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Course: MAC 2233, Spring 2011
School: University of Florida
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11 MAC Project 2233 In 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 the interpretations of the calculations, and how they might impact important decisions. 1. Suppose the total cost C (x) of producing x books is C (x) = 1200 + x2 20x, represented by \$1200 in storage...

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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
Class InfoGame TheoryNormal Form GamesEcon 171 Spring 2010Class 1 - March 30, 2010Index cards: Name, pronunciation, perm no.,major, nativelanguage, Math background, Reason for interest in class,Economics is. . .Web: http:/econ.ucsb.edu/~grossman/E
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
Introduction to Game TheoryEconomics 171 - Spring 2010SyllabusInstructor:Zack Grossmangrossman[at]econ.ucsb.eduOffice: NH 3049Office Hours: R 12:30-1:30Course Homepage: http:/econ.ucsb.edu/~grossman/Econ171S10Lectures: TR 2 3:15, PHELPS 1260Cour
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
Assignment 1: Econ 177Professor GarrattYour assignment is to estimate your own private bid functions that characterize your biddingbehavior in the 2-bidder and 5-bidder first- and second price auctions. We will only consider thecase of no entry fee an
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
University of Florida - MAC - 2233
Project 29MAC 22331. Examine the function h(x) =3 ln(x). What are its domain and intercepts ?xDomain x &gt; 0;intercept ( 1, 0 )Calculate h (x), and h (x) . Use a number line to determine the interval(s) on which thefunction is increasing/decreasing
UCSB - ECON - 177
Suboptimal Bidding and Profits in 2-Bidder First-Price Auction with \$25 Entry Fee4030Dollars2010012345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40-10-20RoundAverage deviation from equ
University of Florida - MAC - 2233
Project 30MAC 22331. Suppose that the number of worldwide users of a certain internet service is growing exponentially. Suppose that, after assessing the data, there were 100 million users originally, and140 million users at the end of the second year.
UCSB - ECON - 177
Chapter 12AppendixBelow are brief descriptions and instructions for the experiments used in thiscourse. In each instance I use the following notation:v = your valueb = your bidB = the highest bid among everyone elser = reserve pricec = entry feeE
University of Florida - MAC - 2233
Project 31MAC 22331. Recall the formula and graph for the logistic function; note that one example is the function100P (t) =. Where does the inection point for the graph occur?1 + 2e0.2tNow sketch the function P (t) on the axes above. Include the i
UCSB - ECON - 177
Auction Theory With ExperimentsbyRodney J. Garratt1April 7, 20111 Departmentof Economics, University of California at Santa Barbara, garratt@econ.ucsb.edu.2OverviewThe goal of this text, its supplement, and software is to provide a meansof teachi
University of Florida - MAC - 2233
Project 32/33MAC 22331. Evaluate each of the following integrals using a basic substitution.8x3dx4 3x43x2 e2x dx1exdx4x21 + 2 ln(x)dx4x2. Demonstrate that F (u) = (u 1)eu is an antiderivative for the function f (u) = ueu .Use the substitut
UCSB - ECON - 177
Entry Decisions in 2-Bidder First-Price Auction with \$25 Entry Fee10.90.80.7Percent0.60.50.40.30.20.1012345678910 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40RoundPercent correct entryP
University of Florida - MAC - 2233
Project 32/33MAC 22331. Evaluate each of the following integrals using a basic substitution.8x3dx4 3x43x2 e2x dxeach of these can be fairly easilyby taking the derivative of your answer1exdx4x21 + 2 ln(x)dx4x2. Demonstrate that F (u) = (u
UCSB - ECON - 177
FPA 2-bidder Spring 2011100Bids outside target range: 13Percent outside target: 0.056522Intercept 0.2717 s.e.: 1.3539Slope: 0.7812 s.e.: 0.012349080Average revenue:Average earnings:7062.92565Highest earnings: 124.84 Subject: 7560Bids52.4174
University of Florida - MAC - 2233
Project 34/35MAC 22331. Examine the parabolic arch formed by the function f (x) = 3x 1 x2 on [ 0, 6 ] . We would2like to approximate its area using rectangles.Sketch the parabola below on [ 0, 6 ] and shade the area beneath it.Now for some approxima
UCSB - ECON - 177
FPA 5-bidder Spring 2011100Bids outside target range: 14Percent outside target: 0.06087Intercept -0.4221 s.e.: 0.7361Slope: 0.8983 s.e.: 0.0139080Average revenue:74.7235170Bids605040302010001020304050Values60708090100
University of Florida - MAC - 2233
MAC 2233 Quiz 1 Solutions1. Find the equation of the line that passes through the point (2, 4) and is perpendicularto the line 3x + 4y 22 = 0.SOLUTION Solve the given equation for y to identify the slope of the given line.The slope of the given line i
UCSB - ECON - 177
Introduction to Auction TheoryEcon 177Spring 2011Introduction: A Historical PerspectiveHerodotus reports that auction were used in Babylon as early as 500B.C.193 A.D. the Pretorian Guard sold the Roman Empire by means ofan auctionWide array of com
