3 = Labour Supply = Wage determination Flashcards
Why would a firm pay wage higher than market clearing wage?
incentivizes workers to work harder - more effort = better productivity
- nutrition
- more required effort
- lower turnover rate = dont want to lose job
- attract high skilled workers
Describe the model of shirking
- firm and worker
- imperfect monitoring
Firm has to set a wage rate and minimum efficiency level
- up to the worker if they want to obey the minimum efficiecny or shirk
- shirk e<e* –> e=0 (reduced strategy space)
- work e>= e* –> e=e*
- when the worker exhibits effort there is a cost = loss in welfare = convex
- but infrequent monitoring of shirking - so can get away with it
What does V mean?
V = unemployment
- the gain from the outside option
- unemployment benefits or another outside job
If a worker chooses to put in no effort what does this mean?
they are indifferent between the outside option and the reservation wage
WR (amount earning from nothing) = V
= indifferent between employment and unemployment
How does wage setting play an important role in shirking or not
- if wage is high enough i wont shirk
- will put in the minimum effort
- dont want to lose my job
- employment > unemployment
How will firms set their prices?
Set the lowest wage that will satisfy the incentive compatibility
- make sure benefit to workers working > shirking
- make them indifferent = lowest wage
What is the payoff to worker for shirking
(1-p(checking)w + vp(checking)
- if they dont check i get wage
- if they check i get fired
What is the payoff to worker for exerting effort?
w - cost(effort)
wage - the cost of effort
How do firm make sure the wage is incentive compatible?
- when will the worker exhibit effort
w - cost(effort) >= (1-p(checking)w + vp(checking)
w - cost(effort) = (1-p(checking)w + vp(checking)
- bind it - because cheapest way
What happens to wage when V increases
(higher outside options)?
wage increases
What happens to wage when cost of effort increases?
wage increases
What happens to wage when probability of being caught increases?
wage decreases
So what are the implications of this for a high paying job
V , C(e) , p
- lots of vacancies - lots of outside options = strong labour demand for workers - need workers
- hard work - requires lots of effort
- its hard to track effort/work
How do firms set wage and effort levels that maximise profits - while making sure workers put in required effort?
want to maximise profits =
output - cost
- output is an increasing function in effort
what is the optimisation problem - max profits subject to workers working
objective function
- max (f(e) - w)
subject to
compatibility constraint
- w - c(e) = (1-p)w + vp
What is the sequential game
- how firms set profit maximising w and e
- firms set w and e
- workers choose to shirk or work
what is the sequential game
- trade unions want to maximise workers welfare
- trade union sets a wage that they demand
- firm chooses to accept or reject
How can TU max welfare (WL)?
maximise welfare subject to firm accepting their offer
What is the firm side problem - trade unions
firms want to maximise their profits subject to their production function
- they will only accept trade unions offer if they make positive profits
- they the choose how many people to hire at this wage to increase profits
What is the firm side problem - trade unions
what is the equation
max profits = p(q)*q - wl
subject to
production function = q(l)
How do you work out this optimisation problem
- firm side
- firm and union
- firm - want to find profit maximising as a function of w
- substitute pf into objective function
- FOC
- L* - sub back in to get a function of w
- firm will only accept if the profit maximising number is positive
- find the wage strategy when will the accept and reject
How do you work out this optimisation problem
- union side
- take the wage that makes the firm indifferent
maximise welfare = wl
subject to
L* = the L that the firm will hire L(w)
- FOC
- find w* = max total income of workers
