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F2008final_sols_001

Course: ECON 171, Fall 2009
School: UCSB
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Word Count: 2230

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171 Econ Fall 2008 Final Exam - Solutions December 10 You have three hours to take this exam. Please answer all questions. Each question is worth 15 points, with the exception of number 3, which is worth 10 points. Point subtotals are in brackets. To obtain credit, you must provide arguments or work to support your answer. 1. [15] Find all Nash equilibria of the following game. L 3, 2 2, 0 1, 1 T M B M 4, 0 3,...

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University of Florida - MAC - 2233
UCSB - ECON - 171
Econ 171 Fall 2008Final Exam - SolutionsDecember 10You have three hours to take this exam. Please answer all questions. Each question is worth15 points, with the exception of number 3, which is worth 10 points. Point subtotals are inbrackets. To obta
University of Florida - MAC - 2233
University of Florida - MAC - 2233
MAC 2233 Calendar Summer C 2010MondayTuesday1011L1, L2Wednesday121718132025L10311NO CLASS78L15, L161415L19L8, L92627EXAM 12356HOLIDAY1213L26, L271920L29, L302627L33, L342REVIEW910EXAM 411L16, L17L18, QUIZ16
UCSB - ECON - 171
Handout on Normal Form GamesEcon 171 Spring 2010Player 2CD2, 20, 33, 01, 1Player 1 CDa)Game a) is typically called. The solution concept we apply (today) to solve it is calledGames that we can solve this way, i.e. for which we can derive a u
University of Florida - MAC - 2233
MAC 2233 CalendarSummer B 2008MondayJune 30L1&amp;L27L8&amp;L914L15&amp;L1621L21&amp;L2228ReviewTest 3*4L34&amp;L35TuesdayJuly 1L3&amp;L48ReviewTest 1*15Wednesday Thursday Friday234L4 &amp; L59HOLIDAY:NO CLASSL6 &amp;L71011L10&amp;L1116ReviewL17&amp;L18Test
UCSB - ECON - 171
Handout on Normal Form GamesEcon 171 Fall 2008Player 1Player 2CD2, 20, 33, 01, 1CDa)Game a) is typically called. The solution concept we apply (today) to solve it is calledGames that we can solve this way, i.e. for which we can derive a uni
University of Florida - MAC - 2233
MAC 2233Student GuideSUMMER A 2007INTRODUCTIONCOURSE CONTENT MAC 2233 is the first in the two-semester sequence MAC 2233and MAC 2234 covering the basic calculus. The content of this course is given on a dayby day basis in the lecture outline in this
UCSB - ECON - 171
Econ 171 Spring 2010Bayesian Games &amp; Incomplete InformationIn-class game: variant of BoS (w/ incomplete information)Consider a variant of BoS in which Player 1 is unsure whether Player 2 wantsto go out with her or avoid her, and thinks that these two
University of Florida - MAC - 2233
MAC 2233Student GuideSUMMER A 2009INTRODUCTIONCOURSE CONTENT MAC 2233 is the first in the two-semester sequence MAC 2233and MAC 2234 covering the basic calculus. The content of this course is given on a dayby day basis in the lecture outline in this
University of Florida - MAC - 2233
Project 1MAC 22331. What do we call the set of all points whose distance from the point ( h, k ) is r? Derive anequation for the graph using distance formula.Rewrite the following equations of circles by completing squares, draw the graphs, and label
UCSB - ECON - 171
Econ 171 Spring 2010Notes for Lecture 2April 1Note: we will begin class by playing some in-class games and by continuing to go through theHandout on Normal Form GamesOverviewIn these notes we will continue looking at games in the normal (or strategi
University of Florida - MAC - 2233
Project 2MAC 22331. Suppose that at the base of a mountain range, the diversity of an insect species (measured inaverage number of species N per acre) depends linearly upon the elevation E in hundreds offeet below sea level according to the equation N
UCSB - ECON - 171
Lecture 4: Nash EquilibriumEcon 171 Spring 2010OverviewNash equilibrium Mixed-strategy Nash equilibrium1Nash EquilibriumBegin with threeACX4, 04, 2games that are not dominance solvable:22Y0, 24, 0O2, 10, 0OBB0, 01, 2H1, 11, 1H
University of Florida - MAC - 2233
