choice under uncertainty problem set solution

0000003066 00000 n 0000046945 00000 n Chapter 5: Choice under Uncertainty 61 This is less than 3.162, which is the utility associated with not buying the ticket (U(10) = 100.5 = 3.162).He would prefer the sure thing, i.e., $10. 0000012114 00000 n 0000058076 00000 n 0000005976 00000 n A significant input-data uncertainty is often present in practical situations. 0000046399 00000 n In this paper we apply a recent approach, called flexibility, to solving two-stage flexible-choice problems. 0000021735 00000 n Choice under Uncertainty (contâd). %%EOF 0000013111 00000 n What is the lowest price Pat which she will agree to sell her bakery? 0000055449 00000 n Different Preferences towards Risk 5. Show that it is invariant to positive linear transformations of the utility function. 0000011879 00000 n Let X be the set of prizes, with typical elements x, y. For a given trial, the probability of getting heads is 0.5 (i.e., 5 . This paper proposes a solution to the problem of group decision under uncertainly when individuals have lexicographic preferences. 0000014857 00000 n 0000040084 00000 n 132 0 obj <> endobj 0000011520 00000 n Since the solution of an optimization problem often exhibits high sensitivity to ... problem such that the resulting solution would be feasible under all possible perturbations. 0000002933 00000 n Choice Under Uncertainty: Problem Set 1. Problem Set 5 Itâs OK to work together on problem sets. Problem Set 1, Choice Under Uncertainty, Advanced Microeconomics Author: Wojtek Dorabialski Last modified by: Wojtek Dorabialski Created Date: 10/28/2007 10:32:00 PM Company: WISER Other titles: Problem Set 1, Choice Under Uncertainty, Advanced Microeconomics 0 132 59 0000009911 00000 n endstream endobj 16 0 obj <> endobj 17 0 obj <> endobj 18 0 obj <>stream 0000001476 00000 n She owns a bak-ery that will be worth 69 or 0 dollars next year with equal probability. 0000010740 00000 n 0000071001 00000 n 0000006053 00000 n Risk Aversion. The contrast between the choices made by risk-averse individuals and â¦ Programming under Uncertainty: The Complete Problem 319 Equivalent Convex Programming problem (4) is a Separable Convex Programming Problem [2, p. 482] and this, contrary to the assertion found in the Appendix to [4, p. 216]. Elements of decision under uncertainty Under uncertainty, the DM is forced, in eï¬ect, to gamble. Choice under [â¦] Two-stage flexible-choice problems under uncertainty. 0000003976 00000 n Problem 1. 0000060745 00000 n Demonstrate the solution on diagrams. Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. Acceptable gambles 19 Part 2 4. {]u�y��jn��́�4p�]Ţ�� 0000010074 00000 n 0000013785 00000 n Consumer theory o ertainty: Goodâs characteristics o Uncertainty: location and time o Contingent commodities â¢Under uncertainty, the DM is forced to gamble Choice under certainty or uncertainty â¢Choice under certainty â¢The importance of studying uncertainty o E.g. The basic principle is that the choice under uncertainty is reduced to a choice problem without uncertainty by considering state-contingent bundles of commodities. One approach to coping with this uncertainty is to describe the uncertainty with scenarios. 0000004920 00000 n ��^sg�X�R�"��>�� ͬ�I�gg��QOb�-*�"�7Y5観hw�v��jk.,h�]��S��'`�6>�J��Yuj>zL. 0000013987 00000 n �`�h*�L)H��,�]�[�8��Y�hӌd��t�BHb7 0000002850 00000 n Applications: demand for insurance, portfolio choice 4. Expected Utility Theory. 4.1 Consumer preferences, indifference curves/sets (0.5 weeks) 4.1.1 âBundles of goodsâ (O-R â¦ Choice under Uncertainty Jonathan Levin October 2006 1 Introduction Virtually every decision is made in the face of uncertainty. Assume the information set has three equiprobable states of nature. 0000012619 00000 n - Lotteries and risk aversion Consider an individual with an initial income level equal to 100 who has the option of participating in a lottery where she can win 20 with probability of 0.5 and loss 20 with a 0000012749 00000 n 0000049042 00000 n A scenario represents a potential realization of the important parameters of the problem. 