Ch02-10e-lecture
LEC02_PT1_CH04-round-offandtruncationerrors
LECTURE 2 -1MAE3100Prof. D.E. SmithLECTURE 2Round-Off and Truncation ErrorsMotivation:Understanding the concept of error and how it develops in numerical methods is important to the effective use of computer techniques.This study focuses on two major forms of numerical error: Round-offError and Truncation Error.Reading Assignment:Chapra Chapter 4 (required)Chapra and Canale Section 4.1 (optional)LECTURE 2 -2MAE3100Prof. D.E. SmithLECTURE 2 OBJECTIVESThe primary objective of this lecture is to provide a basicunderstanding of computational errors introduced bynumerical methods. More specifically, this lecture will:•Expose potential sources of computational errors.•Compare accuracy and precision.•Review numerical precision associated with digitalcomputing.•Provide specific calculations for evaluating error estimates.•Provide a means for estimating truncation error using theTaylor series.•Explore finite difference approximations for first and secondderivatives.MAE3100Prof. D.E. SmithLECTURE 2 -3You’ve Got A Problem•The numerical methods solution to the bungee jumper problem inChapter 1 employed an approximation to the derivative as•What is known?–Numerical error is introduced byapproximation–Approximation error depends on t–Computers have limited precision•What is needed?– A basic understanding of errors associated with computercalculations– A method for assessing the amount of error introduced withthe approximations used by numerical methodsii i i t t t v t v t v dt dv 11)()(MAE3100Prof. D.E. SmithLECTURE 2 -4Sources of Error•Errors in mathematical modelingResult from simplifying assumptions and approximations madewhen representing physical systems by mathematical equations.•BlundersResult from mathematical modeling errors and/or programmingerrors.•Errors in inputBEWARE: garbage in –garbage out•Machine errorsResult from rounding, chopping, underflow and overflow•Truncation errorsResult from simplifying assumptions and approximations madein the numerical procedureOccurs when truncating an infinite series or numericalevaluation of an improper integral. E.g.,!4!3!21432x x x x e xMAE3100Prof. D.E. SmithLECTURE 2 -5Accuracy and Precisiondata scatterdefinesimprecisionoruncertaintysystematic deviation defines inaccuracy or bias inaccurateandimpreciseaccurateandprecise MAE3100Prof. D.E. SmithLECTURE 2 -6Significant Figures•The significant digits of a number are those that can be used withconfidence.•What is the speed?–48 or 49?–48.8 or 48.9?–48.8642138?–#sig-figs = 3•What is the mileage?–87324.4 or 87324.5?–87324.46?–#sig-figs = 7•All results in MAE3100 must display appropriate units and Sig-Figs–Use no less than 3 sig-figs, 4 is preferred–Use the greatest accuracy possible during calculations–Report result with sig-figs consistent with inputMAE3100Prof. D.E. SmithLECTURE 2 -7Error Definitions•True (Absolute) ErrorNote: Issues arise when working with different orders-of-magnitude•True Percent Relative Error•Approximate Percent Relative Error (true value not always known)• A specified percent tolerance s may be used as a stopping criteria:I.e., stop with n decimal place accuracy when ionapproximat value true t E (100%) value true ionapproximat - value true (100%) value true error true t %)100(ion approximat current ionapproximat previous -ion approximat current (100%)ion approximat errore approximat a )%105.0(2n s a MAE3100Prof. D.E. SmithLECTURE 2 -8Round-Off Error•Recall that numbers are stored in binary format–16 bit integer representationRange: -32,768 to 32,767Shown: -173–Floating point representation•Single precision (32 bit)24 bit mantissa7-8 sig-figs Range: 10-38to 1039•Double precision (64 bit)15-16 sig-figsRange: 10-308to 10308Representation used by MATLAB (223210)272625242330292831….sMAE3100Prof. D.E. SmithLECTURE 2 -9Working with Computer Numbers•Computers work in base 2 making it impossible to accuratelyrepresent numbers of interest, e.g.,•MATLAB commands related to machine precision include realmax ,realmin , eps•Round-off errors can accumulate in large computations.•Loss of significant figures occurs when subtracting numbers ofsimilar magnitude:•Small numbers can be lost when added to large numbers using finitemachine precision 333100001.0107641.0107642.0...,7,,,1.0etc e 4444104000.010*******.010*******.0104000.0chopped MAE3100Prof. D.E. SmithLECTURE 2 -10Truncation Error•Taylor theorem : Any smooth function can be written as a polynomial.•Definition: The Taylor Series expansion of f (x )about x = a iswhere the remainder is•The n -th order Taylor Series with h = x –a becomes:• A Maclaurin Series is a Taylor Series expanded about a = 0 (h = x )nk nk k R a x a f k x f 0)()()(!1)(n -th order Taylor Series approximation f n (x )remainder))(()()()!1(111)1(n n n n a x O a x f n R x a nn n hn a f h a f h a f h a f a f h f !)(!3)(!2)()()()()(3)3(2 nn n xn f x f x f x f f x f !)0(!3)0(!2)0()0()0()()(3)3(2 error is ‘on the order of’(x -a )n +1a x XI (ks-eye)MAE3100Prof. D.E. SmithLECTURE 2 -11Truncation Error (cont.)•Accuracy increases as more terms are added to the Taylor Series expansionconstant)a (i.e., 0a function)linear a (i.e., 10h a a )polynomial order 2nd a (i.e.,2210h a h a a MAE3100Prof. D.E. SmithLECTURE 2 -12Taylor Series ExampleFrom Chapra Figure 4.2, pg. 68:Where) (i.e., 0about Expanded 2.125.05.015.01.0)(234x a x h a x x x x x f 0.1)0(25.0)0(2.1)0(f f f xx f 25.02.1)(1225.025.02.1)(x x x f 2.1)(0x fMAE3100Prof. D.E. SmithLECTURE 2 -13Taylor Series -ExampleDetermine the 4-th order Taylor Series of y (x ) = ln(1+x )about x = a = 0By successive differentiation we obtainThe Taylor Series for |x |≤ 1becomes:Note: The error is proportional to x 5: i.e., when x is reduced by afactor of 2, R 4decreases by a factor of 25= 32)1ln()(x x y 0)0(y x x y 11)(1)0(y 2)1(1)(x x y 1)0(y 3)3()1(2)(x x y 2)0()3(y 4)4()1(6)(x x y 6)0()4(y 4324413121)()(x x x x x y x y )()1(51120)(5555)5(4x O x x y R with 5)5()1(24)(y MAE3100Prof. D.E. SmithLECTURE 2 -14Defining the RemainderRecall that the remainder R n is defined in terms the variable asConsider a zero-order (n = 0)Taylor Seriesthen 1)1()()!1()(n n n a x n f R ha a where )()()(0a f x f x f hR f h f R 00)()(= a = x = a = x)(f xa a+hMAE3100Prof. D.E. SmithLECTURE 2 -15Defining the Remainder (cont)Recall our example y (x ) = ln(1+x )with the 4-th order Taylor Series aboutx = 0The remainder becomesCombining these equations givesFor x = 1, we obtainthen or which satisfies the condition 4432413121)(R x x x x x y 55432)1(151413121)1ln(x x x x x x 555554)1(151)0())1(ln(!51x x x dx d R x 12739.058333.0413121)(69315.0)(4324x x x x x y x y 105544)1()1(15110981.058333.069315.0)1()1(y y R MAE3100Prof. D.E. SmithLECTURE 2 -16Defining the Remainder (cont)NOTE:•Determining the number of terms required for a Taylor series torepresent a function of interest is based on the remainder.•Unfortunately, ξis not known exactly but merely lies somewherebetween a and x = a + h (or x i and x i+1).•Also, R n requires derivatives of f (x ),which are not generally known.