferent between