...Economics Utility Functions T.C. Johnson October 30, 2007 1 Introduction “Utility” refers to the perceived value of a good and utility theory spans mathematics, economics and psychology. For example, if you prefer vanilla ice-cream to chocolate, you would assign greater utility to vanilla ice-cream than to the same quantity of chocolate ice-cream. The fact that different agents have different utilities for goods is the basis of all markets. In the context of actuarial science, the focus is on the utility of money, the study of the utility of money started in the early 1700’s with the St Petersburg Paradox. 1.0.1 The St Petersburg Paradox A player pays some fee to a casino in order to play a game where a fair coin will be tossed repeatedly until a ”tail” first appears, ending the game. The payoff of the game is 2N −1 where N is the number of times until the first tail appears. How much should the casino charge to play this game, how much should a player expect to play the game? This game was played in 18th century St Petersburg and numerous mathematicians, including Bernoulli were interested in it, since the expected payoff of the game is infinite ∞ E[X] = k=1 2 k−1 1 = 2k ∞ k=1 1 2 1 Utility functions In 1728, a Swiss mathematician, Gabriel Cramer, observed that “the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it”. 2 Modern psychology explains utility in terms...
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...Title: Utility 2, Cardinalists and Ordinalists I. Objective: Students will know 1. Cardinalists method for measuring utility 2. Ordinalists method for measuring utility II. Materials III. Procedure Warm Up: Ask Students; if you were hungry, how many bowls of borsch might you eat? Would the second bowl be as satisfying as the first? Would you want a third bowl or a fourth? 1. Cardinalists method for measuring utility A. Review of terms Utility: (корисність) Benefits consumers obtain from the goods and services that they consume. Total Utility: The amount of benefit consumer obtains from the entire consumption of a product. Marginal Utility: The increase of total utility a consumer obtains from an additional (marginal) unit consumed. Indifference Curve: A line representing different bundles of goods and services, each yielding the same level of total utility. B. Graphical Explanation First looking at one item, Borsch. Total utility (TU) is a function of the amount of borsch (X) consumed TUX = f(X) Marginal Utility (MU) can be found by dividing the change in total utility by the change in the quantity of borsch. MUX = ∆TUX / ∆X Law of Diminishing marginal utility: The marginal utility of a good declines as more of it is consumed in a given time period. [pic] Each bowl of borsch provides less utility. By the seventh bowl marginal utility is zero, you would be just as well off without it. By the eighth bowl MU is negative...
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...someone receives from consuming commodities is called utulity.Total utility refers to the total satisfaction from consuming some commodity. For example, the total utility of consuming 10 units of any commodity is the total satisfaction those 10 units provide. Marginal utility refers to the change in satisfaction resulting from consuming a little more or a little less of the commodity. The marginal utulity of the tenth unit consumed is the additional satisfaction provided by the consumption of that unit, or in other words, the difference in total utility gained by consuming 9 units and by consuming 10 units. The significance of this distinction can be seen by considering two questions: (1) If you had to give up consuming one of the following commodities completely, which would you choose: water or the movies? (2) If you had to pick one of the following, which would you choose: increasing your water consumption by 35 gallons a month (the amount required for an average bath) or attending one more movie a month? In (1) you are comparing the value you place on your total consumption of water with the value you place on all your attendance at the movies. You are compering the total utility of your water consumption with the total utility of your movie attendance. There is little doubt that everyone would answer (1) in the same way revealing that the total utility derived from consuming water exceeds the total utility derived from attending the movies. In (2) you are compering the...
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...Ivan Moscati How cardinal utility entered economic analysis during the Ordinal Revolution 2012/5 UNIVERSITÀ DELL'INSUBRIA FACOLTÀ DI ECONOMIA http://eco.uninsubria.it In questi quaderni vengono pubblicati i lavori dei docenti della Facoltà di Economia dell’Università dell’Insubria. La pubblicazione di contributi di altri studiosi, che abbiano un rapporto didattico o scientifico stabile con la Facoltà, può essere proposta da un professore della Facoltà, dopo che il contributo sia stato discusso pubblicamente. Il nome del proponente è riportato in nota all'articolo. I punti di vista espressi nei quaderni della Facoltà di Economia riflettono unicamente le opinioni degli autori, e non rispecchiano necessariamente quelli della Facoltà di Economia dell'Università dell'Insubria. These Working papers collect the work of the Faculty of Economics of the University of Insubria. The publication of work by other Authors can be proposed by a member of the Faculty, provided that the paper has been presented in public. The name of the proposer is reported in a footnote. The views expressed in the Working papers reflect the opinions of the Authors only, and not necessarily the ones of the Economics Faculty of the University of Insubria. © Copyright Ivan Moscati Printed in Italy in december 2012 Università degli Studi dell'Insubria Via Monte Generoso, 71, 21100 Varese, Italy All rights reserved. No part of this paper may be reproduced in any form without permission of the Author...