•Despite this, R n is still useful for gaining insight into truncationerrors.•Recall that we do have control over h and can therefore assess whathappens as we change h , i.e.,1)1(1)1()!1()()()!1()(n n nn n h n f a x n f R )())((11n n n h O a x O R xa a+h hMAE3100Prof. D.E. SmithLECTURE 2 -17Using the Remainder R n1)Establish order of error (from definition)2)Verify order of error estimate*> at h = 0.5 > at h = 1.03) Provide error estimate when h is increased or reduced*at h = 0.5, we computed R 4= 0.00442344then at h = 1.0 (doubled), we estimate R 4(0.00442344)(25) = 0.141550))(()()!1()(11)1(n n n n a x O a x n f R 0.109814)1()1(44y y R 0.00442344)5.0()5.0(44y y R 2X ~25X note: 25= 32X*For y (x ) = ln(1+x )about x = 0MAE3100Prof. D.E. SmithLECTURE 2 -18Using the Remainder R n (cont)4)Calculate value of ξwhen exact function value is known*Recall for h = 1and 5)Establish upper or lower bound on error*Recall that when h = 1, we obtain and Then the upper bound of the error may becalculated as the maximum R 4over the validrange of ξas 0.109814)1()1(44y y R *For y (x ) = ln(1+x )about x = 0554)1()1(151R Equating andsolving for ξgives12739.01054)1(151R 51)1(151)1(15110max 055max 4R maxξR 4MAE3100Prof. D.E. SmithLECTURE 2 -19Numerical DifferentiationDerivatives may be evaluated numerically withthe Finite (Divided) Difference method.1.Forward Difference (error is O (h ))2.Backward Difference (error is O (h ))3.Central Difference (error is O (h 2))hx f h x f x f )()()(hh x f x f x f )()()(hh x f h x f x f 2)()()(MAE3100Prof. D.E. SmithLECTURE 2 -20Remainder w/ Finite DifferenceConsider the 1st order Taylor Series and Remainder for f (x )expandedabout a = x (note h = x )which can be rearranged to give forward differenceExample problem: consider f (x ) = sin(x ) at x = /4exact derivative:forward finite difference:error bounded by remainder:2!2)()()()(xf x x f x f x x f R 1xf x x f x x f x f 2)()()()(O (x )7071067811.0)cos()(4/x x x f 6706029729.01.0)4/sin()1.04/sin()(x f (with x = 0.1)error = 0.0370781.04/at 0.0387084/at 0.035355)(2)sin(2)(x x f。
02 CH 充电
· 为防止恶作剧或被盗，离开充电中车辆时务必锁上车门。如果插座盒等带锁，建议也锁上。 结束普通充电时：
① 按下充电接头的释放开关解除锁止并拉到面前，把充电接头从普通充电插口拔下。
目录 CH、充电
关于充电的注意事项 锂离子蓄电池充电的种类和方法 普通充电方法 快速充电方法 便利的充电方法 关于充电相关指示灯 充电故障发现维修指导
正文
02 CH 充电
2.1 关于充电的注意事项
· 使用植入型心脏起搏器或植入型除颤器（ICD）等电子医疗仪器者请向医疗电子仪器制造商确认是否会受充电的 影响。 · 使用植入型心脏起搏器或植入型除颤器（ICD）等电子医疗仪器者请遵守以下事项： — 不要在车内逗留 — 取物品等时，不要进入包含后备箱在内的车室内。 · 勿让孩子等无自控能力的人单独实施充电作业，请在幼儿无法接触到的场所使用充电电缆（EVSE）。 · 勿碰触充电端口·充电接头·插头·插座的金属接点。 · 充电前，确认充电端口·充电接头·插头部分是否有水分·锈·腐蚀、及是否混入异物·存在损伤。有损伤等 时，勿实施充电。 · 切勿分解·修理·改造充电端口或充电机器。 · 充电中，发现异常气味或烟等时，立即中止充电。 · 打雷时勿接触车辆和充电机器。否则可能发生落雷导致的触电等。 · 充电中，动力舱内的冷却风扇可能突然开始旋转，注意勿让手脚、衣服和首饰等类物品接触，以防卷入。
2.2 锂离子蓄电池充电的种类和方法 Leaf 有如下充电方法：
种类
充电端口
充电接头
充电电缆(EVSE)/ 充电器*1
插座形状
ch02国际经济学课后答案与习题（萨尔瓦多）
ch02国际经济学课后答案与习题（萨尔⽡多）*CHAPTER 2Chapter) (CoreCOMPARATIVE ADVANTAGEOUTLINE2.1 Introduction2.2 Mercantilists’ Views on TradeCase Study 2-1 Mercantilism Is Alive and Well in the Twenty-First Century2.3 Trade Based on Absolute Advantage: Adam Smith2.4 Trade Based on Comparative Advantage: David Ricardo2.5 Gains from Trade with Comparative Advantage2.6 Comparative Advantage with MoneyCase Study 2-2 The Petition of the Candlemakers2.7 Comparative Advantage and Opportunity CostsCase Study 2-3 Labor Productivities and Comparative Advantage2.8 Production Possibility Frontier with Constant Costs2.9 Opportunity Costs and Relative Commodity Prices2.10 Basis and Gains from Trade Under Constant CostsAppendix: Comparative Advantage with More than Two Commodities and NationsA2.1 Comparative Advantage with More than Two CommoditiesA2.2 Comparative Advantage with More than Two NationsKey TermstheoryofvalueLabortradeBasisfortheorytrade OpportunitycostGainsfromtrade Production possibility frontierofPatterncostopportunityConstantMercantilismcommodityRelativeprices advantageAbsolutespecializationCompleteLaissez-faireLaw of comparative advantage Small-country case-7-Lecture Guide1. This is a long and crucial core chapter and may require four classes to cover adequately. In thefirst lecture, I would present Sections 1-4 and assign review questions 1-3.2. In the second lecture of Chapter 2, I would concentrate on Sections 5-6 and carefully explain the law of comparative advantage using simple numerical examples, as in the text. Both sections are crucial. Section 5 explains the law of comparative advantage and Section 6 establishes the link between trade theory and international finance. I find that the numerical explanations before the graphical analysis really helps the student to truly understand the law. The simple lawyer-secretary example should also render the law more immediately relevant to the student. I would also assign Problems 4-7.3. In the third lecture, I would cover Sections 7-9 and assign Problems 8-10.4. In the fourth lecture, I would Section 10 and go over problems 4-10. The appendixes could bemade optional for the more enterprising students in the class.Answer to Review Questions and Problems1. The mercantilists believed that the way for a nation to become rich and powerful was toexport more than it imported. The resulting export surplus would then be settled by an inflow of gold and silver and the more gold and silver a nation had, the richer and more powerful it was. Thus, the government had to do all in its power to stimulate the nation’s exports and discourage and restrict imports. However, since all nations could not simultaneously have an export surplus and the amount of gold and silver was fixed at any particular point in time, one nation could gain only at the expense of other nations. The mercantilists thus preached economic nationalism, believing that national interests were basically in conflict.Adam Smith, on the other hand, believed that free trade would make all nations better off.All of this is relevant today because many of the arguments made in favor of restrictinginternational trade to protect domestic jobs are very similar to the mercantilists argumentsmade three or four centuries ago. That is why we can say that “mercantilism is alive and well in the twenty-first century”. Thus we have to be prepared to answer and demonstrate thatthese arguments are basically wrong.2. According to Adam Smith, the basis for trade was absolute advantage, or one country being more productive or efficient in the production of some commodities and other countriesbeing more productive in the production of other commodities.The gains from trade arise as each country specialized in the production of the commodities in which it had an absolute advantage and importing those commodities in which the nation had an absolute disadvantage.Adam Smith believed in free trade and laissez-faire, or as little government interference with the economic system as possible. There were to be only a few exceptions to this policy of laissez-faire and free trade. One of these was the protection of industries important for national defense.3. Ricardo’s law of comparative advantage is superior to Smith’s theory of absolute