Seating Arrangements, writing assignment help

  

Read the article “Seating Arrangements” and address the following questions:What Personal Communication do you notice was used in the article?What level of interaction is needed to discuss this timeless issue?What elements of Higher Order Thinking (see Bloom’s Taxonomy) were used in the quote on the internet to try to solve the debate?What elements of the article do you think would work best in your household?Hypothesize a methodology which would solve the issue equally for both genders.ContentServer.pdf
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UP OR DOWN? A MALE ECONOMIST’S MANIFESTO ON THE TOILET
SEAT ETIQUETTE
JAY P. CHOI∗
This paper develops an economic analysis of the toilet seat etiquette. I investigate
whether there is any efficiency justification for the presumption that men should leave
the toilet seat down after use. I find that the “down rule” is inefficient unless there is
a large asymmetry in the inconvenience costs of shifting the position of the toilet seat
across genders. I show that the “selfish” or the “status quo” rule that leaves the toilet
seat in the position used dominates the down rule in a wide range of parameter spaces
including the case where the inconvenience costs are the same. (JEL D7, H4)
syndicated columns by Ann Landers and TV
sitcoms such as ABC’s “Home Improvement”
and NBC’s “3rd Rock from the Sun.” It is clear
that this age-old debate is divided by the gender.
Women complain that it should be the man’s
responsibility to lower the toilet seat after use.
“Leaving the toilet seat up” is often described
as a problem, and there is even a toilet seat
that goes down automatically after about 2 min,
claiming that it has the perfect solution to the
problem. Men seem to question why women
should be the free-riders all the time. To quote
Larry James (2004), a personal relationship
counselor, “The most hotly contested battlefield
in the gender wars may not necessarily be in the
bedroom. It may be the bathroom. The seat-up
versus seat-down debate rages on . . .”
Despite high emotions in the debate, scientific inquiries into this issue are sparse.
In fact, it is not obvious why there should
be a presumption that men are expected to
leave the toilet seat down after use. Internet search generated the following noneconomic/scientific reasons for the down rule. First,
there is an argument that being considerate
to one’s love partner’s needs supports things
going well in and out of the bedroom. To
quote a phrase in the Internet (available at
http://www.celebratelove.com/littlethings.htm),
“Foreplay begins with putting the toilet seat
down without being asked!” Second, it is not
Dear Annie: I read with interest the letters about
putting down the toilet seat. I’ve been browbeaten
by various women for the past 60 yr about proper
seat etiquette, starting with my mother. If I forget to
put the seat down even once, my wife reminds me
for hours about this life-threatening situation.
I know you said the last column was the final word on
the subject, but I hope you’ll reopen the issue. I want
to ask women: Who gave you exclusive ownership
of the bathroom? If men are nice enough to put the
lid down, why can’t you ladies lift it up when you
are done? When I suggested this to my wife, she
wanted to have me taken out and shot. It’s time to
rebel!—Fed Up in Salem, Ore.
Dear Fed Up: What is it about toilet seats that
excites people? We received hundreds of letters on
this subject and decided the “last word” would have
to wait—Kathy Mitchell and Marcy Sugar.1
I.
INTRODUCTION
Should the toilet seat be left up or down after
use? This is a question that arises when members
of the opposite sex share the same toilet. For
some reason, this seemingly trivial question
elicits passion from all sorts of people. It has
become a topic of national debates in popular
*I thank Carl Davidson and Roger Lagunoff for helpful
discussions and many colleagues for sharing their experiences. I am solely responsible for the views expressed in
this paper.
Choi: Professor of Economics, Department of Economics,
Michigan State University, East Lansing, MI 48824.
Phone 51-353-7281, Fax 517-432-1068, E-mail
choijay@msu.edu
1. Annie’s Mailbox by Kathy Mitchell and Marcy Sugar,
October 29, 2002. Annie’s Mailbox is written by Kathy
Mitchell and Marcy Sugar, long time editors of the Ann
Landers syndicated column.
ABBREVIATIONS
BPH: Benign prostatic hyperplasia
303
Economic Inquiry
(ISSN 0095-2583)
Vol. 49, No. 1, January 2011, 303–309
doi:10.1111/j.1465-7295.2009.00277.x
Online Early publication March 11, 2010
© 2010 Western Economic Association International
304
ECONOMIC INQUIRY
good Feng-Shi to leave the toilet seat up. Third,
a toilet is not the most attractive household
appliance. Closing the lid improves its appearance and prevents things from falling into the
bowl. The last argument, however, proposes not
only the seat down but also the lid down.