Project 3MAC 22331. Examine the function f (x) = 4 | 2 x | .Write f (x) as a piecewise function without absolute value bars, using the denition of absolute value, and graph the function on the axes below:f (x) =Graph the function f (x) again, this ti
UCSB - ECON - 171
Econ 171 Spring 2010Notes on Applications of Nash Equilibrium1April 16OverviewThese notes explore some applications of Nash equilibrium and are intended to supplementChapter 10 of Watson. The rst section presents an extension of the Cournot and Bertr
University of Florida - MAC - 2233
Project 3MAC 22331. Examine the function.Writeas a piecewise function without absolute value bars, using the denition of absolute value, and graph the function on the axes below:Graph the functionagain, this time in a series of steps, beginning wit
University of Florida - MAC - 2233
Project 4MAC 22331. Consider the functions:f ( x) = x2g (x) =1 x2h(x) =xWrite a simplied formula for the function k = f + g g give its domain in interval notation.h(x) = 1; Domain: [ 1, 1 ]Write a simplied formula for the function k = (f + g ) h
UCSB - ECON - 171
Econ 171 Fall 2008Practice Questions &amp; Solutions - Part III: Perfect Bayesian EquilibriumPerfect Bayesian equilibrium practice questions with solutions below:28.2, 28.3, 29.1, 29.3, 29.428.2 (a) No.(b) Yes. The strategy prole is (AA , Y ), with belie
University of Florida - MAC - 2233
Project 5MAC 22331. An apartment complex contains 50 one-bedroom apartments. Whern rent is set at \$550 permonth, all the units will be occupied. Each \$30 increase in rent results in an average of twoless units occupied. Each occupied unit requires an
UCSB - ECON - 171
Econ 171 Spring 2010Some student questions about PS1 and my responsesProblem 4)Student question omitted. Here is the response, though:You are right that there are no PSNE, but there still can be MSNE. It is a good idea tolook for dominated strategies
University of Florida - MAC - 2233
Project 6MAC 22331. Examine the piecewise-dened function below, and sketch the graph carefully on the axes:g (x) =2 1+x0 2 1x1x&lt;0x=00&lt;x&lt;1x&gt;1Evaluate the following limits:lim g (x) = lim g (x) = 1x0x0+lim g (x) = 1lim g (x) = 1x1x1+2
UCSB - ECON - 171
Econ 171 Spring 2010Problem Set 1Due April 13Important: hand in only the two-star problems. (Read the syllabus for the meaning of onestar, two-star, etc.) The notation a.b denotes problem number b from Chapter a inWatson.* Problem 1(a) Create a larg
University of Florida - MAC - 2233
Project 7MAC 22336x1x.1. Write the domain of f (x) =4xxRewrite f (x) as a simplied rational function in lowest terms. Include the restrictions on thedomain. Then, using a number line, nd the intervals on which f (x) is positive and thoseinterva
University of Florida - MAC - 2233
Project 7MAC 22336x1x.1. Write the domain of f (x) =4xxx = 0, 2Rewrite f (x) as a simplied rational function in lowest terms. Include the restrictions on thedomain. Then, using a number line, nd the intervals on which f (x) is positive and thos
UCSB - ECON - 171
Econ 171 Spring 2010Problem Set 1Solutions to the two-star ProblemsIn some cases Ive provided more explanation than was asked of you.* Problem 3Find the rationalizable strategies for this game. For each iteration, list the eliminatedABCW5, 64,
University of Florida - MAC - 2233
Project 8MAC 2233x2 x 24x2 2x31. Examine the function: f (x) =a) What type of function is this? What is the domain of the function? What are its discontinuities?rational function; discontinuities at x = 0, 2b) Evaluate the right and left limits at
UCSB - ECON - 171
Econ 171 Spring 2010Problem Set 2Due May 6Important: hand in only the two-star problems. The notation a.b denotes problem numberb from Chapter a in Watson.* Problem 11LR2ab0, 0Figure 1: An extensive gameIn the game in Figure 1, solve for the
University of Florida - MAC - 2233
Project 9MAC 22331. Consider the following piecewise dened function for various choices of constants p and q .Sketch its graph in the case that p = q = 1. px &lt; 1x2x = 1f (x) = 2x1 &lt; x &lt; 2x+qx2Determine whether f (x) is continuous at x = 1, x
University of Florida - MAC - 2233