advantage inthat it showed that even if a nation is less efficient than or has an absolute disadvantage in theproduction of all commodities with respect to the other nations, there is still a basis for beneficial trade for all nations.The gains from trade arise from the increased production of all commodities that arises wheneach country specializes in the production of and exports the commodities of its comparativeadvantage and imports the other commodities.A nation that is less efficient than others will be able to export the commodities of its compara-tive advantage by having its wages and other costs sufficiently lower than in other nations so asto make the commodities of its comparative advantage cheaper in terms of the same currencywith respect to the other nations.4. a. In case A, the United States has an absolute and a comparative advantage in wheat and theUnited Kingdom in cloth.In case B, the United States has an absolute advantage (so that the United Kingdom has anabsolute disadvantage) in both commodities.In case C, the United States has an absolute advantage in wheat but has neither an absoluteadvantage nor disadvantage in cloth.In case D, the United States has an absolute advantage over the United Kingdom in bothcommodities.b. In case A, the United States has a comparative advantage in wheat and the United Kingdomin cloth.In case B, the United States has a comparative advantage in wheat and the United Kingdomin cloth.In case C, the United States has a comparative advantage in wheat and the United Kingdomin cloth.In case D, the United States and the United Kingdom have a comparative advantage in neither commodities.5. a. The United States gains 1C.b. The United Kingdom gains 4C.c. 3C < 4W < 8C.d. The United States would gain 3C while the United Kingdom would gain 2C.6. a. The cost in terms of labor content of producing wheat is 1/4 in the United States and 1 in the United Kingdom, while the cost in terms of labor content of producing cloth is 1/3 in theUnited States and 1/2 in the United Kingdom.b. In the United States, Pw=$1.50 and Pc=$2.00.c. In the United Kingdom, Pw=￡1.00 and Pc=￡0.50.7. The United States has a comparative disadvantage in the production of textiles. Restrictingtextile imports would keep U.S. workers from eventually moving into industries in which the United States has a comparative advantage and in which wages are higher.8. Ricardo’s explanation of the law of comparative is unacceptable because it is based on the labor theory of value, which is not an acceptable theory of value.The explanation of the law of comparative advantage can be based on the opportunity costdoctrine, which is an acceptable theory of value.9. The production possibilities frontier reflects the opportunity costs of producing bothcommodities in the nation.The production possibilities frontier under constant costs is a (negatively sloped) straight line. The absolute slope of the production possibilities frontier reflects or gives the price of thecommodity plotted along the horizontal axis in relation to the commodity plotted along thevertical axis.10. a. See Figure 1.b. In the United States Pw/Pc=3/4, while in the United Kingdom, Pw/Pc=2.c. In the United States Pc/Pw=4/3, while in the United Kingdom Pc/Pw=1/2.d. See Figure 2.The autarky points are A and A' in the United States and the United Kingdom, respectively. The points of production with trade are B and B' in the United States and the UnitedKingdom, respectively.The points of consumption are E and E' in the United States and the United Kingdom,respectively. The gains from trade are shown by E > A for the U.S. and E' > A' for the U.K.Fig 1.1aU.K. Fig 1.1bFigure1Fig 1.2aFig 1.2bFigure2Multiple-Choice Questions1. The Mercantilists did not advocated:*a. free tradeb. stimulating the nation's exportsc. restricting the nations' importsd. the accumulation of gold by the nation2. According to Adam Smith, international trade was based on:*a. absolute advantageb. comparative advantagec. both absolute and comparative advantaged. neither absolute nor comparative advantage3. What proportion of international trade is based on absolute advantage?a. allb. most*c. somed. none4. The commodity in which the nation has the smallest absolute disadvantage is the commodityof its:a. absolute disadvantageb. absolute advantagec. comparative disadvantaged. comparative advantage5. If in a two-nation (A and B), two-commodity (X and Y) world, it is established that nationA has a comparative advantage in commodity X, then nationB must have:a. an absolute advantage in commodity Yb. an absolute disadvantage in commodity Yc. a comparative disadvantage in commodity Y*d. a comparative advantage in commodity Y6. If with one hour of labor time nation A can produce either 3X or 3Y while nation B canproduce either 1X or 3Y (and labor is the only input):a. nation A has a comparative disadvantage in commodity Xb. nation B has a comparative disadvantage in commodity Y*c. nation A has a comparative advantage in commodity Xd. nation A has a comparative advantage in neither commodity7. With reference to the statement in Question 6:a. Px/Py=1 in nation Ab. Px/Py=3 in nation Bc. Py/Px=1/3 in nation B*d. all of the above8. With reference to the statement in Question 6, if 3X is exchanged for 3Y:a. nation A gains 2X*b. nation B gains 6Yc. nation A gains 3Yd. nation B gains 3Y9. With reference to the statement of Question 6, the range of mutually beneficial trade between nation A and B is:a. 3Y < 3X < 5Yb. 5Y < 3X < 9Y*c. 3Y < 3X < 9Yd. 1Y < 3X < 3Y10. If domestically 3X=3Y in nation A, while 1X=1Y domestically in nation B:a. there will be no trade between the two nationsb. the relative price of X is the same in both nationsc. the relative price of Y is the same in both nations*d. all of the above11. Ricardo explained the law of comparative advantage on the basis of:*a. the labor theory of valueb. the opportunity cost theoryc. the law of diminishing returnsd. all of the above12. The Ricardian trade model has been empirically*a. verifiedb. rejectedc. not testedd. tested but the results were inconclusive13. The Ricardian model was tested empirically in terms of differences ina. relative labor productivities costs in various industries among nationsb. relative labor costs in various industries among nations*c. relative labor productivities and costs in various industries among nationsd. none of the above14. A difference in relative commodity prices between two nations can be based upon a difference in:a. factor endowmentsb. technologyc. tastes*d. all of the above15. In the trade between a small and a large nation:a. the large nation is likely to receive all of the gains from trade*b. the small nation is likely to receive all of the gains from tradec. the gains from trade are likely to be equally sharedd. we cannot say。
讲座-11
§1.1化学电源的定义和必须具 备的条件 §1.2化学电源的组成 §1.3化学电源的分类 §1.4基本概念
15
2.化学电源在实行能量转换的过程 中，必须具备两个必要的条件：
请问是那两个条件？ ①组成化学电源的两个电极上进行的氧 化还原过程，必须分别在两个分开的 区域进行，这一点区别于一般的氧化 还原反应； ②两电极的活性物质进行氧化还原反应 时所需电子必须由外电路传递，这一 点区别于金属腐蚀过程的微电极反应。 （为什么？） 17