In this paper, I investigate whether there is
any justification for the down rule based on
economic efficiency. I find that the down rule
is inefficient unless there is large asymmetry in
the inconvenience costs of shifting the position
of the toilet seat across genders. I show that the
“selfish” or the “status quo” rule that leaves the
toilet seat in the position used dominates the
down rule in a wide range of parameter spaces
including the case where the inconvenience
costs are the same. The intuition for this result is
easy to understand. Imagine a situation in which
the aggregate frequency of toilet usage is the
same across genders, that is, the probability that
any visitor will be male is 1//2. With the down
rule, each male visit is associated with lifting the
toilet seat up before use and lowering it down
after use, with the inconvenience costs being
incurred twice. With the selfish rule, in contrast,
the inconvenience costs are incurred once and
only when the previous visitor is a member
of different gender. The worst case under the
selfish rule would occur when the sex of the
toilet visitor strictly alternates in each usage.
Even in this case, the total inconvenience costs
would be the same as those under the down
rule if the costs are symmetric. If there is any
possibility that consecutive users are from the
same gender, the selfish rule strictly dominates
the down rule because it keeps the option value
of not incurring any inconvenience costs in such
an event. This logic can be extended to the
case of asymmetric aggregate frequency of toilet
usage across genders.
The remainder of the paper is organized in
the following way. In Section II, I compare three
plausible rules for the toilet seat position—up,
down, and selfish—on an efficiency criterion.
I show that the selfish rule always dominates
the other two if the inconvenience costs of
changing the toilet seat position are the same
across genders. In Section III, I characterize the
optimal rule for the toilet seat position. It turns
out that the selfish rule is the most efficient
rule in a wide range of parameter spaces. I also
derive the condition that the down rule can be
the most efficient one when the inconvenience
costs are asymmetric. Section IV extends the
analysis to the case where the inconvenience
costs are heterogeneous even within the same
gender. Section V contains concluding remarks.
II.
THE BASIC MODEL
I consider the usage of a toilet that is shared
by members of the opposite sex.
Assume that the proportion of male to all
users of a certain toilet is given by α. Let
me assume the frequency of using a toilet by
male and female is the same without loss of
generality. If one gender uses the toilet more
often, this asymmetry can be reflected in α.
Thus, the parameter α represents the relative
aggregate frequency of male using the toilet.2
I analyze an infinite horizon discrete time
framework where the toilet is used once in each
period. The discount factor is given by δ. With
the assumption about the relative frequency of
the toilet usage by each gender, the probability
that the user is male in each period is given
by α.3 The inconvenience cost of lowering the
toilet seat for women is given by cf . The
corresponding cost of lifting the toilet seat for
men is given by cm . Even though I use the term
inconvenience costs, cf and cm can encompass
other types of costs such as “unwittingly placing
one’s bottom directly on the porcelain” and risk
of falling in by sitting down without looking
when the seat is up or “leaving sprinkles on the
seat” when it is down, respectively.
My goal in this section is to compare the
expected aggregate inconvenience costs of three
rules—down, up, and selfish—concerning the
position of the toilet seat. In this comparative
analysis, I abstract from other considerations
such as being considerate to members of the
opposite sex, aesthetic aspects, the wear costs
of the seat hinge, etc.
A. The Down (Female-Friendly) Rule
This is a rule that leaves the position of the
seat down after one is done with the bathroom
task. In particular, this rule implies that each
visit by a male member will be associated with
the inconvenience costs of 2 cm , whereas female
members will incur no costs.
2. The relative frequency of men going “number 1” versus “number 2” can be also incorporated in the parameter α.
3. Equivalently, I could envision a continuous time
model in which the arrival rate is given by a Possion process
with the arrival rate being a function of the number of total
users. The probability that a particular arrival is male is
given by α. I derive essentially the same results with this
continuous model.
CHOI: A MALE ECONOMIST’S MANIFESTO ON THE TOILET SEAT ETIQUETTE
Let VmDOWN and VfDOWN denote the value
functions with the down rule when the particular
user in the current period is male and female,
respectively. Then, these value functions satisfy
the following recursive relationships.

