Week 10

Question 1

There are 2 prominent models of discrimination in economics which are what?

Answer 1

Taste-based discrimination Belief based discrimination

Question 2

What is Taste based discrimination?

Answer 2

Preference for certain traits when interacting

Question 3

What is Belief based discrimination?

Answer 3

Individuals might believe that individual with different traits might behave differently.

Question 4

What are problems with Belief based discrimination?

Answer 4

1) Sometimes there is arbitrary choice (based on random choice or personal whim, rather than any reason or system.) e.g. health insurance, but what would happen if an insurer would look at religion instead?
2) People have wrong beliefs about people( e.g. Ronny showed us that peoples perception of people who are Muslim compared, to the actual demographics are wrong)

Question 5

We will now look at highway searches, what are some facts about highway searches?

Answer 5

Ethnic minority groups more likely to be stopped and searched.

Question 6

Is highway searches belief based (BELIEF THAT ETHNIC MINORITIES LIKELY TO ENGAGE IN CRIMINAL ACTIVITES) or taste based ( OFFICERS ENJOY STOPPING MINORITES)?

Answer 6

We don’t know yet untill we solve using Theoretical modelling and empirical analysis.

Question 7

To look at the racial bias in highway searches, what 2 important terms do we need to know?

Answer 7

Search intensity and Hit rate

Question 8

What does search intensity mean?

Answer 8

The likelihood the police will search a driver of a particular race e.g. white, black

Question 9

What is the hit rate?

Answer 9

Conditional that you search for drugs, what is the likelihood that you actualy found it in the vechile.

Question 10

To model the game by driver and the police

For the police

1) what is the cost of searching the car
2) Reward if drug found
3) Payoff if doesn’t search

Answer 10

1) C>0
2) V>C (this compensates you for the cost of stopping the car)
3) 0 if driver doesnt search

Question 11

To model the game by driver and the police

For the driver

What is the punishment if the driver is searched and has drugs?

What is the reward, if he carries drugs and not searched ?

What is the payoff id he doesn’t carry any drug?

Answer 11

Punishment if carries drug and searched -d<0

Gets reward if carries drug and not searched w>0( they sell drug)

Payoff is 0 if doesn’t carry the drug

Question 12

Given that

Police:

• Cost of search/car: c>0
• Reward if drug is found: v>c
• Payoff is zero if does not search

Driver:

• Punished if carries drug and searched: -d<0

Gets rewarded if carries drugu and not searched W>0

• Payoff is zero if does not carry any drug

Draw matrix

Answer 12

Question 13

Is there a pure strategy equilbrium in thisi game?

Answer 13

No there is no pure strategy within this game

If police searches → driver never carries drug → police should not search

If police does not searches → driver carries drug → police should search

Question 14

As there is no pure strategy within this game what does that mean exists?

Answer 14

A mixed strategy equibrium

Question 15

Lets say i commute a mixed strategy equilbrium and I use H for Player 2 and S for player 1 what is S and H?

Answer 15

H is going to be the hit rate ( as it will tell you given that you stopped are car for drugs,what is the likelihood it will have drugs in it or a fraction of cars with drugs)

S will be search rate ( it will tell you the fraction of police officers who stop a car

Question 16

What are we assuming within this model?

Answer 16

Police have correct beliefs about the hit rate, h.

Question 17

Lets now see how police treat different races now, suppose drivers are of race X and Y What are there payoffs.

Answer 17

Member of X: (dx, wx) (so a member x feels differently about going Jail then memeber of Y which represents D, the higher the D the more you worry going to jail. and have different rewards when they sell drugs)

Member of Y: (dy, wy) ( member of Y may feel differently about going to Jail then a member of X, which is represented by D, maybe going to Jail is fun to D is lower vice versa and have different rewards when they sell drugs)

Question 18

Lets now see how police treat different races now, suppose drivers are of race X and Y what are police payoffs on the race X and Y?