Cl2 → 2Cl- - 2e Zn → Zn 2+ +2e
Zn +Cl2 → ZnCl2
1.36 V -(-0.76 V) 2.12V
14
2. The open-circuit voltage is the voltage under a no-load condition and is usually a close approximation of the theoretical voltage. 3. The closed-circuit voltage is the voltage under a load condition. 4. The nominal voltage is one that is generally accepted as typical of the operating voltage of the battery as, for example, 1.5 V for a zinc-manganese dioxide battery.
9
§1.4.3.电池的电压Voltage Level
1. The theoretical voltage. 2. The open-circuit voltage 3. The closed-circuit voltage 4. The nominal voltage (额定，标称电压） 5. The working voltage 6. The average voltage 7. The midpoint voltage 8. The end or cut-off voltage (截止电压）
Campbell10e_Lecture_Ch09
Chapter 9Cellular SignalingLecture OutlineOverview: Cellular MessagingCell-to-cell communication allows the trillions of cells in a multicellular organism to communicate to coordinate their activities.Communication between cells is important for multicellular and unicellularorganisms.Biologists have discovered universal mechanisms of cellular regulation involving the same small set of cell-signaling mechanisms.o The ubiquity of these mechanisms provides additional evidence for the evolutionary relatedness of all life.Cells most often communicate by chemical signals, although signals also takeother forms.实用文档Concept 9.1 External signals are converted to responses within the cell What messages are passed from cell to cell? How do cells respond to thesemessages?Cell signaling evolved early in the history of life.One topic of cell “conversation” is sex.The cells of Saccharomyces cerevisiae, the yeast of bread, wine, and beer, identify potential mates by chemical signaling.There are two sexes, a and , each of which secretes a specific signalingmolecule, a factor and factor, respectively.o These factors each bind to receptor proteins on the other mating type.After the mating factors have bound to the receptors, the two cells grow toward each other and undergo other cellular changes.实用文档o The two cells fuse, or mate, to form an a/ cell containing the genes of both cells.The process by which a signal on a cell’s surface is changed or transduced into a specific cellular response is a series of steps called a signal transductionpathway.o The molecular details of these pathways are strikingly similar in yeast and mammalian cells, even though their last common ancestor lived over a billionyears ago.o Signaling systems of bacteria and plants also share similarities.Similarities in signal transduction pathways suggest that ancestral signalingmolecules evolved long ago in ancient prokaryotes and single-celled eukaryotes and have since been adopted for new uses by their multicellular descendents.Cell signaling remains important in the microbial world.实用文档Cells of many bacterial species secrete small molecules that can be detected by other bacterial cells.The concentration of signaling molecules enables bacteria to sense the localdensity of bacterial cells, a phenomenon called quorum sensing.Signaling among members of a bacterial population can lead to coordination of their activities.In response to a signal, bacterial cells come together to form biofilms,aggregations of bacteria containing regions of specialized function.o The cells in the film generally derive nutrition from the surface.o The slimy coatings on a fallen log, on leaves lying in a forest path, or on your unbrushed teeth are produced by biofilms.Communicating cells may be close together or far apart.Multicellular organisms release signaling molecules that target other cells.实用文档Cells may communicate by direct contact.o Both animals and plants have cell junctions that connect to the cytoplasm ofadjacent cells.o Signaling substances dissolved in the cytosol can pass freely between adjacent cells.o Animal cells can communicate by direct contact between membrane-bound cell-surface molecules.o Such cell-cell recognition is important to processes like embryonicdevelopment and the immune response.In other cases, the signaling cell secretes messenger molecules.Some transmitting cells release local regulators that influence cells in the localvicinity.One class of local regulators in animals, growth factors, includes compounds thatstimulate nearby target cells to grow and multiply.实用文档o This type of local signaling, when numerous cells simultaneously receive and respond to growth factors produced by a single cell in their vicinity, is calledparacrine signaling.Synaptic signaling occurs in animal nervous systems.o An electrical signal along a nerve cell triggers the secretion ofneurotransmitter molecules carrying a chemical signal.o The molecules diffuse across a narrow synapse between the nerve cell and its target cell, triggering a response in the target cell.Beyond communication through plasmodesmata (plant cell junctions), localsignaling in plants is not as well understood.o Because of their cell walls, plants use different mechanisms from those operating locally in animals.Plants and animals use hormones for long-distance signaling.实用文档o In hormonal or endocrine signaling in animals, specialized cells release hormones into the circulatory system, through which they travel to target cellsin other parts of the body.o Plant hormones, called plant growth regulators, may travel in vessels but more often travel from cell to cell or diffuse through air.Hormones and local regulators range widely in molecular size and type.o The plant hormone ethylene (C2H4), a gas that promotes fruit ripening and regulates growth, is a hydrocarbon with only six atoms, capable of passingthrough cell walls.o The mammalian hormone insulin, which regulates blood sugar levels in mammals, is a protein with thousands of atoms.The transmission of a signal through the nervous system is also an example oflong-distance signaling.实用文档o An electrical signal travels the length of a nerve cell and is then converted to a chemical signal when a signaling molecule is released and crosses the synapseto another nerve cell. It is then converted back to an electrical signal.o In this way, a nerve signal can travel along a series of nerve cells, sometimes over great distances.The three stages of cell signaling are reception, transduction, and response.What happens when a cell encounters a secreted signaling molecule?The signal must be recognized and bound by a specific receptor molecule.o The information conveyed by this binding (the signal) must be changed into another form, or transduced, inside the cell, before the cell can respond.E. W. Sutherland and his colleagues pioneered our understanding of cell signalingby investigating how the animal hormone epinephrine stimulates the breakdown of the storage polysaccharide glycogen in liver and skeletal muscle cells.