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...Utility Scales Stan Heister Argosy University Solution-Oriented Decisions Models | B7783 Adolfo Gorriaran May 15, 2014 Utility Scales Introduction Interestingly, when a person is young the number and types of jobs in which they are willing to accept seems to be quite expansive but as we age, that number narrows due to experience, education and learned preferences. Since the author has spent in excess of twenty five years in the professional workforce, the types of positions that are attractive has tapered to a fraction of the potential positions for consideration even ten years ago. Below is a list of five positions that would be acceptable. 1. University Professor 2. Product Manager 3. Chief Learning Officer 4. University Administrator 5. Restaurant/Pub Owner Operator Objectives Contributing to the Decision The objectives or criteria that would contribute to the decision of accepting any of the five positions listed above include: Autonomy, Intrinsic Reward Potential, Personal Contribution to the Success of the Business, Leadership Role, Income Potential, Benefits, Power, Status, Impact to Society, Company Reputation and Culture etc. For the sake of brievety in creating the scale, four of these attributes will be used including: Income Potential, Leadership and Impact to Society, Intrinsic Reward Potential. Utility Scale Utility, in decision making is a subjective measure of a person’s desires versus an objective number or measure –...
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...probability of outcome i and Vi is the value of outcome i 3. If outcomes are expressed in money, utility may not be proportional to money. Instead, the concept of diminishing marginal utility suggests that as the value of the outcome expressed in money increases, the increase in utility resulting from one more dollar decreases. 4. Although it is impossible to specify any one form of a utility function is universally valid for everyone, the following functional form is convenient for illustrating problems related to decision making under uncertainty: U(V) = 100((V/Vmax)^1/k)) where n^k means n to the power k, as in Excel notation U is utility on a scale with U =0 when V=0 and U = 100 when V = Vmax V is the value of an outcome Vmax is the maximum possible value of the outcome k is a coefficient of risk aversion: k = 1 implies risk neutrality k > 1 implies risk aversion k < 1 implies positive risk preference The following graph shows a graph of the utility function for Vmax = 1000 and various values of k 5. The inverse utility function is derived by solving the utility function for V. It gives the value V which has a given utility U: V(U) = Vmax (U/100)^k 6. If a prospect consists of several outcomes, each having a value Vi, a utility Ui, and a probability Pri, then the expected value for the scenario is Ev = Pri * Vi and the expected utility of the scenario is Eu= Pri * U(Vi) 7. The certainty...
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...(1) Electric utility bills. An electric utility company can estimate with reasonable certainty the expected revenue in a given period by taking into consideration some of the following: customer habits, average historical trends, demand and supply forecasts, and environmental changes. The electric utility industry effectively uses an insurance industry concept—the law of large numbers, to determine with certainty, expected revenue. The law of large numbers states, as the number of participants (customers) in a risk class (low, medium, high kilowatt users) increases, the expected outcome (usage for specific class) remains the same but the standard deviation (variability of usage) continues to drop until the probability that the average outcome (average usage) will be different from the expected outcome (expected usage) becomes negligible. This concept is conceptually similar to the Central Limit Theorem, and thus illustrates on average, the more observations per class, the more the usage tends to be bell-shaped and this usage is used for basing revenues per class. This is one way how the utility company can determine period-end revenue. Another way is if customer usage is consistent from period to period it can base reported revenue on actual meter readings. The unreported usage in December would be reported in January, and overall revenues for this year would not be materially misstated. The utility company can also adjust for seasonal changes in demand (i.e less usage in summer...
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...Utility means satisfaction which consumers derive from commodities and services by purchasing different units of money. “Ineconomics, utility is a measure of satisfaction;it refers to the total satisfaction received by a consumer from consuming a good or service. Utility is often affected by consumption of various goods and services, possession of wealth and spending of leisure time.s CONSUMER BEHAVIOUR • It is the study of how people buy, what they buy, when they buy and why they buy. • It attempts to understand the buyer decision processes/buyer decision making process, both individually and in groups. • It also tries to assess influences on the consumer from groups such as family, friends, reference groups, and society in general. • The theory of consumer behavior in managerial economics depends on a) Budget • constrained by income and the price of the goods, • The budget constraint specifies the combination of goods the consumer can afford to buy. b) Preferences • Economists use the concept of utility to describe preferences. • There are some assumptions of consumer behavior theory like :- a) rational behavior b) clear cut preferences • Consumer behaviour can be explained using two main approaches: 1. Marginal Utility Theory (The Cardinalist Approach); and 2. Indifference curve Analysis (The Ordinalist Approach) 1. MARGINAL UTILITY THEORY (THE CARDINALIST APPROACH) • developed by Alfred Marshall who introduced an imaginary unit called the...