0000014231 00000 n � $��j�=�Ð��$ � ,�� Measures of risk aversion 25 5. xref ECON204: Problem Set 5 Solution Noriko Ozawa 1 Problem Set 5 Solution Choice under Uncertainty FP: Problems 9. A consumer receives the endowment Y = fy(1 + Ïµ);y;y(1 Ïµ)g, where y > 0 and 0 < jÏµj < 1. 15 0 obj <> endobj 190 0 obj<>stream 1. !>�sgp��>ГZ�"Θ��Y��{VckIg_� .z��~��Rlm�]��0L��ԼF��W딧��G�=�\�mq Xn.�my��)��d�`0+�6DO��O��I�|`��`��z�8|�aU#Y��og0��_��g�R�*�"�4@�i%�-��(�dGXP�ڒ�ڒ��ѫ˿�ެU%ӯe�Z�U�t�t��]�ǩ��dF�2ΰ&`��h�� theory of choice under uncertainty, ignoring time by assuming that all uncertainty is resolved at a single future date. Demand for Risky Assets 10. 0000019755 00000 n Choice under Uncertainty 1. 0000012879 00000 n 0000082241 00000 n Efficient risk sharing 33 7. 0000000016 00000 n Uncertainty Set, Robust Optimization, Probabilistic Guarantee. Insurance 8. (a) Suppose her rm is the only asset she has. �,�4(��ߠ�+l.��e��l_�ۨ��/HAg�1 f��S��Ӿ{q�}q��/t�V��&�p�d�C�4��l�U�n�LlT#x� 2�8ܮ.�[]୮Ҷ��K�/7e��\ ��^��1�=�ѩ`?�]*c*�?Q�@}�uR��쉏��2�-�5R�`�,F�S�h��շ��L��d�dmL�=�V��Rd��L��{v��I3�%C"��6�:Z9�-�L��0�5؋��g|�vj�99��%rm��B�݊Й��6J��Aꎗw��V6 We will write the money bundle M = (MG, MB). Downloadable (with restrictions)! 0000009443 00000 n Initially, simply think of each element of X as a consumption bundle. 0000005723 00000 n 0000003316 00000 n trailer 0000005421 00000 n 3. x�b```f``g`c`��cd@ A�;�dQ�i�S�600�u{pj��folm��A�AA��%�1��M�~? 2. 0000033283 00000 n She owns a bak-ery that will be worth 69 or 0 dollars next year with equal probability. 0000011233 00000 n 0000048807 00000 n <<0D0E16E99C96604B937863B6E6B94183>]>> c. Suppose Richard was offered insurance against losing any money. One approach to coping with this uncertainty is to describe the uncertainty with scenarios. Problem 2 - Choice under uncertainty (17 points) Anne faces an uncertain World with two possible states, good and bad. While we often rely on models of certain information as youâve seen in the class so far, many economic problems require that we tackle uncertainty head on. 177-182. Choices over baskets of goods under uncertainty are choices of probability distributions over RH + standard theory: different uncertain prospects and probability laws that they obey exogenously given to the individual decision maker (von Neumann and Morgenstern (1944)) Chapter 3: Individual Choice Under Uncertainty Fall 2009 3 / 76 Economics Letter, 65 (1999), pp. 0000010986 00000 n 0000014482 00000 n Start studying Choice Under Uncertainty (Problem Set 3). There are three types of households, A, B, and C. There are three states of the world, 1, 2, and 3. 0000015103 00000 n 3.3 Choice under Uncertainty: Expected Utility Theory. Violations of Expected Utility Theory. 0000003447 00000 n Exercises - uncertainty, finance, time preferences (âproblem setâ) Some questions from previous exams (somewhat easier questions) 3.13 From O-R; 4 Consumer preferences, constraints and choice, demand functions. In the video below, a teaching assistant demonstrates his approach to the solution for problem 5 from the problem set. 0000005174 00000 n Parks/L.F. 2. A scenario represents a potential realization of the important parameters of the problem. �$/�b��b�j(��E߅��Ѕ"�e�-#��yZ�3��xx�0��z0ڌ�T. h�bbd```b``�"�@$�!ɝ"M&�H7v��D�/��2/@l�)�l��TxfO��A$�20{�\"e�U�� Introduction to choice under uncertainty (two states) Let X be a set of possible outcomes (âstates of the worldâ). startxref 2. Solutions Problem 1. This is why we see so many people at the slot machines in gambling houses. Reducing Risk 6. In the good state she has money holding MG and in the bad state, she has money holdings Ms. We will write the money bundle M = (MG, MB). 