Topic 3 - Labor Market

Question 1

Unemployment rate

Answer 1

U / Q
U: Unemployed
Q: Labor force (employed + unemployed)

Question 2

Participation rate

Answer 2

Q / N
Q: Labor force (employed + unemployed)
N: Working age population

Question 3

Employment/population ratio

Answer 3

(Q-U)/N
Q: Labor force (employed + unemployed)
U: Unemployed
N: Working age population

Question 4

Vacancy rate

Answer 4

A / (A + Q - U)
A: Aggregate number of vacancies listed by firms
Q: Labor force (employed + unemployed)
U: Unemployed

Question 5

One-sided search model

Answer 5

• focuses on behavior of unemployed worker
• unemployed worker receives wage offer with probability p (job finding rate).
• wage offer w either accepted, or unemployed worker turns down the offer and continues to search.
• while unemployed, workers get flow value “b” (value of home production, or unemployment benefits).
• while employed a worker can lose its job with probability s (separation rate).
• all workers are either employed or unemployed. Not-in-the-labor-force not modeled.

Question 6

Reservation wage

Answer 6

w: the wage at which the unemployed worker is just indifferent
between accepting and declining a job offer.
w<w: offer declined
w>w*: offer accepted

Question 7

Long-run equilibrium of one-sided search model

Answer 7

Flow of workers from employment to unemployment equals the flow in reverse direction

s: separation rate
U: unemployment
p: job offer frequency
H(w): fraction of workers receiving a wage offer greater than w

Question 8

Consumers in the two-sided search model

Answer 8

Each of the N consumers chooses whether to work outside the market (home production), or to search for work in the market.

N: working age population
Q: number of consumers who search for work
N-Q: not in the labor force
P(Q): expected payoff to searching for work that would induce Q workers to search (essentially the supply curve for searching workers)

Question 9

Firms in the two-sided search model

Answer 9

Firm must post a vacancy in order to match with a worker

k: Cost of posting a vacancy (in units of consumption goods)
A: number of active firms (firms posting vacancies)

Question 10

Matching function

Answer 10

M = em(Q,A)

M: aggregate number of matches
e: matching efficiency
Q: number of consumers who search for work
A: number of active firms

Question 11

Probability consumer finds a match with a firm when searching for a job

Answer 11

Pc = em(Q,A) / Q

Question 12

Labor market tightness

Answer 12

j = A / Q

A: number of active firms
Q: number of searching consumers

Question 13

Payoff of searching for a job
(Supply curve in labor market)

Answer 13

P(Q) = b + em(1,j)(w-b)

Question 14

The probability that a firm with a vacancy finds a worker to fill the job

Answer 14

Pf = em(1/j , 1)

Question 15

Payoff for a firm of finding a worker

Answer 15

z - w

z: production
w: wage

Question 16

Demand curve in labor market

Answer 16

em(1/j , 1) = k/z-w

Question 17

Nash bargaining theory to determine how a matched firm and worker split the total revenue from production

Answer 17

Worker’s surplus: w - b
Firm’s surplus: z - w
Total surplus: z - b
Worker’s share of total surplus: a
w = az + (1-a)b

Question 18

Two equations determining Q and j (from supply side, demand side, and Nash bargaining)

Answer 18

P(Q) = em(1,j)a(z-b)

em(1/j , 1 ) = k / (1-a)(z-b)

Question 19

Unemployment rate
(in equilibrium)

Answer 19

u = 1 - em(1,j)

Question 20

Vacancy rate
(in equilibrium)

Answer 20

v = 1 - em(1/j , 1)

Question 21

Level of aggregate output
(in equilibrium)

Answer 21

Y = Qem(j,1)z

Question 22

Effect of increase in UI benefit

Answer 22

1) Reduces total surplus from a match, z – b.
2) Increases the wage, w, as the alternative to working becomes more tempting for a searching consumer.
3) Posting vacancies becomes less attractive for firms, so labor market tightness, j, falls.
4) For consumers, searching for work becomes more attractive, as the wage is higher. But searching for work is also less attractive, as the chances of finding a job are lower (j
is lower).
5) Q may rise or fall given these two opposing effects.
6) u rises
7) v falls.

Question 23

Effect of increase in productivity

Answer 23

1) Increases the total surplus from a match, z – b.
2) Increases the wage, w, as the worker gets the same share of a larger pie.
3) As profit is higher, posting vacancies becomes more attractive for firms, so labor market tightness, j, rises.
4) For consumers, searching for work becomes more attractive, as the wage is higher, and the chances of finding work are better.
5) Q rises
6) u falls
7) v rises
8) Y rises

Question 24

Effect of decrease in matching efficiency

Answer 24

• No change in total surplus, or in the wage.
  1) Chances of finding a worker are lower, so fewer firms post vacancies and j falls.
  2) For consumers searching is less attractive – the wage is the same, but the chances of finding a job are lower, so Q falls.
  3) u rises
• vacancy rate stays the same
  4) Y falls.
• Potential explanation for the shifting Beveridge curve

Question 25

Beveridge curve

Answer 25

graphical representation of the relationship between the vacancy rate and the unemployment rate