实用文档o The breakdown of glycogen releases glucose derivatives that can be used for fuel in glycolysis or released as glucose in the blood for fuel elsewhere.o Thus, one effect of epinephrine is mobilization of fuel reserves.Sutherland’s research team discovered that epinephrine stimulates glycogenbreakdown by activating a cytosolic enzyme, glycogen phosphorylase.o Epinephrine does not activate the phosphorylase directly in vitro, however, but acts only via intact cells.This suggests that there is an intermediate step or steps occurring inside the cell.It also suggests that the plasma membrane is involved in transmitting theepinephrine signal.Cell signaling involves three stages: reception, transduction, and response.1.In reception, a chemical signal binds to a cellular protein, typically at thetarget ce ll’s surface or inside the cell.实用文档2.In transduction, binding of the signaling molecule changes the receptorprotein in some way, initiating the process of transduction.Transduction may occur in a single step but more often triggers a series ofchanges in a series of different molecules along a signal transductionpathway.The molecules in the pathway are called relay molecules.3. In response, the transduced signal triggers a specific cellular activity.The cell-signaling process helps ensure that crucial activities occur in the rightcells, at the right time, and in proper coordination with the other cells of theorganism.Concept 9.2 Reception: A signal molecule binds to a receptor protein, causing it to change shape实用文档The cell targeted by a particular chemical signal has a receptor protein on or inthe target cell that recognizes the signal molecule.o Recognition occurs when the signal binds to a specific site on the receptor that is complementary in shape to the signal.The signal molecule behaves as a ligand, a small molecule that binds withspecificity to a larger molecule.Ligand binding generally causes the receptor protein to undergo a change inshape.Ligand binding may activate the receptor so that it can interact with othermolecules.o For other receptors, ligand binding causes aggregation of receptor molecules, leading to further molecular events inside the cell.Most signal receptors are plasma membrane proteins, whose ligands are large,water-soluble molecules that are too large to cross the plasma membrane.实用文档o Other signal receptors are located inside the cell.Most signal receptors are plasma membrane proteins.Water-soluble signaling molecules bind to specific sites on receptor proteins that span the cell’s plasma membrane.o The transmembrane receptor transmits information from the extracellular environment to the inside of the cell by changing shape or aggregating withother receptors.There are three major types of membrane receptors: G-protein-linked receptors, receptor tyrosine kinases, and ion channel receptors.A G-protein-linked receptor consists of a receptor protein associated with a Gprotein on the cytoplasmic side.o Seven helices span the membrane.实用文档o G-protein-linked receptors bind many different signal molecules, including yeast mating factors, epinephrine and many other hormones, andneurotransmitters.The G protein acts as an on-off switch.o If GDP is bound to the G protein, the G protein is inactive.o When the appropriate signal molecule binds to the extracellular side of the receptor, the G protein binds GTP (instead of GDP) and becomes active.o The activated G protein dissociates from the receptor and diffuses along the membrane, where it binds to an enzyme, altering its activity.o The activated enzyme triggers the next step in a pathway leading to a cellular response.The G protein can also act as a GTPase enzyme to hydrolyze GTP to GDP.o This change turns the G protein off.实用文档○Now inactive, the G protein leaves the enzyme, which returns to its original state.The whole system can be shut down quickly when the extracellular signalmolecule is no longer present.G-protein receptor systems are extremely widespread and diverse in theirfunctions.o They play important roles during embryonic development.o Vision and smell in humans depend on these proteins.Similarities among G proteins and G-protein-linked receptors of modernorganisms suggest that this signaling system evolved very early.Several human diseases involve G-protein systems.o For example, bacterial infections that cause cholera and botulism interfere with G-protein function.实用文档The tyrosine-kinase receptor system is especially effective when the cell needs to trigger several signal transduction pathways and cellular responses at once.o This system helps the cell regulate and coordinate many aspects of cell growth and reproduction.The tyrosine-kinase receptor belongs to a major class of plasma membranereceptors that have enzymatic activity.o A kinase is an enzyme that catalyzes the transfer of phosphate groups.o The cytoplasmic side of these receptors functions as a tyrosine kinase, transferring a phosphate group from ATP to tyrosine on a substrate protein.An individual tyrosine-kinase receptor consists of three parts: an extracellularsignal-molecule-binding site, a single helix spanning the membrane, and an intracellular tail with several tyrosines.The signal molecule binds to an individual receptor.实用文档Ligands bind to two receptors, causing the two receptors to aggregate and forma dimer.This dimerization activates the tyrosine-kinase section of the receptors, each ofwhich then adds phosphate from ATP to the tyrosine tail of the other polypeptide.The fully activated receptor proteins activate a variety of specific relay proteinsthat bind to specific phosphorylated tyrosine molecules.o One tyrosine-kinase receptor dimer may activate ten or more different intracellular proteins simultaneously.o These activated relay proteins trigger many different transduction pathways and responses.A ligand-gated ion channel is a type of membrane receptor that can act as agate when the receptor changes shape.实用文档When a signal molecule binds as a ligand to the receptor protein, the gate opensto allow the flow of specific ions, such as Na+ or Ca2+, through a channel in thereceptor.o Binding by a ligand to the extra cellular side changes the protein’s shape and opens the channel.o When the ligand dissociates from the receptor protein, the channel closes.The change in ion concentration within the cell may directly affect the activity of the cell.Ligand-gated ion channels are very important in the nervous system.o For example, neurotransmitter molecules released at a synapse between two neurons bind as ligands to ion channels on the receiving cell, causing thechannels to open.o Ions flow in and trigger an electrical signal that propagates down the lengthof the receiving cell.实用文档Some gated ion channels respond to electrical signals instead of ligands.Malformations of cell-surface receptor molecules are associated with manyhuman diseases, including cancer, heart disease, and asthma.o Although cell-surface receptors make up 30% of human proteins, they make up only 1% of all proteins whose structures have been determined by X-raycrystallography.o Their structures are very hard to determine experimentally.The largest family of human cell-surface receptors consists of the nearly 1,000 G protein-coupled receptors (GPCRs).o The structure of several G protein-coupled receptors has been elucidated over the past few years.Abnormal functioning of receptor tyrosine kinases (RTKs) is associated with many types of cancers.