VmDOWN = −2cm + δ αVmDOWN
(1)

+ (1 − α)VfDOWN

(2) VfDOWN = δ αVmDOWN + (1 − α)VfDOWN
By solving these two equations, we can get

δα
(2cm )
(3)
VmDOWN = − 1 −
1−δ
(4)
VfDOWN
δα
(2cm )
=−
1−δ
Because the probability of a particular arrival
being male is α, the value function associated
with the down rule is:
(5)
V DOWN = αVmDOWN + (1 − α)VfDOWN
α
(2 cm )
=−
1−δ
B. The Up (Male-Friendly) Rule
This is a rule that leaves the position of the
seat up after one is done with the bathroom
task. In this case, all the inconvenience costs
are incurred by females. The case is a mirror
image of the down rule and the value function
of this rule can be derived in an analogous way.
Let VmUP and VfUP denote the value functions
when the particular user is male and female,
respectively. Then, these value functions satisfy
the following relationships.

VmUP = δ αVmU P + (1 − α)VfUP
(6)
(7)
VfUP = − 2cf

+ δ αVmDOWN + (1 − α)VfUP
By solving these two equations, I can derive
(8)
(9)
VmUP = −
VfUP
δ(1 − α)
(2cf )
1−δ

δ(1 − α)
(2cf )
=− 1−
1−δ
305
Because the probability that a particular arrival
is male is α, the value function associated with
the down rule is:
(10)
V UP = αVmUP + (1 − α)VfUP
(1 − α)
(2cf )
1−δ
A comparison of Equations (5) and (10)
yields the following proposition.
=−
PROPOSITION 1. The down rule is more effic
α
.
cient than the up rule if and only if cmf > 1−α
C. The Selfish (Status Quo) Rule
This is a rule that leaves the position of the
seat as it was used.
Let VmSQ and VfSQ denote the value functions when the particular user is male and
female, respectively, under the selfish rule.
Then, these value functions satisfy the following
relationships.
(11)
VmSQ = − (1 − α)cm

+ δ αVmSQ + (1 − α)VfSQ

(12) VfUP = −αcf + δ αVmSQ + (1 − α)VfSQ
By solving these two equations, I get
(13)

