ANS: A function is concave if 11 Q0 and H = 11 22− 122 R0, and strictly concave if the Question: Question 1 (1 Point) Indifference Curves Question 1 Options: 1) May Sometimes Intersect. It is a property of cardinal ABSTRACTIn this work, we introduce the star shape preferences in the pseudo -concave and semi-strictly quasi-concave functions that appear in the literature. A function f Concave and convex functions 1Concaveandconvexfunctions 1. If, for example, the mountain is a perfect dome (half of a sphere), then this condition is satisfied, so that the function defined by its surface is concave. We will be primarily interested in "interior" Groves Ledvard equilibria. -I. If in addition we assume preferences are convex (i. Matzkin and Marcel K. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Our main theorem derives concave utility from convexity of preference on the two-dimensional comonotonic cone, without presupposing con-tinuity. It is shown that preferences which are continuous, convex and uniformly proper [ Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented On dit qu'une fonction f est quasi-concave sur un intervalle I si et seulement si −f cf. More generally, a function which decreases up to a point and increases from that point on is quasiconvex (compare unimodality). quasi-concave. A strictly quasi-concave function of a single variable is single-peaked in the sense of Duncan Black (1958). New York: W. microéconomie, Utillité et convexité des préférences : Si on considère des simplex could be induced by quasiconcave preferences. %strictly convex )uis strictly quasi-concave. function, U = U(x,y), that is strictly quasi- concave, which means it forms a strictly convex set for the behavior of an individual who has homothetic preferences Market equilibria for homothetic, quasi-concave utilities and economies of scale in production Kamal Jain∗ Vijay V. Quasi-concave functions and concave functions. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. Preferences are represented by the increasing and strictly quasi-concave utility function U(g,h,x), where g is the level of the local public good in the consumer's community, h is housing services, and x is a composite numeraire commodity. A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set. Analytical Problems . Thus, starting at the symmetric Nash equilibrium, countries mutually gain by symmetrically Does Everyone Have Quasi-Hyperbolic Preferences? by Maribeth Coller, Glenn W. , all agents of the same type have the same maximization problem, and thus, ensure that the hypothesis that individual preferences are convex is testable using a ﬁnite number of binary choices, we show that such data do not allow us to discriminate between the hypotheses that voters have (strictly) concave versus quasi-concave utility representations. This is equivalent to saying that indifference curves are convex to the origin, or that MRS is decreasing, or that the utility function is quasi-concave. c. ) Distributional comparative statics is the study of how individual decisions and Convex preferences can exhibit indifference curves with flat spots, strictly convex preferences cannot. Social choice 3Observe that any concave function is also quasi-concave. quasi-concave utility function can be transformed into a concave utility function. may sometimes intersect. ) is important because it is directly related to questions of existence of a majority voting equilibrium. (X. So if U does not possess these properties, then W 6= U. Craven [12] considered a special case of multi-objective programming assuming that the weighted sum of the objective functions is pseudo-concave for each suitably chosen set of weights. We show that under When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. Wesay preferences aredynamicallyinconsistent ifgivensome non-negative c 1 the projection of preferences of the representative agent at t = 1 over (c 2 ,c 3 ) ∈ R 2 EQUILIBRIUM IN COMPETITIVE INSURANCE MARKETS: AN ESSAY ON THE ECONOMICS OF IMPERFECT INFORMATION* MICHAEL ROTHSCHILD AND JOSEPH STIGLITZ Introduction, 629. Read "Extremist vs. Our main result is a quasi-concave numerical representation for a class of preferences wide enough to accommodate Ellsberg- as well as Allais-type behavior. k. Concavifying the QuasiConcave August 17, 2012 address when preferences over discrete sets can If fis weakly quasi-concave then fis weakly quasiconvex. All utility functions representing convex preferences must be quasi-concave. Zame, Proper preferences, quasi- concave utility functions In this example, the commodity space is 1, (the space of square-summable real sequences); the price space is the dual space, which may be identified with I,. alent to convexity of preferences, that is, in our setup, equivalent to the quasi-. Proposition. Consider a two commodity world - X and Y. Robustness, 638-III. Vazirani, editors, Cambridge University Press, Cambridge, 2007. 3) Are Convex If The Utility Function Is Quasi-concave. ‘‘Behavioral Economics’’ Matthew Rabin (Today & Tomorrow) University of California — Berkeley Since each term on the right hand side is concave it follows from the previous exercise that preferences are convex. In convex programming it is convenient to allow concave functions to take on the value −∞ and convex functions to take on the value +∞. ,Y) is strictly quasi-concave and twice continuously differentiable. Conclusion, 648. the individual's marginal rate of substitution. 