Term 2 week 10 Flashcards
What is a two sided search model?
-Workers search for jobs
-Firms open vacancies and look for workers
-Search frictions prevent labour market from clearing
What is the set up of the model on the household side and on the firm side?
-N number of households who can choose to be in our out of household
-Q number of workers in labour force
-Houses choose whether or not to join labour force based on expected payoff of a job.
Graphically how can you show payooff for searching?
Q labour force x axis
Y payoff to searching
Upward sloping
Firms
firm must post a vacancy
cost k to posting the vacancy
A is number of people who post a vacancy
Firms that do not fill vacancy have no production
They produce z and pay wage w
What is the matches?
What are the properties of the function
~Matching function
M = em(Q,A)
increasing in searching and vacancy
constant returns to scale
diminishing marginal products
shows matching function is subject to frictions.
What is labour market tightness and what can it be denoted by?
-j
A/G
What is the probability of a household finding a job?
ph = M / Q
= em(Q,A) / Q
= em(1,A/Q)
=em(1,j)
What does a high j mean for households and firms?
For households it means easier to find a job
For firms harder to find a job
What is the payoff for households?
Payoff of household searching is: P(Q) = ph . w + (1-ph)b
What is the probability of filling a vacancy?
What is the most simplified version?
pf = M/A
= em(Q,A) / A
= em(Q/A,1) = em(1/j, 1)
em(1/j, 1) = k/ z-w
What is the expected payoff of a firm searching?
pf . (z-w-k) + (1-pf) x (-k)
What is the household job search
The firms vacancy posting
How are wages bargained for?
-When firms and households meet they must bargain a wage
-Follows john nash bargaining
-depends on the bargaining power and alternative for both parts.
What is the surplus of the worker and surplus of the firm?
Difference between agreement and no agreement.
Sw = w - b
SF = z - w
What does the Nash Bargaining theory say and how does it link to surplus
Therefore how can the surplus be written?
How does this help for the equilibrium?
Nash theory says that each person receives a total theory
Let a be fraction of surplus to the worker
and 1-a surplus to the firm
Sw = a x St
Sf = 1-a x St
you then sub in the expression for wage
w-b = a(z-b)
solve for wage
You then solve this in for wage
What does unemployment benefit do for one-sided search model and two sided
What are the two equations in the two-sided search model?
How is the equilibrium found?
P(Q) = b + em(1, j)(w-b)
em(1/j, 1) = k / z-w
To find EQ a wage must be decided
What is total surplus?
Sw+Sf = z-b
How do you show the two-sided search model equilibrium graphically
x axis , labour market tightness
y axis labour force
you draw one graph on top of the other
you find the probability of filling a vacancy equilibrium, then fill the j, then go up from the j and touch the worker cuvre.
What is the following in two sided search model:
Unemployment
Vacancy rate
Agregate output
U = 1 - em(1 , j)
V = 1 - em( 1/j, 1)
Y = Qem(1,j)z
What is the impact of higher productivity on both sides of the market?
Demand side the z in the denominator increases which makes the rhs go down, so LHS has to go down. So J increases, as firms find it more attractive to post vacancies.
-For the supply side (households), wages are higher
-It is easier to find a job as J increases.
What is the comparative statics of an increase in productivity graphically
-On the demand side.
The probability of filling a vacancy is lower so this goes down on y axis.
-Then find new j for new probability of filling a vacancy
-On supply side the labour force will increase so payoff curve will pivo upwards
What does an increase in unemployment benefit do to comparative statics?
as b is in denominator RHS increases so LHS increases which means j goes down.
On supply side
HIgher benefits increase participation rate as you must be part of labour force.
-Positive effect on wage as you can bargain
Unemployment increases , unclear to participation, unclear GDP
How does two sided search model fit the data in terms of productivity?
What is it missing?
-Missing wage rigidities