Project 10MAC 22331. A farmer keeps a small private orchard with apple trees. Suppose the total yield Y (numberof healthy apples) is a function of the number of trees planted p given by Y (p) = 120p 7p2 .Graph Y (p) below.Use the denition of the deri
UCSB - ECON - 171
Econ 171 Spring 2010Problem Set 3Due Tuesday, June 1Important: hand in only the two-star problems. There are no one-star problems on thisproblem set. The notation a.b denotes problem number b from Chapter a in Watson.* Problem 1Consider a two-player
University of Florida - MAC - 2233
Project 11MAC 2233In this project, we explore the average and instantaneous rates of change of total cost, total revenue, and total prot with respect to the number x of items produced/sold. In particular, note theinterpretations of the calculations, an
UCSB - ECON - 171
Econ 171 Spring 2010Problem Set 3 - SolutionsDue Tuesday, June 1Important: hand in only the two-star problems. There are no one-star problems on thisproblem set. The notation a.b denotes problem number b from Chapter a in Watson.* Problem 1Consider
University of Florida - MAC - 2233
Project 11MAC 2233In this project, we explore the average and instantaneous rates of change of total cost, total revenue, and total prot with respect to the number x of items produced/sold. In particular, note theinterpretations of the calculations, an
University of Florida - MAC - 2233
Project 12MAC 22331. Examine the function f (x) = x3 3x. From precalculus, what should be the two distinctpossibilities for the number of turning points of any cubic (degree 3) polynomial function?In order for a smooth graph to turn around, what value
UCSB - ECON - 171
Econ 171 (Grossman) Spring 2010Exam 1April 20You have 75 minutes to take this exam. Please answer all 6 questions, each of which is worth5 points. Point subtotals are indicated. Show your work to obtain full credit.Part 1 4 questions, 20 points (5 ea
University of Florida - MAC - 2233
Project 13/14MAC 22331. An underwater pipe begins to leak oil that spreads outward in the shape of an expandingsphere. Recall that the volume of a sphere is V = 4 r3 , where r is the length of its radius.3Suppose the company that owns the pipe takes
UCSB - ECON - 171
Econ 171 (Grossman) Spring 2010Exam 1April 20You have 75 minutes to take this exam. Please answer all 6 questions, each of which is worth5 points. Point subtotals are indicated. Show your work to obtain full credit.Part 1 4 questions, 20 points (5 ea
University of Florida - MAC - 2233
Project 15MAC 22331. One model that is used for an agricultural yield Y bushels (in thousands) as a function of soilNnitrogen level N points is Y (N ) =.1 + N2Calculate Y (N ) and Y (N ). Give the units for each.Y (N ) =Y (N ) =1 N2(1 + N 2 )2
University of Florida - MAC - 2233
Project 16MAC 22331. Suppose the daily supply x of a certain product in an open-air market is related to the unitprice p (in dollars) by the equation 100p2 + 10xp = x2 + 500.Calculatedximplicitly. What rate of change does it represent?dpFind all t
UCSB - ECON - 171
NAME:Econ 171 (Grossman) Spring 2010Exam 2 SolutionsMay 13You have 75 minutes to take this exam. Please answer all 4 questions, each of which is worth15 points. Point subtotals are indicated. Show your work to obtain full credit.1. Consider the exte
University of Florida - MAC - 2233
Project 17/18MAC 22331. The idea of a differential is pretty simple if you can get past the notation. Consider the following problem: Suppose the value (in dollars) of some electronic equipment t years from1600now is given by V (t) = 400 +.1 + t2Fi
UCSB - ECON - 171
NAME:Econ 171 (Grossman) Spring 2010Exam 2May 13You have 75 minutes to take this exam. Please answer all 4 questions, each of which is worth15 points. Point subtotals are indicated. Show your work to obtain full credit.1. Consider the extensive-form
University of Florida - MAC - 2233
Project 17/18MAC 22331. The idea of a differential is pretty simple if you can get past the notation. Consider the following problem: Suppose the value (in dollars) of some electronic equipment t years from1600now is given by V (t) = 400 +.1 + t2Fi
