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Answer: Determine the surface area of the roof of the

Engineering Mechanics: Statics | 14th Edition | ISBN: 9780133918922 | Authors: Russell C. Hibbeler ISBN: 9780133918922 126

Solution for problem 9-109 Chapter 9

Engineering Mechanics: Statics | 14th Edition

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Engineering Mechanics: Statics | 14th Edition | ISBN: 9780133918922 | Authors: Russell C. Hibbeler

Engineering Mechanics: Statics | 14th Edition

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Problem 9-109

Determine the surface area of the roof of the structure if it is formed by rotating the parabola about the y axis. 16 m y x 16 m y 16 (x2 /16) Prob. 9109

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PAM 2000 McDermott Spring 2016 Prelim 2 Study Guide Lecture and Discussion Notes LECTURE NOTES:  Economics of PATENT LAW o pros: incentivizes innovation o cons: creates monopolies  inefficient market o Stackelberg model and first mover advantage o alternative  shorter patent life  government projects (drug research)  government grants/subsidies o pharmaceutical industry  expensive to generate new drugs  patent: get a monopoly for 20 years o cases  A: with patent, unrestricted  B: no patent  C: with patent but with price regulation  GAME THEORY o John Nash o Prisoners’ Dilemma: a game in which all players have dominant strategies that result in profits (or other payoffs) that are inferior to what they could achieve if they use cooperative strategies  Best response: the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies  Nash equilibrium: a set of strategies such that, when all other players use the best response strategy, no player can obtain a higher payoff by choosing a different strategy  Pure strategy: each player chooses one strategy 100% of the time  assigning a probability of 1 to a single action  action with certainty  no nash equilibrium guaranteed  Mixed strategy: players can choose multiple  nash equilibrium guaranteed  Dominant strategy: the choice preferred by a player regardless of what the other player decides  game is used to talk about cartels and in determining whether players will stick to a collusive agreement  economists argue that self-interested firms will undercut a cartel  for a repeated game this may not be true o Battle of the Sexes: there’s a heteronormative couple who want to do opposite things  pure strategy  multiple Nash equilibria o Dynamic Games  prior games discussed occur where the players move/make a decision simultaneously (no previous certain knowledge about the other players’ actions)  Dynamic Games: players move sequentially or move simultaneously repeatedly over time, so a player has perfect information about the other players’ previous moves  for our purposes, only consider sequentially moving players  extensive form: specifies the n players, the sequence in which they make their moves, the actions they can take at each move, the information that each player has about players’ previous moves, and the payoff function over the possible strategies  the charts used for prior games are called normal form  a subgame:  any node and all the nodes that follow it  usually several subgames  subgame perfect Nash equilibrium: players’ strategies are a Nash equilibrium in every sub game  backward induction:  first determine the best response by the last player to move  next determine the best response for the player who made the next to last move  repeat the process back to the at the beginning of the game  the equilibrium found is technically composed of steps (and so technically not a Nash equilibrium)  credible threat: an announcement that a firm will use a strategy harmful to its rival and that the rival believes because the firm’s strategy is ration in the sense that it is in the firm’s best interest to use it  making a commitment makes a threat more credible  a commitment mechanism: through one, a player is locked into a course of action that one might not otherwise choose but that produces a desired result  reputation matters  The Stackelberg Model  different types of competition exists in imperfect competition: duopoly, oligopoly  sequential with a first mover/first entrant and the other firm(s) following/responding  AUCTION o imperfect information  in the games we discussed earlier, we assumed players knew the payoff functions of the other player(s)  we usually think of these “functions” as values  with an auction players devise bidding strategies without knowing the payoff functions of the other players o auction: a sale in which property or a service is sold to the highest bidder  three key components:  the number of units being sold (typically 1)  the format of the bidding  the value that potential bidders place on the good (privately known)  types of auctions  English o auctioneer starts the bidding at the lowest price that is acceptable to the seller and then repeatedly encourages potential buyers to bid more than the previous highest bidder  Dutch o ends dramatically with the first “bid” o seller starts by asking if anyone wants to buy at a relatively high price o seller reduces the price by given increments until someone accepts the offered price and buys at that price  Sealed Bid o everyone submits a bid simultaneously without seeing anyone else’s bid and the highest bidder wins  First Price Auction: the winner pays its own highest bid  Second Price Auction: the winner pays the amount bid by the second-highest bidder  people will reveal the true value that they are willing to pay for the item  useful for firms trying to extract