...The Coase Theorem In “The Problem of Social Cost,” Ronald Coase introduced a different way of thinking about externalities, private property rights and government intervention. The student will briefly discuss how the Coase Theorem, as it would later become known, provides an alternative to government regulation and provision of services and the importance of private property in his theorem. In his book The Economics of Welfare, Arthur C. Pigou, a British economist, asserted that the existence of externalities, which are benefits conferred or costs imposed on others that are not taken into account by the person taking the action (innocent bystander?), is sufficient justification for government intervention. He advocated subsidies for activities that created positive externalities and, when negative externalities existed, he advocated a tax on such activities to discourage them. (The Concise, n.d.). He asserted that when negative externalities are present, which indicated a divergence between private cost and social cost, the government had a role to tax and/or regulate activities that caused the externality to align the private cost with the social cost (Djerdingen, 2003, p. 2). He advocated that government regulation can enhance efficiency because it can correct imperfections, called “market failures” (McTeer, n.d.). In contrast, Ronald Coase challenged the idea that the government had a role in taking action targeted at the person or persons who “caused”...
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...Pythagorean Theorem: Finding Treasure Patricia Diggs MAT 221 Introduction to Algebra Instructor Bridget Simmons May 12, 2013 Pythagorean Theorem: Finding Treasure In this paper I will attempt to use the Pythagorean Theorem to solve the problem which reads Ahmed has half of a treasure map which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x+4 paces to the east. If they share their information they can find x and save a lot of digging. What is x? The Pythagorean Theorem states that in every right triangle with legs the length a and b and hypotenuse c, these lengths have the relationship of a2 + b2=c2. a=x b=(2x+4)2 c=(2x+6)2 this is the binomials we will insert into our equation x2+(2x+4)2=(2x+6)2 the binomials into the Pythagorean Theorem x2+4x2+16x+16=24x36 the binomial squared. The 4x2can be subtracted out first x2+16x+16=24x+36 now subtract 24x from both sides x2+-8x+16=36 now subtract 36 from both sides x2-8x-20=0 this is a quadratic equation to solve by factoring and using the zero factor. (x- )(x+ ) the coefficient of x2 is one (1). We can start with a pair of parenthesis with an x each. We have to find...
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...A. Objective a. To understand the use of Thevenin’s law and build a circuit to confirm the law b. Use Ohms and Kirchhoff’s laws to calculate the desired measurements B. Equipment c. DC Power Source d. Breadboard e. Extech instruments voltmeter f. 1000 resistor g. 3900 resistor h. 1200 resistor i. 3300 resistor j. 2200 resistor k. Wires C. Procedure l. Review Ohms and Kirchhoff’s laws m. Find the theoretical values for the circuit in Figure 3 n. Use the 1000 W, 3300 W, and 2200 W resistors to create the circuit in Figure 3 o. Set the voltage to 6.9 v and measure the values from the circuit with the Extech instruments voltmeter p. Use the found values to create the Thevenin circuit q. Check the values and confirm that the circuits are the same D. Schematic Diagrams E. Data Tables | VTh | IShort | RTh | Theoretical | 6.875 v | 1.69 mA | 4.05K | Measured | 6.8 v | 1.7 mA | 4K | F. Questions Pre Lab: 1) Find the Thevenin's and Norton's equivalent circuits of network in figure 3, excluding RL. VTh = Open Circuit Voltage VTh = (2.2 / 1 + 2.2) x 10 = 6.875 v What is theoretical IShort for the Figure 4? G. Conclusion In this lab I learned the features and how to operate both an oscilloscope and...
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...In today’s world, there are a multitude of mathematical theorems and formulas. One theorem that is particularly renowned is the Pythagorean Theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of any right triangle. While most people have heard of or even used the Pythagorean Theorem, many know little of the man who proved it. Pythagoras was born in 570 BC in Samos, Greece. His father, Mnesarchus, was a merchant from Tyre who traveled abroad. It is rumored that Pythagoras traveled with his father during his early years and was introduced to several influential teachers, including Thales who was a famous Greek philosopher. Several years and many countries later, Pythagoras found himself in Egypt. It was here that he studied at the temple of Diospolis and was also imprisoned during the Persian invasion. During the time he was imprisoned, Pythagoras began to study the religion called Zoroastrianism (Lauer/Schlager, 2001). It was because of these teachings and ideals that Pythagoras eventually moved to Italy. At age 52, while living in Croton, Italy, Pythagoras established the Pythagorean society. It was through this society and his positions in local government that Pythagoras recruited men and women in order to lead them to the pure life with his spiritual and mathematical teachings. Pythagoras believed that number was limiting and gave shape to all matter and he impressed this upon his followers (Gale, 1998)...
