2-SIDED SEARCH MODEL Flashcards
(45 cards)
We use a simplified version of … model
DMP = Diamond, Mortensen and Pissarides.
How many consumers?
N
How many in LF?
Q
Consumers join the LF based on…
the expected payoff to searching for a job.
Supply curve =
P(Q) = the expected payoff needed to induce Q consumers to search for a job. (i.e. be part of LF)
Firms can only produce if…
They post and vacancy and hire 1 worker
Cost of posting vacancy =
K = in terms of final good
Number of firms posting vacancies =
A = number of vacancies since each firm only posts 1.
Z =
Output produced by the worker / productivity of the worker.
Search frictions imply that
Not all workers searching for a job will find one, and not all firms searching for a worker will find one = can have unemployed workers & vacancies at the same time.
Matching fucntion
M = em(Q, A)
e =
the efficiency of the matching process for given level of A and Q.
4 properties of m(Q, A)
- CRS
- 0 if any Q or A 0
- Increasing in Q and A
- Diminishing marginal products - increase in matches induced by extra Q/A larger if A/Q smaller.
Probability of consumers finding a job =
Pc = M / Q = em(Q, A) / Q = em(1, j) by CRS
j =
j = A / Q = labour market tightness from firm’s perspective.
High j =
Good for consumers
Bad for firms since lots of A but fewer Q
Expected consumer payoff from searching in equilibrium =
P(Q) = pcw + (1-pc)b P(Q) = b + em(1, j)(w - b)
How does j affect P(Q)?
higher j =easier for workers to find a job = higher P(Q) = higher Q i.e. LF participation.
Probability of firms filling a vacancy
Pf = M / A = em(Q, A) / A = em(1/j, 1) by CRS
What do we assume about firms?
FREE ENTRY –> firms post vacancies until expected payoff = 0 otherwise more firms would enter and post vacancies.
Firm free entry conditon
Pf(Z - W - K) = (1-Pf)K
em(1/j, 1) = k / (z - w)
Given that the free entry equality must hold, what happens if K rises?
K rises = higher cost to post vacancy = RHS rises
For firm to still be indifferent, need LHS rise too = lower j = easier to find workers
How is equilibrium wage determined?
According to Nash bargaining theory
2 things the outcome of wage bargaining depends on
- relative bargaining power
2. next-best alternative