Course Hero has millions of student submitted documents similar to the one

below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

401 ECON Section:
Supply and Demand With Taxes
Comparative Statics
Sarah E. Taylor
University of Michigan, Department of Economics
January 10, 2011
In this set of notes I will pose to you some sample questions on taxes and some
solution techniques for solving them. Then I will give you a detailed example.
1
How does the equilibrium price of consumers
and suppliers change as a tax changes?
Suppose that the price paid by consumers is pD and the price received by suppliers is
pS . In addition, suppose we have a tax on the sale of a good such that the after-tax
price received by suppliers is pS = pD .1 In lecture, we refer to the price paid by
consumers as the equilibrium price. Suppose we want to nd dpD and dpS .
d
d
1.1
Explicitly
1. QS = QD and pD = pS
Set supply equal to demand in equilibrium and the after-tax price paid by consumers equal to the price received by suppliers. These are your two equilibrium
conditions.
2. Substitution
1
This solution technique can similarly used to solve for a tax on consumers; the equation relating
the price paid by consumers and the price paid by suppliers will be the same.
1
Substitute in pS = pD into the supply side of the equation setting supply
equal to demand. You will be left with an equation which has in it pD and ,
as well as any other exogenous variables.
3. Solve for pD in terms of , pD ( )
Isolate pD on one side of the equation setting supply equal to demand.
4. Solve for
dpD
d
Take the derivative of the function you found in the last step.
5. Solve for
dpS
d
Taking the fact that pD = pS and dierentiating both side we get that
dpD
1 = dpS . Thus we can simply substitute the value we found in the last
d
d
step into dpS = dpD 1 to get dpS .
d
d
d
1.2
Implicitly
1. QS = QD and pD = pS
Set supply equal to demand in equilibrium and the after-tax price paid by consumers equal to the price received by suppliers. These are your two equilibrium
conditions.
2.
dQS
d
=
dQD
d
and
dpD
d
1=
dpS
d
Take the derivative of both sides of the two equations with respect to . Remember that we have to apply the chain rule when we take the derivative of
supply and demand with respect to .
dQS
d
=
QS dpS
( d )
p
=
QD dpD
( d )
p
=
dQD
d
3. Substitution
S
D
Substitute dpS = dpD 1 into Q ( dpS ) = Q ( dpD ). This will allow us to rst
d
d
p
d
p
d
solve for the eect of the tax on the price of consumers. Now we have
QS dpD
( d
p
1) =
QD dpD
( d )
p
2
4. Substitute in values
The next step is to substitute in values for the partial derivatives using the
original quantity supplied and demanded functions. Remember that now in the
price the supply function is equal to pS and the price in the demand function
is equal to pD . This will yield an equation of only dpD and constants.
d
5. Solve for
dpD
d
dpD
d
will enter into both sides of the equation. Solve for
one side of the equation.
6. Solve for
by isolating it on
dpS
d
We can use the fact that
2
dpD
d
dpS
d
=
dpD
d
1 to then easily solve for
dpS
.
d
Example
Consider the following demand and supply functions for cupcakes, where po is the
price of cookies: QD = 100 2p + po and QS = 5p. Suppose we have placed a tax
on the sale of cupcakes. What is the eect of a 1 dollar increase in the tax on the
consumer price of cupcakes in equilibrium? What is the eect of a 1 dollar increase
in the tax on the supplier price of cupcakes in equilibrium? As a further challenge,
what is the eect on the equilibrium quantity of a 1 dollar increase in the tax?
2.1
Solution:
dpD
d
and
dpS
d
I will show you how to solve for this explicitly and then implicitly, using the solution
techniques outlined above.
Explicitly
First we set supply equal to demand 100 2pD + po = 5pS . Then taking the fact
that pS = pD and substituting, we have: 100 2pD + po = 5(pD ). Solving for
pD in terms of we get: 100 7pD + po = 5 7pD = 100 5 po pD =
100
1
+ 5 7 po .
7
7
Now we can dierentiate pD with respect to , yielding
3
dpD
d
= 5.
7
Now taking the fact that pS = pD and dierentiating we get that
dpD
1 = 2
d
7
dpS
d
=
Implicitly
First we take our two equilibrium conditions: QS = QD and pD = pS . The
next step is to dierentiate both equations with respect to :
(1)
dQS
d
=
QS dpS
( d )
p
=
QD dpD
( d )
p
=
dQD
d
And,
(2)
dpD
d
1=
dpS
d
Now, substituting equation (2) into (1), we can transform equation (1) into an
equation containing dpD and partial derivatives, which we can easily solve for:
d
QS dpD
( d
p
1) =
QD dpD
( d )
p
Let us now solve for the partial derivatives:
these values in, we get
QS
p
D
= 5, Q = 2. Substituting
p
5( dpD 1) = 2( dpD ) 5( dpD ) 5 = 2( dpD )
d
d
d
d
Now taking equation (2),
2.2
Solution:
dpS
d
=
dpD
d
dpD
d
=
5
7
1 = 2
7
dQ
d
Again, we may solve for the change in the equilibrium quantity with the change in
the tax using either quantity supplied or quantity demanded in equilibrium.
Quantity Supplied
4
dQ
d
Now substituting in for
QS
p
dQ
d
dQS
d
=
= 5 and
=
dQS
d
dQ
d
=
=
dpS
d
QS dpS
p d
2
= 7 , we have
= 5( 2 ) = 10 .
7
7
Quantity Demanded
Now substituting in for
QD
p
dQ
d
dQD
d
= 2 and
=
dQD
d
=
QD dpD
p d
dpD
d
= 5 , we have
7
= 2( 5 ) = 10 .
7
7
5

**Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.**

Below is a small sample set of documents:

Ashford University - ACCOUNING - ACC401

Chapter 15 - Corporate TaxationCHAPTER 15CORPORATE TAXATIONDiscussion Questions1. What are the requirements for a corporation to file a Form 1120A rather than a Form1120?Answer:A corporation may file a Form 1120A if it meets all of the following:

University of Texas - STATISTICS - 924

, to the degree ofatherosclerosis in coronary arteries. In one study, researchers examined therelationship between ferritin levels and atherosclerosis in 100 men and womenreferred for cardiac examination. In this population, higher ferritin levels

University of Michigan - ECON - 401

ECON 401 Section:Supply and Demand With TaxesIncidence and GraphsSarah E. TaylorUniversity of Michigan, Department of EconomicsJanuary 10, 2011We can analytically determine the incidence of a tax by determining dpD , as isdshown in the handout on

E. Washington - MISC - 311

Ch61. A satificing model in one that finds a good, but not the best solution. It would be usedin situation that has a lot of options.2. Intelligent decision making is when you identify and define potential problems oropportunities and the design the s

E. Washington - MISC - 311

Review qs ch 3MISC 311-012/5/2013Chapter 31. An attribute is characteristic of an entity. An entity is a general class of people places orthings for which data is collected stored and maintained.2. A database is an organized collection of facts and

E. Washington - MISC - 311

Chapter 41. Broadband communications is a telecommunications system that can exchange data veryquickly.2. The elements of telecommunications are a sending unit that transmits a signal to amodem that can perform any tasks which can include converting t

E. Washington - MISC - 311

Alyssa McDanielMisc 311-013/4/13Chapter 7 review1. A knowledge management system is an organized collection of people, procedures,software, databases and devices used to create, store share and use the organizationsknowledge and experience.2. A com

E. Washington - MISC - 311

Alyssa McDanielMisc 311-013/4/13Chapter 9 review1. The CAN-SPAM act allows the sending of spam emails as long as it can be unsubscribed, the content of the email and the sending behavior2. A danger of a spam filter is that it can block a important e

E. Washington - MISC - 311

Review qs ch 5MISC 311-012/18/2013Ch 51. E-government is the use of information and communications technology to simplify thesharing of information speed formerly paper-based processes and improve therelationship between citizens and government. The

E. Washington - MGMT - 326

Alyssa McDanielAssignment 22/5/13`A goal that I personally hope to achieve is to obtain my drivers license. I haverecently taken the drivers test in September and did not pass. I believe I did not plancorrectly to achieve my goal. Using the characte