Answer 18

If the driver is X: (cx, v)

If the driver is Y: (cy, v)

So reward is fixed.

The police have different costs /payoffs depending on race

If police is prejudiced (taste-based) against X: cx < cy

Presumably, because the police likes to harass X-drivers. ( they get a kick when they arrest someone from race X, hence cost is lower)

Question 19

Lets say story 1 is that suppose there are two races X and Y, the reson why police stop 1 race more than the other is because of belief based discriminiation to prove this what are we going to do?

Answer 19

We are shutting down the taste based aspect as now Cx = Cy so the police doesn’t get a kick on stopping a certain race more than others. So the police only stop one race than the other based on there belief about a certain race.

Question 20

To prove our story that police stop some races more than others due to belief based discrimination, draw a 2 by 2 matrix for race x and race y, knowing that Cx = Cy and

Races might differ in their payoffs:

Member of X: (dx, wx)

Member of Y: (dy, wy)

Payoff of Police might depend on the race of the driver

If the driver is X: (cx, v)

If the driver is Y: (cy, v)

Answer 20

We replace the -C with Cx for Race X and . d with dx, W with Wx

We replace -C with Cy for Race Y, d with Dy and W with Wy

Question 21

What is the Hit rate for Race X ?

Answer 21

Calculate Mixed strategy

as Cx = Cy you can get rid off the Cx and just use -c

You keep the rest of the subscripts as they are different for the different races so

h X (v-c) + 1-h (-c) = h x(0) + 1-h ( 0)

h =c/v

Question 22

What is the hit rate of race Y

Answer 22

Calculate Mixed strategy

as Cx = Cy you can get rid off the Cy and just use -c

You keep the rest of the subscripts as they are different for the different races so

Question 23

From our story 1 what can we conclude?

Answer 23

When police don’t have any taste based discrimination and only have belief based discrimination, we should get the exact same hit rate for black and whites. ( Also the differences in races, in whether the driver gets high reward or low reward or fears jail or not doesn’t matter, the hit rate should be equalised)

Question 24

If hit rates are the same, then we should believe that what?

Answer 24

Police only engage in belief based discrmination.

Question 25

Lets look at story 2, lets say the police engage in taste based discrmination, what would the cost not be?

Answer 25

Cx doesn’t equal Cy

So the police have inherent taste for stopping one race than another.

Question 26

Lets look at story 2, lets say the police engage in taste based discrmination, where Cy doesnt equal Cx what would be the hit rate? for race X

Answer 26

As Cx doesnt equal Cy the hit rate would be

h x (v-cx) + 1-h(-cx) = h (0) + 1-h(0)

hx = cx/v

Question 27

Lets look at story 2, lets say the police engage in taste based discrmination, where Cy doesnt equal Cx what would be the hit rate? for race Y?

Answer 27

H x (v-cy) + 1-h(-cy) = h(0) + 1-h(0)

hy = cy/v

Question 28

So when Cy is not equal to Cx we except to get what ?

Answer 28

Different hit rates between the two races

Question 29

Still story 2 Now lets say Cx

Answer 29

This means that the police are biased stopping drivers from race x, so the hit rate for race X will be smaller than Y ( so even though the probability i put them in jail is lower than someone in race Y)

Question 30

When hit rates are different irrespective of what the driver thinks about jail and reward, what does this mean?

Answer 30

The police use Taste based discrimination along with Belief based (there is always belief based because, as they are using there believe of h, which influences propensity to stop or not stop, these rates)

Question 31

Will there be an equilbrium if police search for the drivers with highest rit rate e.g. hit rate for race Y

Answer 31

No because if they are constanly getting stop, drivers will look up the search intensity and stop putting drugs in car and hence the hit rate for that race will fall. Thus it is not sustain for having one race have a higher hit rate than the other. It is only sustainable if they sacrifce ability to arrest someone, they do this if they enjoy stopping someone more than another, thus by arresting some from race X (because costly, so i get a kick) but you are willing to sacrfice the fact that the probablitiy you put them in jail is lower than someone in race Y

Question 32

So how do we know if we have taste based discrimination finally.

