Signalling and Spence model

Question 1

what is the signal in the spence model

Answer 1

firms may not observe ability but they observe education (the signal)

Question 2

what is the single crossing property *

Answer 2

increasing the level of education is more difficult for low-ability workers,
cost is greater

Question 3

what are the simplifying assumptions for the simple spence model *

Answer 3

out of work utility = 0 regardless of type,
cost of education proportional to level of education,
productivity depends only on ability not education

Question 4

explain assumption for the spence model ‘productivity depends only on ability not education’

Answer 4

signal about underlying ability but is pure signal as education does not affect your underlying productivity

Question 5

what does y(e) represent for the simple Spence model

Answer 5

the firm’s expectation of the worker’s productivity given their level of education e

Question 6

what are the four stages of the simplified Spence model **

Answer 6

the worker’s ability is drawn at random,
the worker (who knows ability) chooses an education level e,
the firm makes a take it or leave it offer to the worker,
the worker decides whether to accept

Question 7

what is the payoff for the worker in the simplified spence if the worker accepts the job

Answer 7

the wage from the job minus the cost of education

Question 8

what is the payoff for the worker in the simplified spence if the worker doesn’t accept

Answer 8

0 minus the cost of education

Question 9

what is e for simplified spence model

Answer 9

level of education

Question 10

in the simplified spence model what is the pure strategy PBE characterised by *

Answer 10

education levels eh and el (education levels chosen given their ability high or low),
wage offer function (w(.)),
the firm’s belief function (u(.))

Question 11

what is a separating equilibrium

Answer 11

where the two different types choose different levels of education

Question 12

what happens if there is a separating equilibrium in the simplified spence game

Answer 12

the firm will be able to tell which workers are high or low productivity based on their education level

Question 13

for a separating equilibrium for the simplified spence game when does the firm know a workers ability

Answer 13

when they observe his education

Question 14

what does a separating equilibrium imply for simplified spence model

Answer 14

there is no point of the low ability workers choosing any level of education because they will be offered the same wage

Question 15

what is the condition characterising a separating equilibrium for the simplified spence game

Answer 15

need to prevent low types from taking high type education,

need low type to be better off by taking no education than masquerading to pretend to be high type

Question 16

what is signalling

Answer 16

informed individuals may send signals about the hidden characteristic to the uninformed party

Question 17

when does the worker and firm move in the spence model

Answer 17

the worker moves at step 2 (chooses edu) and step 4 (decides whether to work),
firm moves at step 3 by making a wage offer

Question 18

under asymmetric information in the spence model what does the firm know

Answer 18

the firm does not know the worker’s ability, only his education

Question 19

what is μ in the spence model

Answer 19

μ is the firm’s belief function

Question 20

what is w in the spence model

Answer 20

wage offer function

Question 21

what is cl and ch in the spence model

Answer 21

cost of education for type l and type h workers respectively

Question 22

in a separating PBE what education do type l and h workers take

Answer 22

l-type workers choose el=0 and h-type workers choose eh (ehmin,ehmax)

Question 23

how does each of the infinite available PBE compare to the perfect information equilibrium

Answer 23

each of the PBE is less efficient than under perfect information, wages are the same but some resources are devoted to producing a signal -education- that does not increase productivity

Question 24

what is the most efficient (least costly) separating PBE where the high type chooses education

Answer 24

most efficient are the ones where eh=ehmin

Question 25

what is a pooling equilibrium

Answer 25

a pooling equilibrium is a PBE where the workers choose the same education level, say e’ regardless of ability

Question 26

where do you start when working out what the equilibrium is for pooling

Answer 26

we start with the firm’s belief about the worker’s productivity when e=e’

Question 27

in a pooling equilibrium what is firm’s belief about the productivity of the workers

Answer 27

the probability that a worker with education e’ has high ability is equal to the proportion of high-ability workers in the whole population θ

Question 28

what is the pooling equilibrium wage when e=e’

Answer 28

E(y) = θyh + (1-θ)yl

Question 29

which equilibrium is better out of any pooling pbe or the no-signalling equilibrium

Answer 29

any pooling pbe is weakly pareto dominated by the no-signalling equilibrium

Question 30

when is a pbe achieved

Answer 30

each worker chooses the optimal signal given his type and the firm’s beliefs and choices,
firm sets optimal wage rates given worker’s signal and beliefs,
firm’s beliefs follow bayes’ rule on the equilibrium path

Question 31

what does it mean for signalling if the market is perfectly competitive full information (ELQ1)

Answer 31

firms know worker’s productivity and have to offer wage equal to this productivity,
several different outcomes depending on whether the reservation wage is met

Question 32

stages you go through to work out least cost saving separating equilibrium when can choose education (ELQ1)

Answer 32

in separating type a will take e- and b will take e_,
firms beliefs must be such that Pr(a|e-)=1 and Pr(a|e_)=0,
so a types get offered whigh and b wlow,
it is then optimal for b to choose edu=0,
work out ehmin and ehmax by doing incentive constraints for a and b,
incentive for b is utility from not signalling has to be greater than if they were to masquerade so would be higher wage - cost of edu,
incentive for a is utility from signalling has to be greater than utility if no signal (baring in mind if no signal then will be taken as low type),
then check reservation values

Question 33

in a pooling equilibrium what is the wage the same as (ELQ1)

Answer 33

in a pooling equilibrium the wage is the same as in the no-signalling case, however if resources spent on signalling then welfare is lower in pooling than no signalling

Question 34

draw the belief functions and derive and draw the corresponding wage offer functions (what do you do ELQ1)

Answer 34

y=Pr(a|e),
x=e,
draw belief function going through (0,0),
then wage offer function is now based on the firm’s expectations of their type based on their education,
wage offer functions are on graph
y=y(e),
x=e

Question 35

what graph do belief functions go on (ELQ1)

Answer 35

y=Pr(a|e),

x=e

Question 36

what graph do the wage offer functions go on (ELQ1)

Answer 36

y=y(e),

x=e