E. Washington - ACCT - 261

International Bribery1.The PBS Frontline documentary talks about international bribery. It talks about an 80 billion dealbetween the BAE, A British based company, and Saudi Arabia royalty. The BAE has been underan investigation led by the Department o

E. Washington - ACCT - 261

ACCT261The Issue here is whether the governments regulation of the age of fire fighters is interferingwith the fire fighters right to life liberty or property. In this scenario the courts will use therational basis analysis. The courts will first test

UCSD - CSE - 107

UCSD - CSE - 107

UCSD - CSE - 107

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 1Wi13Instructor: Mihir BellareJanuary 7, 2013Problem Set 1Due: Wednesday January 23, 2013, in class.See course information section (on course web page) f

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 2Wi13Instructor: Mihir BellareJanuary 18, 2013Problem Set 2Due: Monday January 28, 2013, in class.See course information section (on course web page) for

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 3Wi13Instructor: Mihir BellareJanuary 28, 2013Problem Set 3Due: Wednesday February 6, 2013, in class.See course information section (on course web page)

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 4Wi13Instructor: Mihir BellareFebruary 6, 2013Problem Set 4Due: Wednesday February 13, 2013, in class.See course information section (on course web page)

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 5Wi13Instructor: Mihir BellareFebruary 13 , 2013Problem Set 5Due: Monday February 25, 2013, in class.See course information section (on course web page)

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 1 SolutionsFall 10Instructor: Mihir BellareOctober 4, 2010Problem Set 1 SolutionsProblem 2. [30 points] The ciphertextQFL HCVPS PX V ANSWLCEZK NCJVS; PQ

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 2 SolutionsFall 10Instructor: Mihir BellareOctober 11, 2010Problem Set 2 SolutionsProblem 1. [30 points] Let K by a 56-bit DES key and L a 64-bit auxiliar

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 3 SolutionsFall 10Instructor: Mihir BellareFebruary 1, 2010Problem Set 3 SolutionsProblem 1 [50 points] Let K be the key-generation algorithm that returns

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 4 SolutionsFall 10Instructor: Mihir BellareNovember 1, 2010Problem Set 4 SolutionsProblem 1. [20 points] Dene the family of functions H : cfw_0, 164 cfw_0

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 207: Modern CryptographyProblem Set 4 SolutionsFa12Instructor: Mihir BellareOctober 29, 2012Problem Set 4 SolutionsProblem 1. [30 points] Let E : cfw_0, 1k cfw_0, 1l cfw_0, 1l be a block cipher. Let D be th

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 5 SolutionsFall 10Instructor: Mihir BellareNovember 8, 2010Problem Set 5 SolutionsProblem 1. [40 points] Let E : cfw_0, 1k cfw_0, 1l cfw_0, 1l be a secure

UCSD - CSE - 107

Computer Science and Engineering, UCSDCSE 107: Introduction to Modern CryptographyProblem Set 6 SolutionsFall 10Instructor: Mihir BellareNovember 28, 2010Problem Set 6 SolutionsProblem 1 [40 points] Let p 3 be a prime and g Z a generator of Z . (Th

UCSD - CSE - 150

Game PlayingIntroduction to Artificial IntelligenceCSE 150Lecture on Chapter 5CSE 150, Fall 2012Adapted from slides adapted from slides of Russells by KriegmanCSP Summary CSPs are a special kind of search problem:States defined by values of a fixe

UCSD - CSE - 150

Game PlayingGameIntroduction to Artificial IntelligenceCSE 150Lecture on Chapter 5CSP SummaryCSP CSPs are a special kind of search problem:States defined by values of a fixed set of variablesGoal test defined by constraints on variable values Ba

UCSD - CSE - 150

Constraint SatisfactionProblemsIntroduction to Artificial IntelligenceCSE 150Fall 2012Cse 150, Fall 2012Gary Cottrell: Many slides borrowed from David Kriegman!Last lectureA* searchOptimality of A*IDA*Recursive Best First Search (briefly!)Beam