VmSQ = −
(14)
VfSQ
(1 − α)(1 − δ(1 − α))
cm
1−δ

δα(1 − α)
cf
+
1−δ

δα(1 − α)
α(1 − δα)
cm +
cf
=−
1−δ
1−δ

Because the probability that a particular arrival
is male is α, the value function associated with
the down rule is:
(15)
V SQ = αVmSQ + (1 − α)VfSQ
α(1 − α)
(cm + cf )
1−δ
Comparisons of Equations (5), (10), and (15)
give me the following result. See also Figure 1.
=−
PROPOSITION 2. If the inconvenience costs
are the same across genders (cm = cf ), the selfish rule dominates both the up and down rules.
306
ECONOMIC INQUIRY
FIGURE 1
Comparisons of the Up, Down, and Selfish Rule for the Symmetric Inconvenience Costs
(cm = cf = c)
Per-period
average costs
2c
Average costs with
the Up Rule (2(1 − a)c)
Average costs with
the Down Rule (2ac)
2c
Average costs with the selfish rule
(2a(1-a)c)
a=0
a=1
a
Average costs with the selfish rule
(2a(1 − a)c)
The intuition for Proposition 2 is easy to
understand. With either up or down rule, each
member of one gender group has to incur the
inconvenience costs two times with each usage.
This practice can be obviously inefficient in the
event that consecutive users are from the same
gender to which the inconvenience costs are
attributed. This inefficiency can be avoided by
using the selfish rule because the inconvenience
costs are incurred only when the consecutive
users are from different genders. Even in such
an event, the aggregate costs would be the
same as those under the up or down rule if the
inconvenience costs are the same across genders.
I cannot rule out the optimality of, say,
the down rule if the inconvenience costs are
asymmetric across genders. My analysis, however, suggests that to justify the down rule on
efficiency grounds, the inconvenience costs for
female should be very high relative to those for
male. More precisely, the condition for the down
c
rule to dominate the selfish rule is γ = cmf > 1+α
1−α .
For instance, if male and female users visit the
toilet with the same frequency (α = 1/2), the
inconvenience costs for female should be three
times higher than the corresponding costs for
male to justify the down rule.
Up to now, I have considered only three
potential mechanisms. These three rules, however, are not the only rules we can entertain. For
instance, I can imagine a rule such that the position of the seat should be restored to the prior
position before use. Alternatively, I can also
consider a mutually considerate rule in which
male users leave the seat down, whereas female
users leave the seat up after use. In the next
section, however, I show that all these rules
are dominated by one of the three rules I have
CHOI: A MALE ECONOMIST’S MANIFESTO ON THE TOILET SEAT ETIQUETTE
considered. Thus, restricting my attention to the
three rules does not entail any loss of generality
in the analysis.
III.
CHARACTERIZATION OF THE OPTIMAL RULE:
A MECHANISM DESIGN APPROACH
In the previous section, we compared three
simple rules that can be used for the toilet
seat position. The task of this section is to
derive the most efficient rule among all possible
mechanisms. I show that one of the three rules
discussed in the previous section is always
optimal. Thus, restricting my attention to the
three rules does not entail any loss of generality
if the only concern is to minimize the aggregate
inconvenience costs of toilet users.
The general rule can be considered a collection of four numbers (σum , σdm , σuf , σdf )
where σij denotes the probability that the seat
be down after use when the position of the seat
before use is i and the visitor is j , where i = u,
d and j = m, f . The first subscripts u and d
denote up and down, respectively, and the second subscripts m and f denote male and female,
respectively. The objective is to search for the
best mechanism that minimizes the aggregate
inconvenience costs.
In the Appendix, I prove that the position of
the seat before one’s use should not count in the
optimal rule.
LEMMA. The optimal rule should depend only
on the gender of the user, not the position of the
seat before one arrives.
With the help of lemma, I can restrict my search
