1 = Labour Supply - ICs and BC Flashcards
What is the objective function and equality constraint for utility and labour?
Maximising utility indifference curve subject to budget constraint - Max C and L
- utility function
subject to - c + wL = wLo + R
What is labour supply?
Workers decision - how many hours they are willing/able to supply at a given wage rate
Labour market - what is the good and price?
Good = labour services (hours worked)
price = wage paid
What are the assumptions made in neoclassical model of labour market?
- wage rate is constant irrespective of hours worked
- worker free to work as many hours as they want
What are the features of neoclassical labour market?
3
- 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
What is the consumption - leisure IC?
The locus of L and C which provides equal utility for the worker
- utility increases with more leisure and more consumption
What is MRS - marginal rate of substitution?
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
What is MUL - marginal utility of labour ?
The benefit gained from consuming one more unit of L
How do you find the slope of IC = MRS
- MUL / MUC (always the x axis first)
What are the properties of ICs?
- convex
- dont intersect
- higher utility in NW
- slope = MRS
What is a budget constraint?
The market of exchange between C and L = wage rate
What are the 2 BC’s that we have to maximise utility subject to?
- Fixed time endowment
- Income constraint
What is the fixed time endowment?
Lo = h + L
24 = hours worked + leisure time
What is the income constraint?
What is the price of consumption and price of leisure?
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
How do we find the bundle of C and L that maximises a workers utility subject to workers time and income constraint?
- graph
- substitution
- lagrangian
What is the difference between interior and corner solution?
interior = optimal bundle - uses C and L
corner = only use 1 good
What is the slope of BC?
- w
How do you find optimal bundle - graph?
MRS = -MUL/MUC = -w
When do you find corner solutions?
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
How can you tell if an individual will work or choose to only do leisure?
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
When MRS steeper than wage rate
preference for leisure
has to be compensated with a lot of C to lose 1 L
laid back
When MRS is shallower than wage rate
prefers consumption
will work
workaholic
will sacrifice a lot of L for more C
What happens graphically when wage increases?
- slope increases
- Y intercept higher
- pivots around Lo
- you are more rewarded for every hour you work
What are the 2 effects from increasing wage?
- explain income (increases L) and substitution effects (decreases L)
- income effect
- how does demand change when income changes
- I am richer now so can afford to leisure more - 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
How to find income and sub effect on graph
new IC to the left = income < sub = work more
- new BC2
- push old BC1 out to new IC2
- new e on IC2 = income effect
- go along IC2 until get to BC2 = substitution effect
How do preferences change when non labour income R increases
- only income effect
- no relative prices change
- like winning lottery
- parallel shift up of BC by amount
= less work - more leisure
Effects of increasing wage and one off payments non labour
wage = could increase/decrease hours worked - depends on size of income and substitution effect
lottery = less labour more leisure
What is a convex set?
- how many equilibriums
BCs are either convex or nonconvex
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
What are the possible equilibria in convex linear BCs
- examples of convex BC’s
- linear BC
- progressive tax
- interior solution
- corner solution
What are the possible equilibria in convex progressive tax BCs
- interior solution
- corner solution
- kink solutions (compute by working out utility of kinks and seeing if they are high)
What are the possible equilibria in a non-convex BC
- e.g. part time and full time job
- interior
- corner
- kink
- multiplicity = 2 points they are indifferent between