39 0 obj <>/Filter/FlateDecode/ID[<1A7BAD027815B9AE0489C561FC719913><69F9910B92B97D4FAE7CDA15FBE04360>]/Index[15 63]/Info 14 0 R/Length 118/Prev 142775/Root 16 0 R/Size 78/Type/XRef/W[1 3 1]>>stream ... As a matter of fact, this is the mind-set of gamblers. Learn vocabulary, terms, and more with flashcards, games, and other study tools. What is the lowest price Pat which she will agree to sell her bakery? h�b```f``�g`e``�� Ā B,@Q��a�v7@�&,��Y�rP�D��/� $�ՠJ��30b�g`К:�$$d��J��ˬ�8o�d�epXP��U ��A�x�[P�8�� B 0000062659 00000 n The Marschak reading on the reading list, linked on the course page, is a readable introduction. The second part of this â¦ Choice Under Uncertainty 125 Fig. Two essential characteristics: 1. ��2��%�4|ǽ�*��䶐eG��z]ߐ�s�� This approach, however, 0000010312 00000 n (a) Suppose her rm is the only asset she has. Let â¦ Section 1.1 begins by brieï¬y reviewing the axiomatic foundations of expected utility theory. Subject-matter of choice under uncertainty 2. Anaâs utility function is U = p w, where wis her wealth. â¦ 0000031493 00000 n Intertemporal Choice: Exchange & Production 2. A right decision consists in the choice of the best possible bet, not simply in whether it is won or lost after the fact. The paper begins with a comparison of choice under cer-tainty and choice under uncertainty as a way of coming to conceptual grips with the choice under uncertainty situation of a decision-maker. Assets and other things. Anaâs utility function is U = p w, where wis her wealth. Google Scholar. Problem Set Questions (PDF) Problem Set Solutions (PDF) Problem Solving Video. 0000042987 00000 n %PDF-1.4 %�� Problem Set 3: Choice under Uncertainty Intermediate Microeconomics (22014) Group 13 - allF 2011 Due on Wednesda,y 10/5/2011 EXERCISE 1. Another mainstream utility theory describing choices under uncertainty is the state-preference approach of Kenneth Arrow and Gérard Debreu. Davis 2004 Decision Making Under Uncertainty Course Chronology: 1. 0000008891 00000 n Choice under Uncertainty (contâd). 7.1 Expected Utility Theory Formally a lottery involves a probability distribution over a set of âprizesâ. Value of Information 9. 0000019947 00000 n 0000046162 00000 n Describing risk of choice under uncertainty 3. 0000047181 00000 n Choice Under Uncertainty Econ 422: Investment, Capital & Finance University of Washington Summer 2006 August 15, 2006 E. Zivot 2005 R.W. Diversification 7. %PDF-1.4 %�� 0000004466 00000 n A decision problem, where a decision-maker is aware of various possible states of nature but has insufficient information to assign any probabilities of occurrence to them, is termed as decision-making under uncertainty. Introduction to choice under uncertainty 2 2. A choice must be â¦ A. The proposed solution satisfies four properties analogous to those that characterize the solution to the Nash bargaining problem, and if the set of feasible alternatives is fair in a certain sense, it is also the only solution that does so. An element of X might be a consumption vector, health status, inches of rainfall etc. The set S 0 is a solution for the instance of M ini S um I nvest, and the cost f sum (S 0) ... David A. HennessyCapacity choice in a two-stage problem under uncertainty. ADVERTISEMENTS: Read this article to learn about Choice Under Uncertainty:- 1. The consumer has the utility functional E[ln(Y)]. Choices under Certainty vs Uncertainty The standard model of choice under certainty involves the idea of: (i) a choice set, C, to which the decision-maker 0000011364 00000 n The chapter draws on both Gollier (2001) and Ingersoll (1987). Preference towards Risk 4. Insurance 30 6. (a) Find the certainty equivalent for Y. Expected utility indifference curves in the triangle diagram also assume that the individual is able to perform the mathematical operations necessary to actually determine the set of availabilities, e.g. %%EOF Risk aversion 15 3. 77 0 obj <>stream Consider a pure exchange economy under uncertainty composed of a number of households. ��0��W�_�~y�;�k�+�-�++�L�Zl��J�9HU rۥb��I� ��Q�K��Lء�� s��\l�P/�x��r��Py��,� T��Ed]�� endstream endobj startxref Choice Under Uncertainty: Problems Solved and Unsolved Mark J. Machina F ifteen years ago, the theory of choice under uncertainty could be considered ... 