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...“Fermat’s Last Theorem” Research Summary (Yutaka Taniyama) Pierre de Fermat’s last theorem states that that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. This became one of the most puzzled and complex theorems ever to emerge in the Mathematician world. No one could prove this to be true until British Mathematician Andrew Wiles solved it in 1995. Wiles was first inspired by the Taniyama-Shimura conjecture and used this as a starting point in solving Fermat’s theorem. The Taniyama-Shimura conjecture was developed by Yutaka Taniyama and Goro Shimura. Although both mathematicians are credited, it was essentially Taniyama who was responsible for the theorem. The Taniyama-Shimura conjecture was a partial and refined case of elliptic curves over rationals. Yutaka Taniyama was a brilliant mathematician who committed suicide at the age of 31 in 1958. Due to depression of lack of confidence for a happy future, he ended his life. His ideas were often criticized which most likely led to his death. Goro Shimura stated that he was sad when he heard the terrible news, but was more shocked and puzzled more than anything. Shimura’s famous quote after Taniyama’s death stated “He was not a very careful person as a mathematician. He made a lot of mistakes. But he made mistakes in a good direction. I tried to emulate him. But I've realized that it's very difficult to make good mistakes.” In conclusion, Andrew Wiles...
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...Author : Utkarsh Garg FUNDAMENTAL THEOREM OF ALGEBRA The name suggests that it is some starting theorem of algebra or the basis of algebra. But it is not so, the theorem just say something interesting about the polynomials. Definition: The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with zero imaginary part. PROOF: This is an algebraic proof. I am doing this for a 2 degree polynomial . It can be extended for any degree polynomial. We know that the roots of a quadratic equation az 2 + bz + c = 0 are given by the formula irrespective of the fact whether a, b, c are real or complex numbers. Also it is clear that in this case there are two roots, say α + β = −b/a, αβ = c/a and az 2 + bz + c = a(z − α)(z − β) . Also any α, β satisfying α + β = a, αβ = b are given as roots of the quadratic equation z 2 − az + b = 0 . Now we will show that in order to prove the fundamental theorem of algebra it is sufficient to prove that any non-constant polynomial with real coefficients has a complex root. Let us then assume that every non-constant polynomial with real coefficients has a complex root. Let f (z) = a0 z n + a1 z n−1 + ⋯ + an−1 z + an be a polynomial with complex coefficients. Let g(z) be the polynomial obtained from f (z) by replacing the coefficients with their conjugates. Clearly the...
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...SUBMISSION QUESTION 7 EXTERNALITIES AND COASE THEOREM (a) Explain what is meant by “externalities”? (b) Consider an industry whose production process emit a gaseous pollutant into the atmosphere. Use the simple supply and demand model to demonstrate that, in the absence of any regulation, this industry’s production will result in allocative inefficiency in the use of society’s resources. Externalities is cost or benefit from production or consumption of commodity that flow to external parties but not taken into account by market (Bajada, 2012). The impact of externalities is the distortion in allocation of resources. Externalities will cause individual to pursuit based on their self-interest. Hence, it will cause commodity not produced at the socially optimal level and output become inefficient (Frank, Jennings and Bernanke, 2009). There are two types of externalities: (1) Externalities cost Externalities cost happens if production or consumption of commodities inflict cost to external parties without compensation (Bajada, 2012). When externalities costs occur, producers shift some of their costs onto community making their production costs lower than otherwise, thus the commodity become underprices and over-allocation of resources (Bajada, 2012). The example of externality cost is industry whose production process emits gaseous pollutant into atmosphere. The pollution will impose higher medical or health costs to the society nearby the...
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...Abstract In 1959, Ronald Coase introduced what is now known as the Coase Theorem, which suggests that absent transaction costs, any initial property rights agreement leads to an economically efficient outcome. Straying from previous models supported by most economists, this position was initially met with skepticism. Discussion Prior to 1959, the standard economic understanding held that government regulation enhances efficiency by correcting for claimed imperfections. This thinking was in keeping with A. C. Pigou’s contention that was developed in 1920. Pigou called claimed imperfections, “market failures”. In 1959, Ronald Coase authored an article for the University of Chicago’s Journal of Law and Economics entitled, “The Federal Communications Commission”. In this article, Coase suggested that in the absence of transaction costs, any initial property rights arrangement leads to an economically efficient outcome (McTeer 2003). In Coase’s discussion, he changes the way torts are viewed. In Pigou’s model, one party does harm to another; therefore, government regulation is necessary to ensure that the party filing the claim of harm is no longer harmed. Coase’s model expands the view of harm to include the party accused of inflicting harm on the other party. Specifically, Coase demonstrates that if government regulation is put into place to prevent harm to a party, the entity that is now subjected to the regulation is now being harmed. For example, Company A...