maximum profit from bidders o objectives of bidder  maximize consumer surplus  the difference between the price they pay and the price they would have been willing to pay o Private vs. Common  private value: how much the good is worth to the bidder  no one else knows this  common value: something like a commodity has a value that is the same for any buyer although the value may not be known  in common value auctions: the winner’s curse o winning bid will often exceed the common value of the good  EDGEWORTH BOXES: (simple economy: two consumers) o market demand has to equal market supply o consumer A and consumer B both have a certain amount of good X and good Y that they can trade o build an Edgeworth Box  given two graphs of the two consumers’ preferences, rotate one of them (consumer B)  corners  the bottom right corner: consumer A has all of good X and B has all of Y  top right: consumer B has all of both goods  dimensions  width: total supply of good X  height: total supply of good Y  their two indifference curves intersect  between the two points of intersection, both consumers are indifferent  points to which both consumers would be willing to trade to: between the two curves  “the eye of the economy”  randomly preset price  excess supply = too expensive  excess demand = too cheap  the length (or width) is the total supply so from the left (or bottom) is consumer A’s demand for X (or Y) and from the right (or the top) is consumer B’s demand for X (or Y) o if the demands don’t add up to precisely the supply then there is a surplus or shortage o equilibrium conditions:  1. quantity supplied=quantity demanded  in all markets  2. (when there is an interior solution and we have 2 consumers): (*as with Cobb-Douglas preferences) MRS1=MRS2  which =px/py  PARETO OPTIMALITY o equilibrium: there are no further possible gains from trade at that point o an allocation is pareto optimal if there is no other allocation which makes at least one agent better off without making any other agent worse off  pareto efficient  there are no more pareto improvements  moving to an allocation which makes at least one person better without harming anyone else o contract curve  the set of several pareto optimal allocations in an Edgeworth Box  with linear preferences:  every point on the bottom and right axis (consumer A’s x axis and consumer B’s y axis) is pareto optimal  the contract curve is a backwards L formed by the two axes o First Welfare Theorem  any competitive equilibrium allocation will be pareto optimal  EXTERNALITIES o externality: the direct effect of actions of a person or firm on another person’s wellbeing or a firm’s production capability rather than indirect effect through changes in prices o negative externality: one that harms o positive externality: one that benefits o externalities make competition inefficient 450  private cost: cost of production only, excluding externalities e  social cost: private cost plus cost of the harms from p externalities p  social marginal cost (MC*): the cost of manufacturing one f A e n more toesof paper to tMC paper firms plus the additional o ps 282 externality damage to people in the community from producing r B this laCtDton of paper e pc 240 $ H , 198 G F g MC 84 p 30 0 Q = 84 Q = 105 225and s c Qo,ns of paper perad o deadweight loss: competitive market equates price with private marginal cost instead of social MC o competitive market: produces excessive negative externalities  optimal amount of pollution is greater than zero o government regulation on pollution  emissions fee: tax on air pollution  effluent charge: tax on discharges into the air or waterways  internalizing the externality: to bear the cost of the harm that one inflicts on others or to capture the benefit that one provides to others o monopoly  monopoly outcome (optimal quantity): may be less than the social optimum even with an externality  also could potentially be over-producing  because its decisions depend on its private marginal costs instead of social marginal costs  at the same time: monopoly tends to under-produce because it sets its price above its marginal cost o markets for pollution  cap and trade system: government gives firms permits each of which confers the right to create a certain amount of pollution  each firm may use its permits or sell them to other firms o public good: nonrival and nonexclusive  special type of externality  free riding: benefiting from the actions of others without paying  ASYMMETRIC INFORMATION o symmetric information: everyone is equally knowledgeable or equally ignorant about prices, product quality and other factors relevant to a transaction o asymmetric information: one party to a transaction has relevant information that another party lacks  hidden characteristics: an attribute of a person or thing that is known to one party but unknown to others  hidden actions: an act by one party to a transaction that is not observed by the other party o opportunistic behavior: one party takes economic advantage of another when circumstances permit o problems  adverse selection: occurs when one party to a transaction possesses information about a hidden characteristic that is unknown to other parties and takes economic advantage of this information  consumers may not make purchases to avoid being exploited by better-informed sellers (reaction)  potential consumer and producer surplus lost  reducing adverse selection o restrict ability of the informed party to take advantage of hidden information o equalize information among the parties  moral hazard: an informed party takes an action that the other party cannot observe