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...Overview Combined water and sewer rates in Portland, Oregon are among the highest in the United States. A 2007 survey by Black & Veatch put Portland No. 1 on the list of 50 largest cities water and wastewater survey and No. 6 in 2010.[1] A proposed five year rate increases which started in July, 2011 by the Portland Water Bureau is likely to push Portland's water bills significantly above the average for the 50 largest U.S cities. Portland's combined water and sewer bill would likely total $346 by the year 2015.[2] Quarterly bills for typical residential customers have risen from $74 to $84 in July 2011 following a 13% increase by the Portland Water Bureau.[3] These spiking increases are as a result of a Federal regulation by the Environmental Protection Agency effective 2014 which requires drinking water sources to be guarded against the chlorine-resistant parasite, cryptosporidium which Public Water Bureau of Portland believe to be non-existent in the pristine waters of the Bull Run. About 25 percent of the water rate increases is tied to the Environmental Protection Agency's mandates that Portland deal with cryptosporidium which the City of Portland initially contested but lost. The argument of Portland city authorities is that the city’s water which is drawn from the pristine Bull Run watershed which is pure and clean and does not need any expensive treatment to eliminate any pathogens which evidently is not present in the water.[4] The EPA is however not taking any...
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...Based on the marginal utility theory to analyze students’ demand for… 1. Introduction:.….…………………………3 1.1 Origin of Marginal Utility Theory………………………….3 1.2 Development of Marginal Utility Theory…………………..3 2. The analysis of marginal utility theory...4 2.1 The definition of marginal utility theory………...…………4 2.2 The understanding of marginal utility theory………...……5 2.3 The main influences on marginal utility……….……………5 2.4 The paradox of water and diamonds………………………..8 3. Discussion on marginal utility theory….8 3.1 The limitation of marginal utility theory………………….8 4. Conclusion………………………………..9 5. Reference………………………………..10 1. Introduction 1.1 Origin of Marginal Utility Theory The origin of marginal utility theory can date back to Aristotle. It is widely considered that Aristotle was the first man to bring forward the idea of value in use. He pointed out that goods gain their value from personal utility, scarcity and costs. And an increase in a specific good will bring an decrease in value and the value can even become a negative one. This is the original form of the principle of diminishing marginal utility. The term marginal utility was first used in this connection by the Austrian Wieser. (Marshall Alfred 1920 Principles of economics chapter Ⅲ.Ⅲ ,p14) Adopted by Prof. Wicksteed, it corresponds to the term Final used by Jevons. His list of anticipators of his doctrine is headed by Gossen...
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... A Spatiotemporal Approach to Managing Utility Work Schedules Chien-Cheng Chou1, Yi-Ping Chen2 and Chien-Ming Chiu2 1Assistant Professor, Department of Civil Engineering, National Central University, Taiwan; PH: 886-34227151 ext.34132; FAX: 886-34252960; e-mail: ccchou@cc.ncu.edu.tw 2Graduate Research Assistant, Department of Civil Engineering, National Central University, Taiwan Abstract As more and more utility installation and/or maintenance activities are located in highly congested urban roadways, frequent pavement utility cuts in such areas may cause more traffic disruption as well as deteriorate pavement life and quality. Utility owners normally need to obtain permits from public road authorities before commencing utility activities; however, public road authorities in Taiwan currently just issue permits without trying to coordinate and communicate with utility owners involved to schedule their utility-related activities in a more consecutive way. An information model based on the spatiotemporal objects database technique was proposed to help public road authorities identify the utility activities that might be combined together to avoid unnecessary pavement utility cuts. In the proposed model, constraints pertaining to pavement moratorium, utility clearance distance and traffic conditions were considered. The software architecture is discussed, followed by research conclusions. Keywords: Pavement, Utility cut, Utility permit, Spatiotemporal objects database...