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...Research on Butterfly Theorem Butterfly Theorem is one of the most appealing problems in the classic Euclidean plane geometry. The name of Butterfly Theorem is named very straightforward that the figure of Theorem just likes a butterfly. Over the last two hundreds, there are lots of research achievements about Butterfly Theorem that arouses many different mathematicians’ interests. Until now, there are more than sixty proofs of the Butterfly Theorem, including the synthetical proof, area proof, trigonometric proof, analytic proof and so on. And based on the extension and evolution of the Butterfly Theorem, people can get various interesting and beautiful results. The definition of the Butterfly Theorem is here below: “Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD cuts PQ at X and BC cuts PQ at Y. Prove that M is also the midpoint of XY.” (Bogomolny) This is the most accurate definition currently. However, Butterfly Theorem has experienced some changes and developments. The first statement of the Butterfly Theorem appeared in the early 17th century. In 1803, a Scottish mathematician, William Wallace, posed the problem of the Butterfly Theorem in the magazine The Gentlemen’s Mathematical Companion. Here is the original problem below: “If from any two points B, E, in the circumference of a circle given in magnitude and position two right lines BCA, EDA, be drawn cutting the circle in C and D, and meeting in A; and...
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...Assignment 1–Advanced Operations Research - MATH 3010 Posted 23 August 2014 Due date: 19 September 2014, by 5pm In all the statements below, the notation, as well as references to page numbers, equations, etc, are as in the textbook Primal-dual interior-point methods, by Wright, Stephen, which is available online for UniSA staff and students. All relevant chapters of the textbook are also available in the webpage of the course. For solving this assignment, you need to read the handwritten Lecture Notes posted in the web and the material in the book up to Chapter 4, page 70. Question 1 (2+2+3+3+3+3=16 points) Fix A ∈ Rm×n , b ∈ Rm , and c ∈ Rn . (a) Write down the KKT conditions for the following problem, on the variable x ∈ Rn : min cT x Ax = b ; x ≥ 0. (1) (b) Write down the KKT conditions for the following problem, on the variable (λ, s) ∈ Rm+n AT λ max λT b + s = c; s ≥ 0, (2) Show that both the KKT conditions associated with both problems are identical. (c) Given x, s ∈ Rn , define the matrices X = diag(x1 , . . . , xn ), S = diag(s1 , . . . , sn ), and the vector e = (1, . . . , 1)T ∈ Rn . Let F : R2n+m → R2n+m be defined as T A λ+s−c . Ax − b F (x, λ, s) = XS e Show that a solution of F (x, λ, s) = 0 does not necessarily satisfy the KKT conditions of part (a) (or part (b)). Prove that, on the other hand, every vector (x, λ, s) that satisfies the KKT conditions must satisty F (x, λ, s) = 0. (d) Recall that the search direction (∆x, ∆λ, ∆s) generated by a Newton...
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...Nernst Heat Theorem Introduction : In the chemical thermodynamics, it was difficult to find a quantitative relation between ∆G and ∆H in chemical reaction. & To find out ∆G from thermal data i.e.… ∆H Various attempts to relate ∆G & ∆H are as follow (1) Joule-thomsan concept : They found that ∆G & ∆H values are same in case of Daniel cell :: they proposed that ∆G & ∆H are identical. (2) Berthelot’s concept : He suggested that “when heat is given out in a reaction, the free energy of System decreases. ” qt describes the qualitative relationship between ∆G & ∆H qt was found to be true in case of condensed system at ordinary imperative but failed in no. of other cases. (3) Gibbs – Helmholtz Concept : For the first time they deduced quantitative relation between ∆G & ∆H by the Gibbs – Helmholtz equation, The limitation of the Gibbs- Helmholtz equation that it does not allow to calculate ∆G from thermal date i.e. ∆H. *1* (4) Richard’s concept: In 1902 Richard measured the emf of cells at law temperature and Concluded that…… ∂ (∆G / ∂T) gets decreased gradually with lowering of temperatures. i.e. ∆G and ∆H approach each other marl closely at extremely low temperature. i.e. Lit ∆G = ∆H T -> O * The Nernst Heat Theorem: From the data of Richard in 1906, Nernst postulated that………. “For a process in condensed system...