and that harms the less informed party o market is efficient when goods go to the people who value them the most o quality  externality: a firm doesn’t completely capture benefits from raising the quality of its product  EFFICIENCY o in markets without perfect information, we have a couple definitions of efficiency  allocation is efficient if it maximizes ex ante expected surplus  before the event  (ex post efficient)  after the event o health insurance example  risk averse consumers (trying to avoid the potential for paying large bills due to sickness)  market is efficient when the healthy are willing to participate in the market (along with the sick)  expected cost  3000 for healthy  9000 for sick  willingness to pay  5000 for healthy  12000 for sick  efficient price 5000  equilibrium price at 50% sick 12000  expected cost = 6000, so healthy won’t pay  so charge max that the sick will pay  check the net profit given the consumers’ percentages  inefficient  equilibrium price at 20% sick 5000  expected cost = 4200  charging at max the healthy will pay gives the firm a profit o net surplus is always the same between 4200 and 5000, whether the consumers or the firm has it  efficient  cut off value in percentage  9000x + (1-x)(3000) = 5000  33.333% o equalizing information  Screening: an action taken by an uninformed person to determine the information possessed by informed people  nonlinear wages (weed out workers who don’t want to work as hard)  signaling: an action taken by an informed person to send information to an uninformed person o third-party information  standard: a metric or scale for evaluating the quality of a particular product  certification: a report that a particular product meets or exceeds a given standard o Cheap talk: unsubstantiated claims or statements  informed person voluntarily provides information to an uninformed person o efficiency  total social output falls with signaling if signaling is socially unproductive but may rise if signaling if signaling also raises productivity or serves some other desirable purpose DISCUSSION NOTES:  EDGEWORTH BOXES o o  AUCTIONS Type Optimal Strategy English Bid your true value Dutch Bid at something less than your true value First Price Sealed Auction Bid your true value Second Price Sealed Auction Bid at something less than your true value   ASYMMETRIC INFORMATION o Q1. Apples are high (H) or low (L) quality. Buyers don’t know beforehand. Buyers value H at $3 and L at $2. Sellers’ reservation prices are H at $2.5 and L at $1.5 o (a) 60% are H. Describe equilibrium.  from buyer’s perspective:  EV = .6 ($3) + (1-.6)($2) = $2.6  $2.6 > $2.5 so market is efficient o (b) 20% are H. Describe equilibrium.  from buyer’s perspective:  EV = .2 ($3) + (1-.2)($2) = $2.2  $2.2 < $2.5 so market is inefficient  sellers won’t sell the high quality apples o (c) 0% are H. Describe equilibrium.  from buyer’s perspective:  EV = .0 ($3) + (1-.0)($2) = $2  $2 < $2.5  sellers won’t sell their high quality apples BUT they have none to sell so  market is efficient o (d) What % of H result in market efficiency  EV = x($3) + (1-x)($2) = $2.5  3x + 2 – 2x = 2.5  x= .5  % ≥ 50% or = 0% o (e) If inefficient, what can governments do  subsidize, regulate information, market  EXTERNALITY o Q2. Firm sells immunizations for a contagious disease. o (a) Is this positive/negative externality Why  Positive. Herd immunity. o (b) Draw a fully labeled graph.  There is one MC curve because the positive externality doesn’t effect the price  MB = consumer’s benefit  MB = society’s benefits S  deadweight loss where MC < MB   PRACTICE (similar example to HW3 problems) o Q1.  Andy: u(b,w) = 3b + w 1/21/2  Bob: u = b w  MU = (b -1w )/2 b 1/2 -1/2  MU =w(b w )/2  Initial endowment: Andy has 9 beers, Bob has 9 wines o (a) Sketch and label Edgeworth Box   C: equilibrium allocation  D: initial endowment o (b) Optimality conditions  MRS =AMRS = p Bp b w  MRS =A3  MRS B = MU /bU = w/b  3 = w/b = p /b w o (c) Solve equilibrium allocation.  MRS =Bp /pb w  w/b = 3 w = 3b p = 3p b w  M = bp +bwp w M B 9 x p w  9p w p (ww + p (bb  9p w p (3w) + 3p (b)w  9 = 6b b = 1.5 w = 3b = 4.5  Bob: b = 1.5, w= 4.5  Andy: b = 7.5, w = 4.5  because he gave 1.5 to Bob and Bob gave him 4.5 o Q2. Chris is sole producer of drug  P = 880 – 40q  MR = 800 – 80q  MC = 80 + 10q o (a) Equilibrium  MR = MC  800 – 80q = 80 + 10q  q = 8  P = 880 – 40(8) = $560 o (b) Competitors enter. New equilibrium  P = MC  880 – 40q = 80 + 10q  q = 16  P = 880 – 40(16) = $240

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Chapter 9, Problem 9-109 is Solved
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Textbook: Engineering Mechanics: Statics
Edition: 14
Author: Russell C. Hibbeler
ISBN: 9780133918922

Since the solution to 9-109 from 9 chapter was answered, more than 254 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 9-109 from chapter: 9 was answered by , our top Engineering and Tech solution expert on 11/10/17, 05:25PM. Engineering Mechanics: Statics was written by and is associated to the ISBN: 9780133918922. The answer to “Determine the surface area of the roof of the structure if it is formed by rotating the parabola about the y axis. 16 m y x 16 m y 16 (x2 /16) Prob. 9109” is broken down into a number of easy to follow steps, and 34 words. This textbook survival guide was created for the textbook: Engineering Mechanics: Statics, edition: 14. This full solution covers the following key subjects: area, axis, determine, formed, parabola. This expansive textbook survival guide covers 11 chapters, and 1136 solutions.

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