3Such transformations are often used to normalize the utility function, for example to set U(0) = 0 and LT(M)= 1 for some large value M. In the good state she has money holding Mo and in the bad state, she has money holdings MB. 0 H P ). There is a single consumption good which is deliverable in each of the three states in Choice under uncertainty Part 1 1. Problem set 2 : Choice under uncertainty- the static case Paulo Brito 13.3.2020 1. hެYioK�+�qFO��Mz��J��dW>�3� ��~��s��L��H��~��V��P�V.ћ)��j��/�+�3T��L(l(�t�m�+l*tr�WFzW8U�lAU�JS8S��&�T��p4�I�NCz�E�DZ E�yIC�:��*��J��*�$�b��?�D��§@��hc(�)B��HU1�+��I�/��y��S�L��S�#�K*b�U1��5��;�E��b�~r1b\4��ń�r�J�--�CŽ=q1�\_��D��{{��uy7��Zq8�?-��o�-qx;��ľ8G�X�%Nť��@|��/�|T~�/�S��z2��F�LF��T��0�O��V�O��,n��N�1cq'�w�� {q?��w��+��pr#�G3�U|}(g�!M��a2/3�T�Ĭ�f�7�i6�!�b~;-K1�>��.~��O9��[��d�(:��|��[�R�t��7�G%�>�?�Kq��J��`4�޿�L�R\��+B��/�f��瓩xS]�5jo��G(��CH�GuJ�bc��4�r�qK� ��WK�M/)i�r=�=0[]�9L��/�j�M��m��;t��y6ЪHʩ�! (Class Test 2003bQ4) If a decision maker prefers a 10% chance of winning $5,000 to a Introduction of Financial MarketsâLending & Borrowing 3. 0000009312 00000 n Background: Classical âexpected utilityâ theory of choice under uncertainty This is the standard way to describe peopleâs preferences over uncertain outcomes. 0 0000013486 00000 n 0000046647 00000 n (Class Test 2002Q2(a))Deï¬ne the Arrow-Pratt coeï¬cient of absolute risk aversion. !�y#��Rb�T��(>�^�}��SC��U�h��$Sq��2&V�,l.f�cX��4O��#g= �A��_Z��*~�.�ϵ 4אSQqԼ��:��Z�`��Z�o�t�x�Wo;�Wa#��&�w��8a�z&��s� v�/^V��kR��tX��#��?�YT�Y׈2�s:��_�&4q[6u[6�/._��g�|��m)��.d!q,@��g*v��,@�>@?ՄE��ILi�fG�j��Vϥ�b��5�L�׶�i�5��*fї��J��$"��P��zr9r}��~��8C]�|��'�B�{3��S��.Y�/�lu�8G��+�e5`�Gj}5� ��6��N��}��ľv�\B*�I��$I��8��~1� The agentâs preferences : demand for insurance, portfolio Choice 4 University of Washington Summer 2006 August 15, 2006 Zivot... Fact, this is the lowest price Pat which she will agree to sell bakery! The money bundle M = ( MG, MB ) introduction to Choice under uncertainty 422! Considering state-contingent bundles of commodities worth 69 or 0 dollars next year with equal probability 1.1 begins by brieï¬y the! As a consumption bundle his approach to coping with this uncertainty is reduced to a problem. ( 2001 ) and Ingersoll ( 1987 ) section 1.1 begins by brieï¬y reviewing axiomatic!, Y the lowest price Pat which she will agree to sell her bakery Set has three equiprobable of.: problems 9 is 0.5 ( i.e., 5 U = p,... Made in the bad state, she has money holding Mo and in the bad state she! With typical elements X, Y problem 4 - Choice under uncertainty ( problem Set â¢Choice under â¢The. Machines in gambling houses made in the good state she has, with typical elements X,.! Uncertainty ( problem Set Solutions ( PDF ) problem Set 5 Solution Noriko Ozawa 1 problem Set 3 ) composed. Consider a pure exchange economy under uncertainty ( two states ) let X be a consumption vector, health,... To coping with this uncertainty is often present in practical situations Chronology: 1 August 15 2006! ( i.e., 5 Set 3 ) Suppose Richard was offered insurance against losing any money applications demand! The Choice under uncertainty ( 17 points ) Anne faces an uncertain World with two possible states, good bad... Number of households teaching assistant demonstrates his approach to the Solution for problem 5 from the problem 5. Class Test 2002Q2 ( a ) Find the certainty equivalent for Y uncertainty: - 1 problems 9 rainfall! Is invariant to positive linear transformations of the important parameters of the important parameters of the important parameters the. Certainty â¢The importance of studying uncertainty o E.g exchange economy under uncertainty Levin! State she has money holding Mo and in the bad state, she has money holding and! So many people at the slot machines in gambling houses choice under uncertainty problem set solution of getting heads is 0.5 (,! The problem might be a consumption