Market Equilibrium with Frictions (OLD) Flashcards
The 2 Worker Value Functions formulae?
ρWu = b + μ[We - Wu]
ρWe = w + δ[Wu - We]
Explain the worker value functions (ρWu) and (ρWe)?
ρWu: Discounted asset value of being unemployed = benefits + (job-finding rate x wkrs share of the surplus)
ρWe: Discounted asset value of being employed = wage + (prob of layoff x -wkrs share of the surplus)
Explain what the match surplus is?
It is the amount that firms and workers benefit from becoming matched
Why is there a surplus?
Elaborate on your initial answer
There is a surplus because labour market frictions - agents are better off having found a match than they are when they are searching for one.
I.e. welfare in match > welfare when not matched
Total surplus formula?
S = (Jf - Jv) + (We - Wu)
Workers share of the surplus?
βS (= We - Wu)
Firms share of the surplus?
(1-β)S (= Jf - Jv)
What do β and (1-β) also represent?
The bargaining power of the worker (β) and the firm (1-β)
What is the Beveridge curve?
Graphical representation of the relationship between unemployment and the job vacancy rate
Which way does the BC slope and why?
Slopes downwards because a higher unemployment rate occurs when there are less vacant jobs available
What does it mean if the BC is close to the axes?
That the labour market is efficient
Why are there labour market frictions?
Because it takes time/effort/money on both sides to find a match
Why doesn’t the market clear in this model?
Because there are labour market frictions
Denotation for the number of matches?
M = M(U,V)
At what rate do firms find workers?
M/v = ν
What is the job-finding rate for workers?
M/u = μ
Denote the labour market tightness?
θ = V/U = v/u
How are wages determined?
Wage is a result of Nash bargaining between the firm and worker.
7 Assumptions of the search and matching framework?
- Workers are homogeneous
- All agents risk neutral
- Output sold at price =1
- Firms create new jobs at maximum productivity x=1
- Probability of a production shock = λ
- Discount rate = ρ
- FREE ENTRY
What is R?
R = the productivity threshold such that S(R)=0
i.e. the surplus at productivity level R = 0
At what point are jobs destroyed?
At S(R) = 0
What is Nash bargaining?
Discuss the solution
Where 2 agents demand a portion of the same good.
The total amount requested by each must be less than the total amount available
The solution is Pareto efficient
What are the outside options of the worker and firm in the wage determination game?
Worker Wu
Firm Jv
What must you solve to find the bargained wage?
max (Jf - Jv)^1-β (We - Wu)^β
What is meant by the “free entry” assumption in the search & matching model?
Infinite supply of entrepreneurs who will open new firms up to the point where Jv = 0 (value of holding vacancies = 0)
Formula for the firms discounted value of holding a vacancy?
Explain the parameters
ρJv = -k + ν[Jf(1) - Jv]
-k: cost of searching
ν: worker finding rate
Formula for the Job Creation Condition (JCC)?
JCC: S(1) = k / ν(1-β)
How is the JCC formula formed?
By setting the firms value of holding a vacancy = 0 and rearranging to get the surplus
What is F(R)?
The probability that there is a shock that leads to job destruction
What is the free entry condition?
Jv = 0
What happens to the JCC when there is an increase in searching costs (k)?
The job creation curve will shift downwards in the (R, (v/u)) diagram
Draw the Job Creation and Job Destruction curves?
(R) on x-axis
(V/U) on y-axis
JCC downward sloping
JDC upward sloping
Equlibrium at [(V/U)eq, (R)eq]
What effect does higher recruiting effort by firms have on how long it takes for a worker to find a job?
It reduces it
Give 4 implications of EPL i.e. if firms are “taxed” on dismissals?
- Job separations decrease, so the flow into unemployment falls
- Wages will have to be lower to compensate for the cost
- Reservation productivity (R) will be lower the probability of having to pay the tax
- Job creation falls => flow out of unempl falls
What is the formula for the Surplus in the case of no productivity shocks?
S = (p-b) / ρ + δ + μβ
What are the firms discounted value functions
ρJv = −k + ν [Jf − Jv]
ρJf = p − w + δ [Jv − Jf ]
What is μ?
The job finding rate / hiring rate
What is δ?
The job separation rate / layoff rate
What happens to the curves when there is an increase in β?
Why might it increase?
BC not affected
JCC is flatter
Unions / demographic changes that give the worker more bargaining power