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...I. Stoplet-Samuelson Theorem In order to understand the Stoplet-Samuelson Theorem we need to understand the Hekscher-Ohlin model first, as the theorem is within the context of that model. In that model there are two countries with different factor endowments, one capital abundant and the other one labor abundant. There are two products, one capital intensive and the other one labor intensive. There are two factors, one is labor and the other one is capital. In this context, the theorem shows that there is a positive relationship between the changes of the price of an output and the changes in the price of input factor used in a higher percentage (intensively) (for example: labor intensive or capital intensive) in producing the final product. And there is a negative relationship between changes in the price of an output and changes in the price of the factor not used intensively in producing that product. To explain the theorem, we can have a look at the real world and think about what happens when the U.S. ( a capital abundant and labor scarce country) takes part of the international trade. Would the high-waged labor lose because of international trade? This is the first thing I would ask myself, and it seems to be logical that labor will lose competitiveness with other labor abundant countries, and therefore labor would lose because of international trade. Samuelson and Stolper demonstrated that free trade lowers the real wage of the scarce factor and raises that of...
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...• Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, & 8 1. In the manufacture of a certain type of automobile, four kinds of major defects and seven kinds of minor defects can occur. For those situations in which defects do occur, in how many ways can there be twice as many minor defects as there are major ones? 2. A machine has nine different dials, each with five settings labeled 0, 1, 2, 3, and 4. a) In how many ways can all the dials on the machine be set? b) If the nine dials are arranged in a line at the top of the machine, how many of the machine settings have no two adjacent dials with the same setting? 7. There are 12 men at a dance. (a) In how many ways can eight of them be selected to form a cleanup crew? (b) How many ways are there to pair off eight women at the dance with eight of these 12 men? 8. In how many ways can the letters in WONDERING be arranged with exactly two consecutive vowels? • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2 o Exercise 2.2, problems 3 o Exercise 2.4, problems 1 o Exercise 2.5, problems 1 2. Identify the primitive statements in Exercise 1 below: Exercise 1. Determine whether each of the following sentences is a statement. a) In 2003 GeorgeW. Bush was the president of the United States. b) x + 3 is a positive integer. c) Fifteen is an even number. d) If Jennifer is late for the party, then her cousin Zachary will be quite angry...
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...you a guarantee that the statement has to be true. But when you dissect a proof right down to its base axiom, there you will have to rely on an assumption- that our intuition deems valid. I am not here to argue on the basis of the correctness in our underlying assumption of the base axiom. Proofs are merely a way to deduce results from a given premise. And the premise here is the truth of the axiom. I am uncomfortable about the fact that people are willing to accept the intuition behind the base axiom but not the intuition behind the results that follow. True, in most cases it is easier to be aware of the former- and the latter may be hard to see as obvious. A case in point would be Fermat’s last theorem. Andrew Wiles did come up with an absolutely marvellous proof of the theorem- something that puzzled the greatest minds for three and a half centuries. But in those three and a half centuries, what if some person saw it as obvious. Does he/she have to prove it in Wiles’ way or any other way to actually believe in it? Indeed Fermat himself could have been one such person. ‘The truly marvellous proof that this margin is too small to contain’ may have very well referred to a product of intuition that words find hard to explain. Let a world in which everybody speaks...
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...Pythagorean Theorem The Pythagorean Theorem is used to show the relationship among the three sides of a right triangle. In simple terms the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Since the fourth century AD, Pythagoras has commonly been given credit for creating the Pythagorean Theorem. The theorem dates back to Pythagorean triples found on Megalithic monuments from circa 2500 in Egypt and northern Europe incorporating right triangles with integer sides. The Middle Kingdom Egyptian papyrus Berlin 6619, written between 2000 and 1786 BC, includes a problem whose solution was a Pythagorean triple. Even though the theorem had been previously utilized by the Babylonians and Indians and no evidence shows that Pythagoras worked on or proved this theorem, he and his students are credited for constructing the first proof. Pythagoras was born between 580 and 572 BC on the island Samos of the coast of Greece. As a young man Pythagoras was advised to head to Memphis in Egypt to study with priests who were renowned for their wisdom. It may have been in Egypt that Pythagoras learned geometric principles that fueled the theorem named after him. Pythagoras later migrated to Croton, Calabria, Italy and established a secret religious cult very similar to the earlier Orphic cult. Toward the end of his life, Pythagoras fled Croton because of a plot against him and his followers, Pythagoreans, by a noble of Croton named...
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