实用文档o Excessive levels of a receptor tyrosine kinase called HER2 on breast cancer cells correlates with a poorer prognosis for patients.o Using molecular biological techniques, researchers have developed a protein called Herceptin that binds to HER2 on cells and inhibits their growth,reducing tumor development.o In some clinical studies, treatment with Herceptin improved patient survival rates by more than one-third.One goal of ongoing research into cell-surface receptors and other cell signaling proteins is development of successful treatments.Some receptor proteins are intracellular.Intracellular signal receptors are found in the cytoplasm or nucleus of target cells.To reach these receptors, a chemical messenger pa sses through the target cell’s plasma membrane.实用文档o Such chemical messengers are either hydrophobic enough or small enough to cross the phospholipid interior of the plasma membrane.Hydrophobic messengers include the steroid and thyroid hormones of animals.Another chemical signaling molecule with an intracellular receptor is nitric oxide (NO), a gas whose small size allows it to pass between membrane phospholipids.Testosterone is secreted by the testis and travels through the blood to enter cells throughout the body.o Only cells that contain receptor molecules for testosterone respond.o In these cells, the hormone binds and activates the receptor protein.o The activated proteins enter the nucleus and turn on specific genes that control male sex characteristics.How does the activated hormone-receptor complex turn on genes? Theseactivated proteins act as transcription factors.实用文档o Transcription factors control which genes are turned on—that is, which genes are transcribed into messenger RNA.Some intracellular receptors (such as thyroid hormone receptors) are found in the nucleus and bind to the signal molecules there.Many intracellular receptor proteins are structurally similar, suggesting anevolutionary kinship.Concept 9.3 Transduction: Cascades of molecular interactions relay signals from receptors to target molecules in the cellThe transduction stage of signaling is usually a multistep pathway that greatlyamplifies the signal.o If some molecules in a pathway transmit a signal to multiple molecules at the next step in the series, the result can be a large number of activated moleculesat the end of the pathway.实用文档Multistep pathways also provide more opportunities for coordination andregulation than do simpler systems.Pathways relay signals from receptors to cellular responses.The binding of a specific signaling molecule to a receptor in the plasmamembrane triggers the first step in the chain of molecular interactions—the signal transduction pathway—that leads to a particular response within the cell.Signal transduction pathways act like falling dominoes. The signal-activatedreceptor activates another protein, which activates another, and so on, until theprotein that produces the final cellular response is activated.The relay molecules that relay a signal from receptor to response are oftenproteins.o The interaction of proteins is a major theme of cell signaling.o Protein interaction is a unifying theme of all cellular regulation.实用文档The original signal molecule is not passed along the pathway and may not even enter the cell.When the signal is relayed along a pathway, information is passed on.o At each step, the signal is transduced into a different form, often by a conformational change in a protein.o The conformational change is often brought about by phosphorylation.Protein phosphorylation, a common mode of regulation in cells, is a major mechanism of signal transduction.The phosphorylation of proteins by a specific enzyme (a protein kinase) is awidespread cellular mechanism for regulating protein activity.Most protein kinases act on other substrate proteins, unlike tyrosine kinases,which act on themselves.实用文档Most phosphorylation occurs at serine or threonine amino acids of the substrate protein.Many of the relay molecules in a signal transduction pathway are protein kinases that act on other protein kinases to create a “phosphorylation cascade.”Each protein phosphorylation leads to a conformational change because of the interaction between the newly added phosphate group and charged or polaramino acids on the protein.Phosphorylation of a protein typically converts it from an inactive form to anactive form.o Only rarely does phosphorylation decreases the activity of the protein.A single cell may have hundreds of different protein kinases, each specific for adifferent substrate protein.o Fully 2% of our genes are thought to code for protein kinases.实用文档o Together, they regulate a large proportion of the thousands of the proteins ina cell.Abnormal activity of protein kinases can cause abnormal cell growth and maycontribute to the development of cancer.The responsibility for turning off a signal transduction pathway belongs toprotein phosphatases.These enzymes rapidly remove phosphate groups from proteins, a process called dephosphorylation.o By dephosphorylating and thus inactivating protein kinases, phosphatases provide the mechanism for turning off the signal transduction pathway whenthe initial signal is no longer present.o Phosphatases also make the protein kinases available for reuse, enabling the cell to respond again to a signal.实用文档The phosphorylation/dephosphorylation system acts as a molecular switch in the cell, turning activities on and off as required.o At any given moment, the activity of a protein regulated by phosphorylation depends on the balance between active kinase molecules and activephosphatase molecules.o When the extracellular signal molecule is absent, active phosphatase molecules predominate, and the signaling pathway and cellular response areshut down.Certain signal molecules and ions are key components of signaling pathways (second messengers).Many signaling pathways involve small, water-soluble, nonprotein molecules or ions called second messengers.实用文档o The extracellular signaling molecule that binds to the membrane receptor is apathway’s “first messenger.”Second messengers diffuse rapidly throughout the cell.Second messengers participate in pathways initiated by both G-protein-linkedreceptors and tyrosine-kinase receptors.o Two of the most widely used second messengers are cyclic AMP and Ca2+.o A large variety of relay proteins are sensitive to the cytosolic concentration of one orthe other of these second messengers.Once Sutherland knew that epinephrine causes glycogen breakdown withoutentering the cell, he looked for a second messenger that transmits the signalfrom the plasma membrane to the metabolic machinery in the cytoplasm.Binding by epinephrine leads to increases in the cytosolic concentration of cyclicAMP, or cAMP.