Market Equilibrium with Frictions (OLD)

Question 1

The 2 Worker Value Functions formulae?

Answer 1

ρWu = b + μ[We - Wu]

ρWe = w + δ[Wu - We]

Question 2

Explain the worker value functions (ρWu) and (ρWe)?

Answer 2

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)

Question 3

Explain what the match surplus is?

Answer 3

It is the amount that firms and workers benefit from becoming matched

Question 4

Why is there a surplus?

Elaborate on your initial answer

Answer 4

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

Question 5

Total surplus formula?

Answer 5

S = (Jf - Jv) + (We - Wu)

Question 6

Workers share of the surplus?

Answer 6

βS (= We - Wu)

Question 7

Firms share of the surplus?

Answer 7

(1-β)S (= Jf - Jv)

Question 8

What do β and (1-β) also represent?

Answer 8

The bargaining power of the worker (β) and the firm (1-β)

Question 9

What is the Beveridge curve?

Answer 9

Graphical representation of the relationship between unemployment and the job vacancy rate

Question 10

Which way does the BC slope and why?

Answer 10

Slopes downwards because a higher unemployment rate occurs when there are less vacant jobs available

Question 11

What does it mean if the BC is close to the axes?

Answer 11

That the labour market is efficient

Question 12

Why are there labour market frictions?

Answer 12

Because it takes time/effort/money on both sides to find a match

Question 13

Why doesn’t the market clear in this model?

Answer 13

Because there are labour market frictions

Question 14

Denotation for the number of matches?

Answer 14

M = M(U,V)

Question 15

At what rate do firms find workers?

Answer 15

M/v = ν

Question 16

What is the job-finding rate for workers?

Answer 16

M/u = μ

Question 17

Denote the labour market tightness?

Answer 17

θ = V/U = v/u

Question 18

How are wages determined?

Answer 18

Wage is a result of Nash bargaining between the firm and worker.

Question 19

7 Assumptions of the search and matching framework?

Answer 19

1. Workers are homogeneous
2. All agents risk neutral
3. Output sold at price =1
4. Firms create new jobs at maximum productivity x=1
5. Probability of a production shock = λ
6. Discount rate = ρ
7. FREE ENTRY

Question 20

What is R?

Answer 20

R = the productivity threshold such that S(R)=0

i.e. the surplus at productivity level R = 0

Question 21

At what point are jobs destroyed?

Answer 21

At S(R) = 0

Question 22

What is Nash bargaining?

Discuss the solution

Answer 22

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

Question 23

What are the outside options of the worker and firm in the wage determination game?

Answer 23

Worker Wu

Firm Jv

Question 24

What must you solve to find the bargained wage?

Answer 24

max (Jf - Jv)^1-β (We - Wu)^β

Question 25

What is meant by the “free entry” assumption in the search & matching model?

Answer 25

Infinite supply of entrepreneurs who will open new firms up to the point where Jv = 0 (value of holding vacancies = 0)

Question 26

Formula for the firms discounted value of holding a vacancy?

Explain the parameters

Answer 26

ρJv = -k + ν[Jf(1) - Jv]

-k: cost of searching
ν: worker finding rate

Question 27

Formula for the Job Creation Condition (JCC)?

Answer 27

JCC: S(1) = k / ν(1-β)

Question 28

How is the JCC formula formed?

Answer 28

By setting the firms value of holding a vacancy = 0 and rearranging to get the surplus

Question 29

What is F(R)?

Answer 29

The probability that there is a shock that leads to job destruction

Question 30

What is the free entry condition?

Answer 30

Jv = 0

Question 31

What happens to the JCC when there is an increase in searching costs (k)?

Answer 31

The job creation curve will shift downwards in the (R, (v/u)) diagram

Question 32

Draw the Job Creation and Job Destruction curves?

Answer 32

(R) on x-axis
(V/U) on y-axis

JCC downward sloping
JDC upward sloping

Equlibrium at [(V/U)eq, (R)eq]

Question 33

What effect does higher recruiting effort by firms have on how long it takes for a worker to find a job?

Answer 33

It reduces it

Question 34

Give 4 implications of EPL i.e. if firms are “taxed” on dismissals?

Answer 34

1. Job separations decrease, so the flow into unemployment falls
2. Wages will have to be lower to compensate for the cost
3. Reservation productivity (R) will be lower the probability of having to pay the tax
4. Job creation falls => flow out of unempl falls

Question 35

What is the formula for the Surplus in the case of no productivity shocks?

Answer 35

S = (p-b) / ρ + δ + μβ

Question 36

What are the firms discounted value functions

Answer 36

ρJv = −k + ν [Jf − Jv]

ρJf = p − w + δ [Jv − Jf ]

Question 37

What is μ?

Answer 37

The job finding rate / hiring rate

Question 38

What is δ?

Answer 38

The job separation rate / layoff rate

Question 39

What happens to the curves when there is an increase in β?

Why might it increase?

Answer 39

BC not affected
JCC is flatter

Unions / demographic changes that give the worker more bargaining power