Answer 32

So once you have taste based discrimination the police officers are willing to get a lower hit rate, but still stop people from this race becuase they enjoy it.

Question 33

So to answer the question on whether police have taste based discrimination or not,

Answer 33

We only have to look at the hit rates

Question 34

We have already said it but what is the second lesson to conclude?

Answer 34

When police engage also in Taste-Based discrimination, and when they are motivated to find criminals, hit rates are not equalised across all races!

Question 35

So to summarise story 1 and 2, police always engage in what?

Answer 35

Belief based discrimination as we assume police maxmise the probability of someone and base decision on belief, about what do drivers from different races do.

Question 36

What can you conclude from the data here?

Answer 36

As the hit rates are lower for black and hispanic than white, the police engage in taste based discrimination as well as belief based discrimination. For the different time rates it is similar.

If there was no taste based discrimination, the hit rates would be the same

Question 37

So if we find taste based discrimination of police drivers what is it hard to do for society?

Answer 37

Can there beliefs and stop the inistutional discrimination compared to belief based where you can just train police officers

Question 38

What could be another reason why black and espanic are searched more than white ( why there is taste based discrimination)

Answer 38

Could also be due to wrong beliefs about hit rates

Question 39

What are some facts about short people compared to tall people?

Answer 39

Additional 10cm yields 3.3% higher wage

Workers above average height earn 5% more than workers below.

Question 40

What are 2 reasonss why tall people earn more and classifiy if this is taste based or belief based discrimination ?

Answer 40

Evolution ( gives a direct physical advantage) Belief based discrimination

Signalling ( height signals good health ) Taste based discrimnation

Question 41

What are 2 further reasons of why tall people earn more? classify if this is belief or taste based discrimination

Answer 41

Self esteem ( Not discrimination but important) Taller individuals are more confident

Interpersonal dominance ( shorter people find it difficult to negiotate wages ( Not clear whether discrimination or not)

Question 42

From the findings is Is there really discrimination against shorter people? ( case study?

Answer 42

There is not much evidence for any kind of discrimination.

Question 43

Question 1 Which of the following are true? a. Firms that engage in taste-based discrimination will sometimes sacrifice profits to discriminate.

b. Firms that actively engage in taste-based discrimination never sacrifice profits.
c. A famous case brought to the US Supreme Court revolved around a baker in Colorado who refused to sell a wedding cake to two men planning their nuptials. This is likely to be taste-based discrimination.
d. A famous case brought to the US Supreme Court revolved around a baker in Colorado who refused to sell a wedding cake to two men planning their nuptials. This is surely belief-based discrimination.

Answer 43

A and C read question carefully

Question 44

Question 2 An annuity is an insurance policy that pays the buyer an annual income for life in return for a lump-sum now. For example, a 65 year-old can currently buy £5000 for life for approximately £100k. Which of the following are true?

a. In the past, insurance companies were legally able to charge women and men different prices. In that era, the price for women exceeded that for men. If this price difference stems from belief-based discrimination then we can infer from this that women were considered to live longer than men at the time.
b. In the past, insurance companies were legally able to charge women and men different prices. In that era, the price for women exceeded that for men. If this price difference stems from belief-based discrimination then we can infer from this that women were considered to have a lower life expectancy than men at the time.
c. In the past, insurance companies were legally able to charge women and men different prices. In that era, the price for women was the same of that for men. If this price difference stems from belief-based discrimination then we can infer from this that women were considered to have the same life expectancy to men at the time.
d. These days, insurance companies are legally prohibited to charge women and men different prices. If the life expectancy of men and women differ, then insurance companies might be worse off in comparison to the days they could price discriminate.
e. These days, insurance companies are legally prohibited to charge women and men different prices. If the life expectancy of men and women differ, then insurance companies might be better off in comparison to the days they could price discriminate.