实用文档o This increase occurs because the activated receptor activates adenylyl cyclase,which converts ATP to cAMP in response to epinephrine.o When epinephrine outside the cell binds to a specific receptor protein, the normal cellular concentration of cAMP can be boosted 20-fold within seconds.o cAMP is short-lived because phosphodiesterase converts it to AMP.o Another surge of epinephrine is needed to reboost the cytosolicconcentration of cAMP.Many hormones and other signal molecules trigger the formation of cAMP.G-protein-linked receptors, G proteins, and protein kinases are other components of cAMP pathways.cAMP diffuses through the cell and activates a serine/threonine kinase calledprotein kinase A.o The activated kinase phosphorylates various other proteins, depending on celltype.实用文档Cell metabolism is also regulated by G-protein systems that inhibit adenylylcyclase.o These systems use a different signal molecule to activate a different receptor that activates an inhibitory G protein.Certain microbes cause disease by disrupting G-protein signaling pathways.o For example, the cholera bacterium, Vibrio cholerae, may be present in water contaminated with human feces.o This bacterium colonizes the small intestine and produces a toxin that modifies a G protein that regulates salt and water secretion.o The modified G protein is unable to hydrolyze GTP to GDP and remains stuck in its active form, continuously stimulating adenylyl cyclase to make cAMP.o The resulting high concentration of cAMP causes the intestinal cells to secrete large amounts of water and salts into the intestines, leading to profusediarrhea and possible death from loss of water and salts.实用文档Treatments for certain human conditions involve signaling pathways.One pathway uses cyclic GMP, or cGMP, as a signaling molecule. Its effectsinclude the relaxation of smooth muscle cells in artery walls.o A compound was developed to treat chest pains. This compound inhibits the hydrolysis of cGMP to GMP, prolonging the signal and increasing blood flowto the heart muscle.o Under the trade name Viagra, this compound is now widely used as a treatment for erectile dysfunction.o Viagra causes dilation of blood vessels, allowing increased blood flow to the penis.Many signaling molecules in animals, including neurotransmitters, growth factors, and some hormones, induce responses in their target cells via signal transduction pathways that increase the cytosolic concentration of Ca2+.Calcium is even more widely used than cAMP as a second messenger.实用文档○In animal cells, increases in Ca2+ concentrations may cause contraction of muscle cells, secretion of certain substances, and cell division.o In plant cells, increases in Ca2+ trigger responses such as the pathway for greening in response to light.Cells use Ca2+ as a second messenger in both G-protein pathways and tyrosine-kinase pathways.The Ca2+ concentration in the cytosol is typically much lower than theconcentration outside the cell, often by a factor of 10,000 or more.o Various proteins actively transport Ca2+ outside the cell or into the endoplasmic reticulum (ER) or other organelles.o As a result, the concentration of Ca2+ in the ER is usually much higher than the concentration in the cytosol.实用文档Because the concentration of cytosolic Ca2+ is so low, small changes in theabsolute numbers of ions cause a relatively large percentage change in the Ca2+concentration.Signal transduction pathways trigger the release of Ca2+from the cell’s ER.The pathways leading to calcium release involve still other second messengers,diacylglycerol (DAG) and inositol trisphosphate (IP3).o DAG and IP3 are created when a phospholipase cleaves a specific membrane phospholipid.o The phospholipase may be activated by a G protein or by a tyrosine-kinase receptor.o IP3 activates a gated calcium channel, releasing Ca2+ from the ER.o Calcium ions activate the next protein in a signal transduction pathway.Because IP3 acts before calcium in these pathways, calcium could be considered athird messenger.实用文档o However, scientists use the term second messenger for all small, nonprotein components of signal transduction pathways.Concept 9.4 Response: Cell signaling leads to regulation of transcription or cytoplasmic activitiesUltimately, a signal transduction pathway leads to the regulation of one or more cellular activities.The response may occur in the nucleus or the cytoplasm.Many signaling pathways ultimately regulate protein synthesis, usually by turning specific genes on or off in the nucleus.o Like an activated steroid receptor, the final activated molecule in a signaling pathway may function as a transcription factor. Often a transcription factorregulates several different genes.实用文档Signaling pathways may regulate the activity of proteins rather than theirsynthesis, directly affecting proteins that function outside of the nucleus.o A signal may cause the opening or closing of an ion channel or a change in cell metabolism.o For example, epinephrine helps regulate cellular energy metabolism by activating enzymes that catalyze the breakdown of glycogen.Signaling events may also affect cellular attributes such as overall cell behavior.One example of this regulation can be found in the activities leading to themating of yeast cells.o In yeast, the mating process depends on the growth of localized projections in one cell toward a cell of the opposite mating type.o Binding of the mating factor causes directional growth via activation of signaling-pathway kinases that affect the orientation of the growth ofcytoskeletal microfilaments.实用文档o Cell projections emerge from areas that receive the highest concentration of the mating factor and thus have the highest likelihood of reaching the cell ofthe opposite mating type, the source of the signaling molecule.Signal receptors and relay molecules participate in a variety of nuclear andcytoplasmic response pathways, some leading to cell division.o The molecular messengers that produce these responses include growth factors and certain plant and animal hormones.o Malfunctioning of growth factor pathways can contribute to the development of cancer.Signaling pathways with multiple steps provide signal amplification, allow fine-tuning of the cell’s response, and contribute to the specificity of the response.Whether the response occurs in the nucleus or cytoplasm, it is fine-tuned atmultiple points.实用文档。
Lecture-09-Constraint_Satisfaction
Instructor:
TA:
Sofus A. Macskassy, macskass@
Harris Chiu (chichiu@), Wed 2:45-4:45pm, PHE 328 Penny Pan (beipan@), Fri 10am-noon, PHE 328
CS561 - Lecture 9 - Macskassy - Fall 2010
7
Constraint graph
Binary CSP: each constraint relates at most two variables Constraint graph: nodes are variables, arcs show constraints
Simple example of a formal representation language
Allows useful general-purpose algorithms with more power than standard search algorithms
3
CS561 - Lecture 9 - Macskassy - Fall 2010
General-purpose CSP algorithms use the graph structure to speed up search. E.g., Tasmania is an independent subproblem!
