Week 11 lecture – unemployment, vacancies and wages
A search model
- Each firm has a single job slot for a single worker
- Jobs are either filled or vacant
- If filled, the output is y
- We assume for simplicity that output is constant
- If the output is constant, the wage will be constant
- And so will θ, f and q
- We denote the lifetime profit of a firm with a currently filled job slot as J
o
o Profit of the firm with a filled job slot
o In the current period, the output is y and cost of labour is w
o With probability (1-T) the job remains filled and productive in the next
period; if so, discounted future profit in that period is again J
o With probability T the job match breaks down in the next period; if so,
discounted future profit in the period is V
- And the lifetime profit of a firm with a vacant job slot as V
o
o No y because no output because no worker
o Firms must pay a cost of to post a vacancy
o With probability q the vacancy is filled and the job becomes productive in the
next period
o With the probability (1-q) the vacancy remains unfilled
o V = 0 because of the pressure from new entrants
o If V was positive firms would go into the market
If you can go into a market without a worker and make a profit you
will
- V=0 so
o The profit of a currently filled and productive job simplifies to
o The profit of a current vacancy simplifies to
o The value of a firm with a productive job match is positive (J>0) even if the
value of V is 0
o This is because a firm with a productive job match does not have to incur the
cost of hiring a new worker
- The value of having a productive worker depends on the profit of a firm and the cost
of replacing the worker
, - Combining the last two equations
o
o Vacancy creation curve
o Substituting out q
o
- Higher wages lead to less employment and more unemployment
- Similar to the labour demand curve
o A higher wage implies a lower value for (r + T) ℽ/q
o This requires a higher value of q
o Since q = mθ^-⍺, a higher q implies a lower θ
o Since f = mθ^1-⍺, a lower θ implies a lower job-finding rate
o If workers find jobs at a lower rate, more workers are unemployed
o So there is more unemployment
Vacancy creation curve
- w and θ^⍺
- it will shift out if
A search model
- Each firm has a single job slot for a single worker
- Jobs are either filled or vacant
- If filled, the output is y
- We assume for simplicity that output is constant
- If the output is constant, the wage will be constant
- And so will θ, f and q
- We denote the lifetime profit of a firm with a currently filled job slot as J
o
o Profit of the firm with a filled job slot
o In the current period, the output is y and cost of labour is w
o With probability (1-T) the job remains filled and productive in the next
period; if so, discounted future profit in that period is again J
o With probability T the job match breaks down in the next period; if so,
discounted future profit in the period is V
- And the lifetime profit of a firm with a vacant job slot as V
o
o No y because no output because no worker
o Firms must pay a cost of to post a vacancy
o With probability q the vacancy is filled and the job becomes productive in the
next period
o With the probability (1-q) the vacancy remains unfilled
o V = 0 because of the pressure from new entrants
o If V was positive firms would go into the market
If you can go into a market without a worker and make a profit you
will
- V=0 so
o The profit of a currently filled and productive job simplifies to
o The profit of a current vacancy simplifies to
o The value of a firm with a productive job match is positive (J>0) even if the
value of V is 0
o This is because a firm with a productive job match does not have to incur the
cost of hiring a new worker
- The value of having a productive worker depends on the profit of a firm and the cost
of replacing the worker
, - Combining the last two equations
o
o Vacancy creation curve
o Substituting out q
o
- Higher wages lead to less employment and more unemployment
- Similar to the labour demand curve
o A higher wage implies a lower value for (r + T) ℽ/q
o This requires a higher value of q
o Since q = mθ^-⍺, a higher q implies a lower θ
o Since f = mθ^1-⍺, a lower θ implies a lower job-finding rate
o If workers find jobs at a lower rate, more workers are unemployed
o So there is more unemployment
Vacancy creation curve
- w and θ^⍺
- it will shift out if