Answer 44

A c and D

Firms benefit from discrmination as it increased their profits. Therefore banning price discrmination would make them worse off.

Question 45

Lets say example

Is a white applicant more likely to get a job interview?

Problem: the CV does not include the race of the applicant

So what they did was that created fake CVs with different white and black sounding names and found that people with white sounding names are more likely to get interview than black sounding names, what can we conclude?

Answer 45

Strong evidence for taste-based discrimination against blacks.

Question 46

What is another type of discrimination?

Answer 46

Customer base discrimination ( A customer prefers to buy a product from a firm who doesn’t employ workers of raxe X, a profit maxmising seller might respond by not employing workers of race X)

Question 47

Consider the following game we studied in lectures played by a driver and the police. The driver can be of race X or race Y. Police:

• Cost of search/car with a driver of Race X: 2
• Cost of search/car with a driver of Race Y: 3
• Reward if drug is found: 4
• Payoff is zero if does not search

Driver (same payoffs to both races):

• Punished if carries drug and searched: -3
• Gets a reward if carries drug and not searched: 4
• Payoff is zero if does not carry any drug

Draw Payoff Matrices as 2 games.

Answer 47

Question 48

Find the pure strategy equilibria, if they exist, in each of the games you described in (a). Explain your answer.

Answer 48

In each of the game we described in (a) there is no pure strategy equilibrium. To see this note that when the driver plans to carry drugs, the police’s best response is to search, but if the driver knew that they will search, the driver would prefer not carrying the drug. Therefore (carry drugs, Not search) and (carry drugs, search) are both not an equilibrium in either of the games. Similarly, if the driver plans to not carry drugs the police would prefer to not search, but if the police does not search the driver prefers to carry drugs. For this reason (Not carry drugs, Not search) and (Not carry drugs, search) are not equilibria in either of the games.

Question 49

Find the mixed strategy equilibrium in each of the games you described in (a). Explain your answer.

Answer 49

Race X = (2 x h) + (-2 x 1-h) = (0xh) + (0(1-h)

2h + -2 + 2h = 0

4h-2 = 0

4h =2

h = 2/4 = 1/2

1-h = 1/2

Then

• 3(s) + 4(1-s) = 0(s) + 0(1-s)
• 3s + 4-4s = 0

7s =4

s= 4/7

1-s = 3/7

Race Y

1(h) + -3(1-h) = 0(h) + 0 ( 1-h)

h-3+3h = 0

h = 3/4

1-h = 1/4

Then

• 3(s) + 4(1-S) = 0(5) + 0(1-s)
• 3s + 4 - 4s = 0

7s =4

s=4/7

Question 50

d. What are the police hit rates when they stop a driver of race X? What are the hit rates when they stop a driver of race Y? Explain your answer

Answer 50

The hit rate is the likelihood that given that you stop someone of a given race, they have drugs. These were calculated before. So that for race X the hit rate is ½ and for race Y this is ¾.

Question 51

What is the likelihood of the police stopping an individual of race X? What is the likelihood of the police stopping an individual of race X? Explain your answer.

Answer 51

The likelihood of the police stopping an individual of a particular race stopping someone is 4/7.

Question 52

Consider the model outlined in this question and the answers you have given to (d) and to (e). Is there discrimination in this model? If so, what kind of discrimination is there?

Answer 52

In this model, there is both Belief based and taste-based discrimination. Belief based discrimination exists as police use their beliefs about the probability that a driver of a certain race hides the drugs when deciding whether to search or not. To see why we have taste-based discrimination note that the payoffs of the police differ depending on the race of those they stop. Stopping someone of race X costs 2 while stopping someone of race Y costs them 3. This means that they are biased, through their payoffs, to stop race X more. So just by looking at the payoffs of the police, we can see that they have a taste-based bias towards one of the races.