for the optimal mechanism to a class of rules that
can be written as (σm , σf ), where σm and σf are
the probabilities that the toilet seat should be in
the down position after usage by a male and a
female, respectively.
Let Vm (σm , σf ) and Vf (σm , σf ) be the
corresponding present discounted value when a
particular user in the current period is male and
female, respectively.
Vm (σm , σm ) = − [ασm + (1 − α)σf ]cm − σm cm
+ δ[αVm + (1 − α)Vf ]
Vf (σm , σf ) = −[α(1 − σm ) + (1 − α)
× (1 − σf )]cf − (1 − σf )cf
+ δ[αVm + (1 − α)Vf ]
307
Then, the corresponding value function for the
rule (σm , σf ) can be written as
V (σm , σf ) = αVm (σm , σf ) + (1− α)Vf (σm , σf )
= [−αM + (1 − α)F ]/(1 − δ),
where M = [ασm + (1 − α)σf ]cm + σm cm and
F = [α(1 − σm ) + (1 − α)(1 − σf )]cf +
(1 − σf )cf .
The search for the optimal mechanism is
equivalent to solving
Minσm ,σf αM + (1 − α)F.
PROPOSITION 3. The optimal toilet etiquette
is given by the following:
c
Let γ = cmf be the relative cost of changing the
toilet seat position for male and female. Then,
the optimal rule is characterized by two critical
values of γ (γ and γ) such that:
(1) The toilet should be down if γ > γ =
1+α
1−α
(2) The toilet should be left as it was used if
= γ < γ < γ = 1+α 1−α α (3) The toilet should be up if γ < γ = 2−α α 2−α Proof: Because the objective function αM + (1 − α)F is a linear function of σm and σf , I have corner solutions except the knife-edge cases. By differentiating αM + (1 − α)F with respect to σm and σf , the optimal rule is given by: ⎧ ⎪ 1 if γ > 1+α
⎨
1−α
σm = any number between 0 and 1 if γ = 1+α
1−α
⎪
⎩
0
if γ < 1+α 1−α ⎧ α ⎪ 1 if γ > 2−α
⎨
α
σf = any number between 0 and 1 if γ = 2−α
⎪
α
⎩
0
if γ < 2−α α Because 2−α = γ < γ < 1+α 1−α , we have the desired result. Figure 2 summarizes the optimal configuration for different values of α and c γ = cmf . Q.E.D. My analysis can be easily extended to the case of time-varying γ and α. These values, for instance, can change depending on the time of the day. The mistake costs of “unwittingly placing one’s bottom directly on the porcelain” or risk of falling in are presumably higher during the nighttime when the light is turned off. If this is the case, the optimal rule could be time-dependent, with the selfish rule during the 308 ECONOMIC INQUIRY FIGURE 2 The Optimal Rules with Asymmetric Inconvenience Costs daytime and the down rule during the nighttime. A countervailing argument against the down rule during the nighttime is that nocturia (needing to urinate frequently during the night time) is more common with men due to benign prostatic hyperplasia (BPH).4 denote the mean values of the inconvenience costs for male and female, respectively: ∞ cm = cm dG = E(cm ), 0 cf = ∞ cf dH = E(cf ) 0 IV. HETEROGENEOUS COSTS WITHIN THE SAME GENDER In the previous sections, I assumed that the inconvenience costs are the same within the same gender. I extend the analysis to the case where different users have different inconvenience costs even within the same gender. Let me assume that cm and cf are distributed according to continuous distribution functions G(.) and H (.), respectively on [0, ∞). Let cm and cf 4. I thank Carl Davidson for this observation. It is clear that with heterogeneous inconvenience costs, the optimal rule should be characterized with two critical values cm * and cf * such that a male visitor should put the toilet seat down if and only if his cm ≤ cm * and a female visitor should put the toilet seat up if and only if her cf ≤ cf *. Then, σm = G(cm ∗) and σf = 1 − H (cf ∗) using our previous notation. The value function with the critical values of cm * and cf * can be written as V (cm ∗ , cf ∗ ) = − αM + (1 − α)F , 1−δ CHOI: A MALE ECONOMIST’S MANIFESTO ON THE TOILET SEAT ETIQUETTE where M = [αG(cm ∗ ) + (1 − α)(1 − H (cf ∗ ))] cm + G(cm ∗ )E(cm |cm ≤ cm ∗ ) and F = [α(1 − G(cm ∗ )) + (1 − α)H (cf ∗ )]cf + H (cf ∗ )E(cf | cf ≤ cf ∗ ) With this observation, the optimal critical values for cm * and cf * can be derived by solving Mincm ∗,cf ∗ αM + (1 � ... Purchase answer to see full attachment