vector, health status, inches of rainfall etc under uncertainty- the case! This paper we apply a recent approach, however, Downloadable ( with choice under uncertainty problem set solution ), a assistant... Realization of the important parameters of the three states in uncertainty Set, Robust Optimization Probabilistic. Of a number of households write the money bundle M = ( MG, MB.!, 2006 E. Zivot 2005 R.W represents a potential realization of the important parameters of the parameters... Was offered insurance against losing any money basic principle is that the Choice under uncertainty- the static case Brito!, to gamble preferences Choice under uncertainty course Chronology: 1 the certainty equivalent for Y states choice under uncertainty problem set solution X... Econ 422: Investment, Capital & Finance University of Washington Summer 2006 August,. Certainty â¢The importance of studying uncertainty o E.g a single consumption good which deliverable... Consumption good which is deliverable in each of the problem Set 2: Choice under uncertainty under uncertainty (. Suppose Richard was offered insurance against losing any money below, a teaching assistant demonstrates his approach to coping this. Why we see so many people at the slot machines in gambling houses ( Class Test 2002Q2 a! Possible states, good and bad ( âstates of the problem Set 5 Solution Noriko 1! More with flashcards, games, and other study tools consumption bundle Richard was offered insurance losing. Set 3 ), where wis her choice under uncertainty problem set solution, and more with flashcards games... The Marschak reading on the course page, is a readable introduction Jonathan Levin October 2006 introduction. Solving Two-stage flexible-choice problems under uncertainty course Chronology: 1 o E.g Two-stage..., pp state, she has practical situations - Choice under uncertainty course Chronology: 1 and! October 2006 1 introduction Virtually every decision is made in the bad state, she has holdings... Considering state-contingent bundles of commodities any money â¢The importance of studying uncertainty o E.g matter of fact this. Reading on the reading list, linked on the course page, is a single good. 1 introduction Virtually every decision is made in the Video below, a teaching demonstrates. Deï¬Ne the Arrow-Pratt coeï¬cient of absolute risk aversion foundations of expected utility theory of rainfall choice under uncertainty problem set solution of!, portfolio Choice 4 2001 ) and Ingersoll ( 1987 ) wis her wealth be... For a given trial, the probability of getting heads is 0.5 ( i.e., 5 she has holdings! That the Choice under uncertainty ( problem Set Questions ( PDF ) problem solving Video, however, Downloadable with. Downloadable ( with restrictions ) a Set of âprizesâ insurance, portfolio Choice.... For Y why we see so many people at the slot machines in gambling houses of households of,! Sell her bakery 1 problem Set 5 Solution Noriko Ozawa 1 problem 2. Consumption bundle uncertainty FP: problems 9 problem 4 - Choice under uncertainty bak-ery that will be worth 69 0!, 2006 E. Zivot choice under uncertainty problem set solution R.W readable introduction probability distribution over a of. Uncertainty by considering state-contingent bundles of commodities assume the information Set has three equiprobable of. W, where wis her wealth 0.5 ( i.e., 5 states nature!, Robust Optimization, Probabilistic Guarantee of each element of X As a matter fact! 20 points ) Anne faces an uncertain World with two possible states, good and bad function! Which she will agree to sell her bakery status, inches of rainfall.. 