8
CS561 - Lecture 9 - Macskassy - Fall 2010
Continuous variables
新概念英语二册lesson10教师版讲义
辅导课题：新概念 2 lesson 10提分第一阶段：复习上节课内容和遗忘知识点单词短语听写提分第二阶段：梳理本节课知识要点，查漏补缺10 Not for jazz 不适于演奏爵士乐【课文】We have an old musical instrument. It is called a clavichord. It was made in Germany in 1681. Our clavichord is kept in the living-room. It has belonged to our family for a long time. The instrument was bought by my gra ndfather many years ago. Recently it was damaged by a visitor. She tried to play jazz on it! She struck the keys too hard and two of the strings were broken. My father was shocked. Now we were not allowed to touch it. It is being repairedby a friend of my father's.【课文翻译】我们有一件古老的乐器,叫击弦古钢琴 .它是 1681 年德国制造的, 我们这架钢琴放在客厅里.我们家拥有它很长时间了 ,这件乐器是许多年前我祖父买来的.最近它被一位客人弄坏了,她用它弹奏爵士乐! 她按键太猛 ,把两根弦按断了.我父亲为之震怒. 现在他不允许我们再碰它.父亲的一位朋友正在修理这件古老的乐器.【生词和短语】jazz n.爵士音乐musical a.音乐的instrument n.器具call vt. 叫做clavichord n.击弦古钢琴Germany n.德国keep vt.保存living-room n.客厅belong vi. 属于recently ad.最近damage vt.损坏play vt.弹奏key n.琴键strike vt.敲hard ad.重重地string n.弦break vt.弄断shock vt. 震惊touch vt.碰allow vt.允许repair vt. 修理 .提分第三阶段：考试考点例题讲解，掌握解题思路★ jazz n. 爵士音乐a kind of music★ musical adj. 音乐的musical student有音乐天赋的人music student学音乐的人〔the student who learned music 〕★ instrument n. 乐器instrument=musical instrumentinstrument 常用的意思是“器械〞、“器具〞，尤指医疗、机器等方面的。
Ch02-lecture
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散射
地球大气中有空气分 子、云滴、雨滴和各 种气溶胶粒子，当电 磁波辐射在大气中遇 到这些粒子后，会产 生散射现象，入射到 大气粒子的辐射改变 方向，向各个方向的 散射，原入射方向上 的能量因此被削弱。
太阳辐射光谱
散射
地面观测的太阳光谱
4R 2
R
R 2
22
地球接收太阳的短波辐射， 放出红外长波辐射
23
地球表面的温度
根据目前测量得到的数据， S0 = 1376 w/m2 (+3.4% ~ -3.5%)
= 0.3 R = 6370 km 计算得到 T = 2550K （ -180C） 它远低于地球表面的实际平均温度 150C 问题出在那里呢？就是大气中温室气体的温室 效应，它使地面的平均温度上升了 330C，从 –180C 变为 150C。
15
太阳和地球的辐射波谱
16
Wien 定理
右图给出的是Planck公式中辐射能量 随λ的分布。它有一个单一的峰值， 利用简单的数学运算，我们可以得到 对应最大辐射能量的λmax值。Wien发 现λmax和物体的温度的积 是一个常 量，这就是 Wien 定理。
max
C T
C 2.8978103 mK
8
热传导
The transfer of heat from molecule to molecule within a substance is called conduction.
热传导总是把热量从高温处传 向低温处
热传导中单位时间传递的热量 与二点的温度梯度成正比，比 例系数称为热传导系数。
吸收
散射与波长和粒子的大小有关
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© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Opportunity Cost
As we move down along the PPF, we produce more pizzas, but the quantity of cola we can produce decreases. The opportunity cost of a pizza is the cola forgone.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
In moving from F to E: The quantity of cola increases by 5 million cans. The quantity of pizzas decreases by 1 million. The opportunity cost of the first 5 million cans of cola is 1 million pizzas. One of these cans of cola costs 1/5 of a pizza.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Opportunity Cost Is a Ratio Note that the opportunity cost of a can of cola is the inverse of the opportunity cost of a pizza. One pizza costs 5 cans of cola. One can of cola costs 1/5 of a pizza.
© 2012 Pearson Addison-Wesley
Using Resources Efficiently
All the points along the PPF are efficient. To determine which of the alternative efficient quantities to produce, we compare costs and benefits.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Any point on the frontier such as E and any point inside the PPF such as Z are attainable.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Tradeoff Along the PPF
Every choice along the PPF involves a tradeoff. On this PPF, we must give up some cola to get more pizzas or give up some pizzas to get more cola.
© 2012 Pearson Addison-Wesley
Using Resources Efficiently
Figure 2.2 illustrates the marginal cost of a pizza.
As we move along the PPF, the opportunity cost of a pizza increases. The opportunity cost of producing one more pizza is the marginal cost of a pizza.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Any point inside the frontier, such as Z, is inefficient.
At such a point, it is possible to produce more of one good without producing less of the other good. At Z, resources are either unemployed or misallocated.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
Increasing Opportunity Cost Because resources are not equally productive in all activities, the PPF bows outward. The outward bow of the PPF means that as the quantity produced of each good increases, so does its opportunity cost.
© 2012 Pearson Addison-Wesley
Using Resources Efficiently
In part (b) of Fig. 2.2, the bars illustrate the increasing opportunity cost of a pizza.
The black dots and the line MC show the marginal cost of producing a pizza. The MC curve passes through the center of each bar.
THE ECONOMIC PROBLEM
2
Why does food cost much more today than it did a few years ago? One reason is that we now use part of our corn crop to produce ethanol, a clean biofuel substitute for gasoline. Another reason is that drought in some parts of the world has decreased global grain production. We use an economic model—the production possibilities frontier—to learn why ethanol production and drought have increased the cost of producing food. We also use this model to study how we can expand our production possibilities; how we gain by trading with others; and why the social institutions have evolved.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
The production possibilities frontier (PPF) is the boundary between those combinations of goods and services that can be produced and those that cannot. To illustrate the PPF, we focus on two goods at a time and hold the quantities of all other goods and services constant. That is, we look at a model economy in which everything remains the same (ceteris paribus) except the two goods we’re considering.
© 2012 Pearson Addison-Wesley
Production Possibilities and Opportunity Cost
In moving from E to F: The quantity of pizzas increases by 1 million. The quantity of cola decreases by 5 million cans. The opportunity cost of the fifth 1 million pizzas is 5 million cans of cola. One of these pizzas costs 5 cans of cola.
© 2012 Pearson Addison-Wesley
Using Resources Efficiently
Preferences and Marginal Benefit Preferences are a description of a person’s likes and dislikes.
Points outside the PPF are unattainable.
© 2012 Pearson Addison-Wesley