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...San Francisco Public Utilities Commission Case Study Question 1 San Francisco Public Utilities Commission (SPFUC) is a branch of the city council of San Francisco that handles ensuring that there is water, power services, and water treatment to the city. Just like any other organization, it has its business goals that it is out to achieve. The basic goal of SPFUC organization is to provide its clients, who are the residents of the Bay area and San Francisco with wastewater treatment and high quality reasonably priced water. Additionally these goals will be achieved while responsibly and efficiently managing natural, human, and physical resources. SPFUC is facing a major challenge in handling the knowledge of its workers. Approximately 20% of the employees will be retiring, and the biggest headache is that the jobs that they do is technical, not recorded anywhere therefore they risk losing knowledge through retirement. Question 2 SPFUC is facing a critical challenge in maintaining the knowledge of its employees within the company. Following the retirement of some employees of whom a significant number carried out technical duties, SPFUC risks losing its knowledge among the employees through retirement. The situation is even in a more critical position when it comes to training new employees will be more complicated. Therefore, capturing of, managing, transferring, and sustaining consistency and accountability notwithstanding a larger influx of workers will prove a challenge...
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...Chapter 4 Logical Database Design and the Relational Model 1 Objectives • • • • Define terms for the relational data model Brief introduction to SQL Transform E-R diagrams to relations Create tables with entity and relational integrity constraints 2 Steps in Database Problem Solving Study and Analyze w/Team Interviews & Integrated Model Conceptual Model (E-R) Transformation (Six Cases) Logical M d l L i l Model (Relations) Normalization (Three Steps) Logical Model (3NF Relations) IMPLEMENTATION 3 Business Problem Advantages of Relational Model g • • • • • Can represent all kinds of information Based on Math (relations) Natural to people Relatively simple p We know how to implement it fast 4 Motivating Example • Make a list of students in the class, keeping their ID, name and phone number 5 Motivating Example • Make a list of students in the class, keeping their ID, name and phone number • You’d probably come up with something like this: p y p g ID xx yy Name Mike Mik Elisa Phone 111 222 • This is the basic structure of the relational model, a table or relation 6 Extra Assumptions • You would not repeat the same row twice • No two rows have the same ID, but they may have the same name and phone number p ID xx yy Name Mike Mik Elisa Phone 111 222 • ID would be the PRIMARY KEY (PK). 7 Now add emails … (many!) • Now you need to add the emails of each student, but you do not know how many emails • Can you come up with a solution...
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...In the movie “Crimson Tide” the two main characters, the Executive Officer and the Captain, both possess ignorance on what should be the right thing to do for SS Alabama. The captain possesses invincible ignorance and the executive officer possesses vincible ignorance which afterwards shifted to invincible ignorance. The captain’s duty as the chief of SS Alabama is to carry out whatever mission given to him by the command post. He should carry out his mission at all cost even if he needs to make his subordinate undergo very strict measures. As the chief of SS Alabama, everyone depends on him that he shouldn’t perform mistakes in delivering protocols for if he committed a mistake he might risk the lives of the crew of the submarine. Because of this, the captain becomes ignorant of what is the proper thing to do. He has always remained true to his duty as the chief of the submarine which blinded him of the truth. His ignorance is invincible because his doings are based on his responsibility as the captain. He need to execute every protocol to him because it is his duty to do so, it will be hard for him to dispel this because there are lives that would be risked if he failed to accomplish his duty. He also need to response quickly on protocols for the sake of Alabama, he is not aware that he needed enlightenment. On the other hand Executive Officer possesses vincible ignorance. His duty was to repeat the duty of the captain in order to concur the protocols. At the movie he seemed...
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...Introduction Utilities are the companies involved in the production, delivery and service of natural assets. The increasing demand for utility services, particularly for electricity, is leading to the growth of the sector. The utilities sector is highly regulated as the essential supplies cater to basic human needs, and governments try to ensure the prices of these supplies stay within reasonable limits. The utilities try to increase prices through the filing of rate cases. The investments and costs incurred for the modernization and maintenance of reliable services are recovered through these rate cases. As per a recent U.S. Energy Information Administration report, global energy use will increase to 770 quadrillion Btu in 2035 from 505 quadrillion Btu in 2008. The majority of this usage is expected to come from countries outside the Organization for Economic Cooperation and Development. The energy market of non-OECD nations has a larger scope for improvement compared to the more mature OECD nations. Utilities can be broken down into three main industries: ← Electric Utilities The EIA reports that electricity consumption in the U.S. will increase from 3,841 billion kilowatt hours in 2011 to 4,930 billion kilowatt hours in 2040, increasing at an average annual rate of 0.9%. For the fuel type in energy generation, renewables and natural gas will play an increasing role while coal and nuclear power will gradually fall out of favor. Natural gas-fired...
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