# SOLUTION: University of Houston Economics Payment Gap & Identification of Parties Questions

Quiz 2
March 11, 2021
Read the entire test before you start freaking out.
Questions with a
,
require no explanation
(and any explanation given will be ignored). All other questions require either a simple mathematical
derivation or a short, simple written explanation. You must submit this quiz on MS Teams by 11:59pm
on 3/11/21. Make sure that you actually turn it in on Teams. No late exams will be accepted, and
do not submit documents in read-only format. Please be clear, concise, and above all correct. Good
luck!!
1. 0 pts. Write the statement, I [your name here] attest that I have not communicated with any
humans other than the professor and TA of this course about anything related to this quiz. I
have also not consulted any materials except what is posted to the class Team or Wikipedia. If
this statement is false, then I will receive 0 points for this quiz and may be subject to further
discipline. But because I am a good, pro-social person, I would not violate this agreement. If
you do this successfully, you will get 4 bonus points.
R and D. 100 individuals identify as
Rs, and 100 individuals identify as Ds. There is a single issue E , which either takes the value
E1 or E2 (think of it as some economic issue, e.g., E1 is higher tax and E2 is lower tax). 60
of the Rs personally prefer E1 , and 40 of them personally prefer E2 . The same is true for D s.
2. 48 pts. Identity Politics. There are two political parties,
(On average, there are no dierences in the policies individuals in each party actually like). If
an individual votes for the policy they like, they get a benet of
α > 0.
For now, let’s assume
that we have a direct democracy with majority rule, and there are no elected representatives.
Everybody is required to vote. If there is a tie,
(a)
,1
support
loss of
i.
is enacted.
pt. If a referendum was held today, which policy would be enacted?
(b) Now suppose that
ii.
E1
E2 .
Rs
believe that they should support
E1 ,
and
Ds
believe that they should
If a person votes against what they think they should do, then they suer a
β.
,1
,1
β α, which policy would be enacted?
Suppose β > α and you can switch parties at
pt. If
pt. If
iii. 3 pts.
a cost of
c.
What is the maximum
that a person would be willing to pay to switch parties? Of the four types of individuals
(Rs who like
E1 , Rs
who like
to switch parties? Assuming
E2 , Ds who like E1 , and Ds who like E2 ) who might
c is very small, which policy is enacted? Explain.
(c) For part (c) only, suppose that only 50 of the
Ds
personally prefer
pay
S1
and the rest prefer
c
that is very small.
S2 .
i.
ii.
iii.
,1
,1
,2
β α, which policy would be enacted?
pts. Suppose β > α and you can switch parties
pt. If
at a cost of
Which party will have more people in the long-run?
(d) For part (d) only, suppose that if a
βR , but if a D
er a loss of
a loss of
i.
βD
,2
pts. Suppose
,2
pts. Suppose
R
votes against what they think they should do, then
votes against what they think they should do, then they suer
βR > α > βD
and you can switch parties at a cost of
c
that is very
c
that is very
small. Which party will have more people in the long-run?
ii.
βR > β D > α
and you can switch parties at a cost of
small. Which party will have more people in the long-run?
1
iii. 4 pts.
Is the
R
party bigger in scenario (d)i or in scenario (d)ii?
In 3-5 sentences,
interpret this result and explain the relationship between identity and party polarization.
Does a stronger sense of identity result in more or less polarization?
Does an
asymmetric sense of identity result in more or less polarization?
iv. 4 pts. Assume that policy preferences are xed. Which parameters in this model do
political consultants/advertisers have control over? Based on this model in (d), who
Rs
or
Ds?
Why?
(Hint: There may be multiple correct
S (which is either S1 or S2 ) and E (which is
E1 or E2 ). Think of these as social and economic issues. There are two candidates,
1 and 2, and they support the respective issues. As before, 60 Rs and 60 Ds prefer E1 to
E2 , but now 80 Rs support S1 and only 50 Ds support S2 . Rs believe that they should
support E1 and S1 , and D s believe that they should support E2 and S2 . If a person votes
for a candidate who supports the opposite social issue, they suer a loss of βS , and if they
vote for a candidate who supports the opposite economic issue, they suer a loss of βE .
(e) Now let’s suppose that there are two issues,
either
i. 4 pts.
In what way (if at all) does it matter whether preferences are across the two
Rs
S2 .)
issues? (Hint: compare the situations in which all 60
S1
versus the scenario in which 20 of them support
ii. 4 pts.
If
βS
is much greater than
βE
who support
E1
(both of which are greater than
also support
α)
then what
policy would be enacted? Explain.
(f ) Answer each of these parts in 3-5 sentences. Using what you’ve learned over the course of
i. 4 pts. …do you think identity politics make it easier or harder for the largest number
of people to get the policies that they prefer? Why?
ii. 4 pts. …who benets the most from identity politics (e.g., people in the majority? in
the minority? people with the strongest sense of identity? weakest?)
iii. 4 pts. …do you think identity politics are more dangerous when there are many issues
that people care about or just a single issue?
(g) 6 pts.
How has working through this problem changed your prior beliefs about identity
politics? Answer in 4-6 well written sentences.
3. 42 pts. Mind the gap. You have undoubtedly seen statements like, Women earn
every dollar than men earn. Where
X
X
pennies for
is commonly a number between 70 and 85. In this problem
we’re going to think through how we should arrive at that
X
and how we should interpret it.
(a) Suppose there is a single rm in town and a single job at that rm. Everybody is required
by law to work. Let
wW
the wage that women are paid and
wM
be the wage that men are
paid.
i. 6 pts. Suppose everybody is equally productive. How could you test for gender bias?
(A test would be a series of statements of the form If ____ is greater than/less
than/equal to ____ then there is bias against ____ where the statements cover all
possibilities.)
ii. 4 pts. Suppose women are twice as productive as men. How could you test for gender
bias?
iii. 4 pts. Suppose women are more productive than men, but you don’t know how much
more. In what scenarios could you detect or rule out gender bias? In what scenarios
would you be unsure?
(b) Now suppose that the rm has two ranks of jobs:
boss and grunt.
Workers may have
dierent levels of skill/productivity, but men and women are equally skilled on average.
Bosses are more highly paid and are selected on their skill. Let
2
B
wW
and
B
wM
be the wages
that female and male bosses are paid respectively, and Let
G
wW
and
G
wM
be the wages that
female and male grunts are paid respectively.
i. 6 pts.
If
B
B
wW
= wM
and
G
G
wW
= wM
,
can we conclude that there is no gender bias?
Explain in 4-6 sentences.
ii. 6 pts. If the average female wage (across all types of workers) is equal to the average
male wage (across all types of workers), can we conclude that there is no gender bias?
3-5 sentences.
iii. 4 pts.
How does this make you reconsider how journalists/social commentators talk
gaps? Explain in 2-3 sentences.
(c) 8 pts. In 6-8 sentences, explain the connection between you answers in part (b) and the
discussion in class over testing for racial bias in police use of force.
(d) 4 pts. Come up with another context in which we want to test for bias. How does this issue
come into play? 3-5 sentences.
3

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