UCSB - ECON - 171
Econ 171 Spring 2010Final ExamJune 8You have three hours to take this exam. Please answer all 5 questions, for a maximum of100 points. Point totals and subtotals are indicated in brackets. To obtain credit, you mustprovide arguments or work to suppor
University of Florida - MAC - 2233
Project 19MAC 223321. Examine the function h(x) = x 3x 3 . What is the domain of h(x) ? What are its intercepts?Calculate h (x), and use a number line to determine the interval(s) on which the function isincreasing/decreasing.What are the local extr
University of Florida - MAC - 2233
Project 20/21MAC 22331. Note that the information learned in this lecture should prepare you for curve sketching!Recall this function from a prior project:2f (x) = 3x( 7 x2 ) 3f (x) =7(3 x2 )(7 x2)13f (x) =28x( 9 x2 )43( 7 x2 ) 3(Again, i
UCSB - ECON - 171
Econ 171 Spring 2010Final ExamJune 8You have three hours to take this exam. Please answer all 5 questions, for a maximum of100 points. Point totals and subtotals are indicated in brackets. To obtain credit, you mustprovide arguments or work to suppor
University of Florida - MAC - 2233
Project 22/23MAC 22331. Examine the function h(x) =27x2. What is its domain ?x (x + 1)3Determine the horizontal asymptotes and vertical asymptotes, if any, for the graph of h(x) .Does the function have any removable discontinuities?What are the in
UCSB - ECON - 171
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University of Florida - MAC - 2233
Project 22/23MAC 22331. Examine the function h(x) =27x2. What is its domain ? x = 0, 1x (x + 1)3Determine the horizontal asymptotes and vertical asymptotes, if any, for the graph of h(x) .Does the function have any removable discontinuities?27xan
UCSB - ECON - 171
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University of Florida - MAC - 2233
Project 24MAC 22331. (From lecture) You are required to construct a closed rectangular box with a surface area of 48square feet so that the length is twice the width. What dimensions will maximize the volumeof the box?2. Sketch the graph of the funct
University of Florida - MAC - 2233
Project 24MAC 22331. (From lecture) You are required to construct a closed rectangular box with a surface area of 48square feet so that the length is twice the width. What dimensions will maximize the volumeof the box?Max volume when width is 2, leng
UCSB - ECON - 177
Professor GarrattEconomics 177AuctionsMW 11:00-12:15, 387 103www.econ.ucsb.edu/~garratt/Econ177Auctions have been used to allocate goods for thousands of years, but in the past 25 years there hasbeen a surge in popularity. Auctions are now routinely
University of Florida - MAC - 2233
Project 25/26MAC 22331. Carefully sketch the graph of f (x) = 4 + e(x2) below , including any intercepts and asymptotal lines, AND state its domain and range in interval notation.Domain:Range:Formula: g (x)=Now suppose g (x) is the function obtained
UCSB - ECON - 177
Cummulative Distribution Function of Bids for All Pay AuctionSpring 2011100.00%90.00%80.00%70.00%60.00%2 bidders5 bidders10 bidders50.00%40.00%30.00%20.00%10.00%0.00%05101520253035404550Bid556065707580859095100
University of Florida - MAC - 2233
Project 28MAC 22331. A population of wolves increases so that the number of wolves x years from now is given bythe function W (x) = 200(1 ex ). Calculate W (x).At what rate does the population change after 1 year? 3 years? (Include units and round to
UCSB - ECON - 177
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University of Florida - MAC - 2233
Project 29MAC 22331. Examine the function h(x) =3 ln(x). What are its domain and intercepts ?xCalculate h (x), and h (x) . Use a number line to determine the interval(s) on which thefunction is increasing/decreasing, concave up/down. Are there any
UCSB - ECON - 177
Assignment 2: Econ 177Professor GarrattConsider the following two payment options:Scenario A: A gamble that pays \$100 with probability p and \$0 with probability (1-p).Scenario B: A payment of \$x with probability 1.In the table below, for each cash am