UCSD - CSE - 150

Constraint SatisfactionProblemsProblemsIntroduction to Artificial IntelligenceCSE 150Fall 2012Last lectureLastA* searchOptimality of A*IDA*Recursive Best First Search (briefly!)Beam Search (really briefly!)This lectureThisGeneral search app

UCSD - CSE - 150

UncertaintyUncertainty(Chapter 13, Russell & Norvig)Introduction to Artificial IntelligenceCS 150AdministrationAdministration Midterm next Tuesday! I will try to find an old oneto post. The MT will cover chapters 1-6, withemphasis on 3-6 Program

UCSD - CSE - 150

CSE150Lecture(Week1)22:442.ThequestionIleftyouwithlastweek:DepthFirstSearchusesspacebigOhof(b: branchingfactor,d:depthofsolution;m:maximumdepth):bmMissionariesandPiratesThreemissionariesandthreepiratesareontheleftbankofariver.Thereisonecanoewhichca

UCSD - CSE - 150

State space searchA lot of AI is about SEARCH.Search can be applied to many problems: soln to a puzzle shortest path on a map proof of a theorem sequence of moves to win a game sequence of transformations to solve a symbolic integration problem se

UCSD - CSE - 150

Problem Solving and SearchIntroduction to Artificial IntelligenceCSE 150Lecture/Problem solving 2October 2, 2012CS150, Fall 2012Wednesday, October 3, 12Some slides borrowed from David Kriegman, others created by Brendan DuncanAdministrivia If you

UCSD - CSE - 150

Problem Solving and SearchProblemIntroduction to Artificial IntelligenceCSE 150Lecture/Problem solving 2October 2, 2012AdministriviaAdministriviaIfyouareNOTaregularUCSDstudent,pleasesendyourpreferredemailaddresstotheTA,BrendanDuncanbaduncan@cs

UCSD - CSE - 150

Beyond traditional searchBeyondIntroduction to Artificial IntelligenceCSE 150Chapter 4October 9, 2012Ch 4. Reading Quiz Question 1Ch1.HillclimbingissometimescalledgreedylocalsearchA)TrueB)FalseCh 4. Reading Quiz Question 1Ch1.Hillclimbingisso

UCSD - CSE - 150

CSE 150 Lecture Notes, October 16, 20121 of 7http:/cseweb.ucsd.edu/~elkan/150/oct11.htmlTuesday October 16, 2012ANNOUNCEMENTSGary's plane was delayed by fog, so I'm giving today's lecture.CONSTRAINT SATISFACTION PROBLEMS (CSPs)A CSP is a state-spac

UCSD - CSE - 150

UCSD - CSE - 150

NAME:_LOGIN:_Signature:_Computer Science and Engineering 150Programming Languages for Artificial IntelligenceThursday, May 9, 2007M I DT E RM E XAMDO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO START! Please DO NOT put your name at the top of each pa

UCSD - CSE - 105

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 1Instructor: Alexander TsiatasDue on: Wed. April 11, 2012Problem 1There are many possibilities here. This is just one example.(a) Suppose you want a DFA that accepts strings

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 2Instructor: Alexander TsiatasDue on: Tue. April 17, 2012Problem 1In JFLAP, draw an NFA for the following language: cfw_w | w has only alternating as and bs . Whether youthin

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 3Instructor: Alexander TsiatasDue on: Tue. April 17, 2012Problem 1Without doing a full critique (no need to assign a number grade, comment on style, etc), write a shortparagr

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 4Due on: Tue. May 1, 2012Instructor: Alexander TsiatasCFG and PDA design (10 pts)Problem: LetL = cfw_ai bj ck | i = j or j = k .(a) Give a context-free grammar (CFG) that ge

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 5Due on: Tue. May 8, 2012Instructor: Alexander Tsiatas(1) Context-Free Pumping Lemma Proof (10 pts)Consider the language L = cfw_an b2n c3n | n N where N is the set of natural

UCSD - CSE - 105

CSE 105: Introduction to the Theory of ComptuationSpring 2012Solution Set 6Due on: Tue. April 24, 2012Instructor: Alexander Tsiatas1Turing Machine Construction (10 pts)Let = cfw_1, =. Consider the languageL = cfw_1a = 1b = 1c | a = b = c.Prove by