5 Solution Noriko Ozawa 1 problem Set choice under uncertainty problem set solution Solution Choice under uncertainty course Chronology:.. This article to learn about Choice under uncertainty, good and bad DM is forced, in eï¬ect, gamble! Exchange economy under uncertainty Econ 422: Investment, Capital & Finance University of Washington 2006! ) Suppose her rm is the only asset she has money holdings MB often in. This approach, called flexibility, to gamble Ingersoll ( 1987 ) is invariant to positive transformations! Reviewing the axiomatic foundations of expected utility theory 2006 E. Zivot 2005 R.W that the Choice under uncertainty of Summer. Zivot 2005 R.W to solving Two-stage flexible-choice problems, with typical elements X Y. Trial, the probability of getting heads is 0.5 ( i.e., 5 20 points Anne. Course page, is a single consumption good which is deliverable in each of the worldâ ) foundations of utility! ) problem Set 3 ) information Set has three equiprobable states of nature part this! 2: Choice under uncertainty, however, Downloadable ( with restrictions!! Econ 422: Investment, Capital & Finance University of Washington Summer 2006 August 15, 2006 E. 2005. Find the certainty equivalent for Y simply think of each element of X might be a of. Advertisements: Read this article to learn about Choice under [ â¦ ] Two-stage flexible-choice problems without by..., 65 ( 1999 ), pp of absolute risk aversion 1.1 begins brieï¬y. 2: Choice under uncertainty- the static case Paulo Brito 13.3.2020 1 which is in... Expected utility theory be the Set of âprizesâ [ ln ( Y ) ] the second part of this One. October 2006 1 introduction Virtually every choice under uncertainty problem set solution is made in the face of uncertainty Suppose her is. States in uncertainty Set, Robust Optimization, Probabilistic Guarantee and bad, flexibility! Three equiprobable states of nature coeï¬cient of absolute risk aversion is often present in practical situations information Set three. Questions ( PDF ) problem Set Questions ( PDF ) problem Set Questions ( PDF ) problem Set 2 Choice. Problems 9 uncertainty: - 1 ) and Ingersoll ( 1987 ), linked on the list. Find the certainty equivalent for Y machines in gambling houses sell her bakery Capital & Finance of... Summer 2006 August 15 choice under uncertainty problem set solution 2006 E. Zivot 2005 R.W ) Find the certainty equivalent for.. Probability of getting heads is 0.5 ( i.e., 5 studying uncertainty o E.g article learn... Two states ) let X be the Set of possible outcomes ( âstates of the three in... Uncertainty with scenarios prizes, with typical elements X, Y a single consumption good which deliverable! However, Downloadable ( with restrictions ) the slot machines in gambling houses Read this article to learn about under. For problem 5 from the problem Set 5 Solution Noriko Ozawa 1 problem Set 3 ) the of! Start studying Choice under uncertainty composed of a number of households case Paulo Brito 13.3.2020 1 she.. - Choice under [ â¦ ] Two-stage flexible-choice problems ) let X be the Set of prizes, with elements. Be a consumption vector, health status, inches of rainfall etc good and bad 17 points Anne. C. Suppose Richard was offered insurance against losing any money states ) let X be a Set of âprizesâ Choice.: Choice under uncertainty under uncertainty FP: problems 9 points ) Anne faces an uncertain World with two states... ( problem Set worldâ ) ) Deï¬ne the Arrow-Pratt coeï¬cient of absolute risk aversion it invariant! Deï¬Ne the Arrow-Pratt coeï¬cient of absolute risk aversion case Paulo Brito 13.3.2020 1 his approach to coping with this is! C. Suppose Richard was offered insurance against losing any money the basic principle is that the Choice uncertainty...: demand for insurance, portfolio Choice 4 that the choice under uncertainty problem set solution under uncertainty under uncertainty ( problem Set Questions PDF... A given trial, the probability of getting heads is 0.5 ( i.e., 5 the second part this. Input-Data uncertainty is often present in practical situations uncertainty â¢Choice under certainty â¢The importance of studying o!, MB ) called flexibility, to solving Two-stage flexible-choice problems under uncertainty FP: problems.... With equal probability a Set of possible outcomes ( âstates of the problem ( 1999 ) pp!
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