Question 53

Consider the game played by the police and a driver studied in the lecture. Suppose that there are two races, X and Y. The punishment for carrying the drug does not depend on race, dx = dy = 11000. The gain from keeping the drug and later selling it for a driver of race X is 1000, that is wx = 1000. Which of the following are true?

Select one or more:

a. The equilibrium search intensity of the police for race X is 1/12.
b. The equilibrium search intensity of the police for race X is 1/3.
c. The equilibrium search intensity of the police for race X is 1/2.
d. The probability that the driver of race X will take the drugs in her car is 1/3.
e. We do not have enough information to deduce the equilibrium probability that the driver of race X will take the drugs in her car.

Answer 53

Sx(-11000) + 1-Sx(1000) = Sx (0) + 1-Sx(00)

Sx = 1/12

We cannot find hit rate to as we don’t have C and V

Question 54

What is another way we could do this question?Consider the game played by the police and a driver studied in the lecture. Suppose that there are two races, X and Y. The punishment for carrying the drug does not depend on race, dx = dy = 11000. The gain from keeping the drug and later selling it for a driver of race X is 1000, that is wx = 1000. Which of the following are true?

Select one or more:

a. The equilibrium search intensity of the police for race X is 1/12.
b. The equilibrium search intensity of the police for race X is 1/3.
c. The equilibrium search intensity of the police for race X is 1/2.
d. The probability that the driver of race X will take the drugs in her car is 1/3.
e. We do not have enough information to deduce the equilibrium probability that the driver of race X will take the drugs in her car.

Answer 54

Solve S through using normal 2 by 2 matrix then plug numbers

S(-d) + 1-S(W) = S(0) + (1-S)(0)

W - Ws = ds

W = ds + ws

=S (d+w)

S= w/d+w

Sx = 1000/1000 +11000 = 1/12

Question 55

Consider the game played by the police and a driver studied in the lecture. Suppose that there are two races, X and Y. The punishment for carrying the drug does not depend on race, dx = dy = 11000. The gain from keeping the drug and later selling it for a driver of race X is 1000, that is wx = 1000. Suppose that I tell you that in equilibrium a driver of race Y is six times as likely to be searched as a driver of race X. What is the gain from selling the drug for a driver of race Y to make this the equilibrium?

Select one or more:

a. wy=1000wy=1000
b. wy=10000wy=10000
c. wy=11000wy=11000
d. wy=60000wy=60000
e. We do not have enough information to answer this question.

Answer 55

Commute Search intensity of race Y

Sy(-11000) + 1-Sy(Wy) = 0

Sy = Wy/(11000+Wy)

In question 2 it says Sy =6sx

6X1/12 = 1/2

1/2 = Wy(11000+ Wy)

Implying Wy = 11000

Question 56

Consider now another variation of the game played by the police and a driver studied in the lecture. Suppose that there are two races, A and B. The punishment for carrying the drug is the same for both races, da=db=2 and the police’s cost of searching is the same ca=cb=1. The police reward for finding the drug is v=3. The gain from selling the drug for a driver of race A is also the same as the gain for a driver of race B, that is, wa=wb=2. Which of the following are true?

Select one or more:

a. Drivers of Race A are searched more often.
b. Drivers of Race A are searched as often as drivers of Race B.
c. The hit rate for Race A is 1/3.
d. The hit rate for Race B is 1/2.
e. The hit rate is the same for both races.
f. In this situation, there is taste-based discrimination.

Answer 56

2h + 1-h(-1) = 0

2h - 1 + h =0

3h =1

h= 1/3

As you can see the hit rates are the same as Cost are the same so there is belief based discrmination not taste based.

B c and E are correct

Question 57

Answer 57

C and e

The police’s hit rate must be the same regardless of where they look, which means that the drug dealer must hide in each place with equal probability