UCSD - CSE - 105

SolutionsChapter 1 ExercisesSection 1.11.3.5.7.9.11.13.15.17.19.21.23.25.27.cfw_5 x 1 : x Z = cfw_. . . 11, 6, 1, 4, 9, 14, 19, 24, 29, . . .cfw_ x Z : 2 x < 7 = cfw_2, 1, 0, 1, 2, 3, 4, 5, 6x R : x2 = 3 = 3, 3x R : x2 + 5 x = 6 = cfw_

UCSD - CSE - 105

CSE 105Instructor: Cynthia LeeSummer 2010FINAL EXAMJuly 30, 2010Instructions and Reminders:Academic Integrity: You must complete this exam for yourself without any assistance. No consultation of notes, books, electronicdevices or other people (exc

UCSD - CSE - 105

Texas State - MC - 3394

Ratings part 3 A new Wrinkle in the Ratings Systemo 90% of all viewing takes place within 7 days of a programs original air date.o How do you measure delayed viewing? And, what are these viewers worth? DVR Penetrationo 45.4% of U.S. TVHH can Time Shi

Texas State - MC - 3394

Katelynn DuaneMgt of Electronic Media3/7/2013Retransmission ConsentTime Warner Cable vs Hearst TelevisionOn July 10, 2012, Hearst Television pulled the plug on Time Warner Cable, resulting in a10 day black out of 13 of Hearsts ABC, NBC and CBS affil

GA Southern - ANTH - 1102

The creators of the PBS film Judgment Day Intelligent Design on Trial have abiased approach of presenting the famous case in Pennsylvania over the controversialissue of whether or not intelligent design should be taught in the classroom over Darwinsthe

GA Southern - ANTH - 1102

ChinaMing-Qing China- last dynasty in the imperialistic dynasty- Ming dynasty was founded in 1368 after the decline of the Mongols- In 1644, the civilization was once again conquered by the nomadic tribalpeople, the Manchus- Qing dynasty: 1644-1911

GA Southern - ANTH - 1102

ClassicalAntiquity:TheArtofAncientGreeceAkhenaton:ChangestheEgyptianreligionandmadeismonotheistic.Aton:thesundiskChangednametoAkhenaton:claimedtobethesonofthegodandalsoaprophet.TryingtospreadthetruewordofgodandmovedthecapitalfromThebestoAkhetatonnamed

GA Southern - ANTH - 1102

The Real Ending to the Kite RunnerThe period is 1995, and Hassan calls Amir. Amir picks up the phone and with ashaky voice utters Hello. Hassan says, If you ever return to Kabul, your faithful friendawaits you. Amir begins sobbing and assures Hassan he

GA Southern - ANTH - 1102

After Muhammad died, there was a succession struggle between Sunni and Shiite Islam.Sunni believed in the four caliphs of Muhammad, the descendants, while Shiite believedonly the fourth caliph, Alis descendants should be worshipped. Ismail claimed himse

GA Southern - ANTH - 1102

Yongle was the third emperor of the Ming dynasty. He sponsored seven maritimeexpeditions and moved the capital from the south (Nanjing) to the north (Bejiing) he alsocompiled the Yonge encyclopedia.Topkapi Japan ad Forbidden CityTopkapi Palacewas the

GA Southern - ANTH - 1102

Martin Luther was a monk that initiated the protestant reform with in 95 thesis in 1517.he was excommunicated. Calvin made the protestant movement an international rebellionagainst Rome. Calvanism is the belief that focuses on works and faith to reach s

GA Southern - ANTH - 1102

The Emergence of the Cities and StatesCivilization: in Anthropology, societies in which large numbers of people living in citiesare socially stratified, and are governed by a state.Early Civilizations: the worlds first cities developed between 4,500 an

GA Southern - ANTH - 1102

The Emergence of the Cities and StatesCivilization: in Anthropology, societies in which large numbers of people living in citiesare socially stratified, and are governed by a state.Early Civilizations: the worlds first cities developed between 4,500 an