University of Florida - MAC - 2233
MAC 2233 Quiz 2 SolutionsJune 5, 20091. Let f be a function which is dierentiable at a point x. Write the limit denition of f (x),the derivative of f at x.Solution: limx0f (x+h)f (x)h2. (a) Write the power rule for the dierentiating the function f
University of Florida - MAC - 2233
MAC 2233 Quiz 3 SolutionsJune 12, 20091. Let f be a function which is dierentiable at a point x. Write the limit denition off (x), the derivative of f at x.Solution: limx0f (x+h)f (x)h2. Find and simplify f (x) if f (x) =Solution: f (x) = 3x+3 3
UCSB - ECON - 177
Getting StartedWe seek a theory of bidding behavior in auctions.Our theory will attempt to explain how peoples bids are related to theirindividual valuations, or simply values, for the item being auctioned.In mathematical terminology, we want a mappin
University of Florida - MAC - 2233
MAC 2233 Quiz 4 SolutionsJuly 1, 2009You must show all work to receive credit1. Let f (x) = 3x4 6x3 + x 8. Find the open intervals where f is concave down.Solution It suces to nd all open intervals where f (x) &lt; 0.Begin by computing f and f . We have
UCSB - ECON - 177
Bidding BehaviorWe assume people attempt to maximize their payo from participating inan auction.Hence, we are in a sense trying to determine their optimal bids.However, an auction is a game in which the payo an individual earnsfrom any given bid depe
University of Florida - MAC - 2233
MAC 2233 Quiz 5May 10, 20091. Let f (x) = 3x4 + 8x3 . Find all absolute extrema of f on the interval [1, 1].Solution: First, nd the critical points of f that are in the given interval:f (x) = 12x3 + 24x2= 12x2 (x + 2)so the critical points are x = 0
UCSB - ECON - 177
Expected RevenueHere we calculate the expected revenue under the ecient equilibriumbidding strategies for the rst- and second-price auction formats.In a rst-price auction with F () uniform on [0,100], the symmetricequilibrium bidding strategy has each
University of Florida - MAC - 2233
MAC 2233 Quiz 6 SolutionsJuly 24, 20091. Let f (x) = (x 1)e3x+2 . Determine the intervals where f is increasing.Solution: We want to determine where f &gt; 0. First, nd f :f (x) = 1 e3x+2 + (x 1) 3 e3x+2= e3x+2 (1 + 3(x 1)= e3x+2 (3x 2).22Since e3x+
University of Florida - MAC - 2233
UCSB - ECON - 177
Professor Rod GarrattECON 177MidtermApril 27, 2011The exam is worth a total of 30 points. You have 1 hour and 15 minutes to complete thisexam. Good Luck!In all the questions that follow you may assume each of the i=1,.,n bidders' values aredrawn in
University of Florida - MAC - 2233
MAC 2233 Review Worksheet Answers1. a. 5/8 grams1. b. 20 years2. m = 7/23.x 8 x 4 ln xC4.23/ 2 x 1 2 x 1 C35.1C3x3 e 3x 6.13/ 2ln4x 2 x 2C217. e x 2C8.ln 229. 838 fish10. 56/9
UCSB - ECON - 177
Discrete BidsAverage Bid if saw 0: 1.364Average Bid if saw 3: 2.73Average Profit = .462 millionNumber positive = 6, Number negative = 4, Number zero = 3Continuous BidsAverage Bid if saw 0: 1.316Average Bid if saw 3: 2.605Average Profit = .649 mill
University of Florida - MAC - 2233
MAC2233 Chapter 2 Review1. For the function f (x) = x2 3x 4 state the domain and evaluate thefunction at x = 1, 0, a + h.2. For the function y = t2 +1 2 state its domain as well as the dependenttand independent variables and evaluate the function at
UCSB - ECON - 177
PDFs for Revenue of First- and Second-Price Auctions (2-bidders)10.90.8Probability0.70.60.50.40.30.20.10051015202530354045505560Revenue1st price2nd price65707580859095100
University of Florida - MAC - 2233
MAC2233 Chapter 3 Review1. Find the derivative of h(x) = (x 2)(2x + 3).2. Find the derivative of f (t) = 3t4 2 + t5 .2t24x3. Find the derivative of f (x) = 3x x+2+2 .22t4. Find the equation of the tangent line to y = t4 3+2+1 at t = 0.t25. Th
University of Florida - MAC - 2233
MAC2233 Chapter 4 Review1. Find the intervals where the function g (t) = t22t is decreasing and+1increasing.2. Use the First Derivative Test to nd the relative extrema of the function f (x) = x3 3x2 .3. Sales in the Web-hosting industry are projected
UCSB - ECON - 177
Popcorn Experimentslope 2 bidder = .802 s.e. = 0.061slope 27 bidder = .834 s.e. = .08400030002000100000100020003000guess27bidderPredicted 27bidderPredicted 2bidder2bidder4000
University of Florida - MAC - 2233
MAC2233 Chapter 5 Review1. Evaluate 23/4 43/2 .2. Simplify the expression x3/5 x8/3 .3. Solve the following equation for x: 5x2 3= 51x .24. Jada deposited an amount of money in a bank 5 years ago. If the bankhad been paying interest at the rate of
UCSB - ECON - 177
2 Bidder, V=0 and V=3060Average Reserve5040V=0V=303020100123456789 10 11 12 13 14 15 16 17 18 19 20Round
University of Florida - MAC - 2233
MAC2233 Chapter 6 Review1. Find the indenite integral7x3 dx.2. Find the indenite integral6 x 9x2 + 5ex dx.3. Find the indenite integral2x2 7dx.x34. Find the indenite integral(x + 2)3 dx.5. Given f (x) = ex 2x and f (0) = 2, nd f (x).6. Find th