1 Concave and convex functions 1. Most of the familiar parametric densities employed in economics are log-concave: the uniform, normal, exponential, logistic, Weibull, gamma, all belong; others like the Student t densities fail to be log-concave, but are ˆ-concave. Consider the following three market baskets. Preferences and Utility Simon Board⁄ This Version: October 6, 2009 First Version: October, 2008. • This is inconvenient. (A function is . Quasi Linear Concave 44 Quasi Linear Preferences Utility function: for 1 = P0 Q T 5, 6 L T 5 Ô E T 6 Indifference curve: T 6u F T 5 Ô Note indifference curves are vertical translations of each other Also note that slope of indifference curve goes to infinity when T 5goes to 0 but does not go to zero as T 6goes to zero 45 Quasi Linear Microeconomics 1 – Lecture notes 2 LN 2 - Rev. preferences are convex (utility functions are quasi-concave) production sets are convex (production functions are concave) a number of technical assumptions a satisfied The convexity assumptions are sufficient to guarantee that the demand and supply functions are continuous in prices. b. ISBN 0-393-92702-4 The correct answers are (C) net substitutes. 2: Are her preferences convex or strictly convex? 4. Miller This chapter presents the basic elements of the standard spatial model commonly used as a framework for developing theories of legislative, electoral, and other forms of social choice and concave, but not necessarily smooth. (a) fis concave i for any a;b2Cand any 2[0;1], this system of taxation, his preferences over amounts of public goods are represented by the induced utility function, U7'(Y) = Ut(Wi -cti Y, Y). As with single-peaked preferences, we will take Pto be ordered (e. x≤ w is the budget constraint (a. E-mail: mj182@le. , x n) • Where x 1, x 2,…, x n are the quantities of each Consider a two good world, where preferences are strictly quasi-concave and the expenditure function is given by: ep p u(1 2,,). The preferences represented by x 2 1 +x 2 do not sat-isfy convexity. Example Preferences For example, we could have that given aggregates and policies, individual objective functions are strictly quasi-concave so that each agent has a unique optimal action x i (p,Y (x,p),a i) = argmax x2X i u(x i,Y (x,p),p ja i). Write the (n+1) dimensional consumption vector x as (y;z) where y is a scalar and z is an n dimensional consumption vector. Chapter 3. Furthermore, it is essentially the basis of the indivisible labor model by Hansen (1985) and Rogerson (1988), which is one of the benchmark macroeconomic mod-els. this, for . ox. Review of basic consumer theory 2. The assumption that voting data arise from the maximization of a (quasi)concave utility representation generates nontrivial testable restrictions on the location of voter ideal points preferences to make collective decisions, and concerns issues such as fairness and e ciency. quasiconcave preferences. Non-printable version on the web and DIMAP Workshop (Warwick University) introducing the book. budget. Consumer Theory: Preferences A indifference set or indifference curve contains the bundles that provide the same level of satisfaction or welfare for a given individual. work. – Typeset by FoilTEX – 4 u is strictly quasi-concave ⇔ t is strictly convex. Hal R. 15 Mar 2017 While the investor's risk aversion is governed by a standard utility function, the ambiguity preferences are thus represented by a quasiconcave In speaking of a quasi-concave function, some specific domain of definition, as the basic Weak Axiom of Revealed Preference follow directly from quasi-. In this case, the solution is a corner solution because the agent's budget will be spent entirely on the "good". (x) consists of all Preferences are said to be convex if, for any A utility function is quasi–concave if and only if. Vazirani† Yinyu Ye ‡ Abstract Eisenberg and Gale (1959) gave a convex program for Convex Preferences =⇒ Upper Contour Set is Convex. Rasmusen Abstract We revisit a classic question of Fenchel from 1953: Which quasiconcave func- Quasi-concavity and quasi-convexity Definition: a function f defined on a convex subset U of Rn is quasiconcave if the upper level set is a convex set for every real number a. Keywords: Time-inconsistency, Quasi-geometric discounting, Hyperbolic discounting, Panel data JEL classification: D91, C23. Setup Some assumptions, which will be used selectively: (A1) Assume that u(⋅) is a continuous utility function which represents a weakly monotone, 1 If f is quasi-concave, the set of maximizers is convex. monotone, continuous and quasi-concave utility function u(q). Show a quasi-concave can be convex and you're good. Concave in p (consumer adjusts to changes in prices doing at least not worse than linear change); Continuous in p and u (from continuity of px and h(p,u)). Since all the logarithmically homogeneous utility functions U are strongly concave on X under the strict quasi-concavity assumption, and since the demand functions derived from the logarithmically homogeneous utility functions are 1-homogeneous with respect to prices, if we ); the consumer™s preferences have entirely conventional properties, including monotonicity and strict convexity, and are represented by a continuous utility function, u(x), or simply u, which is everywhere continuous, strictly increas-ing, and, except where otherwise stated, strictly quasi-concave and smooth. , temporary stress relief) with the future utility of non-smoking (long-term good health After the study in Lecture Note 1 of consumer preferences and their representation by a numerical function, the utility function, after the definition in Lecture Note 2 of the analytical notions of concavity and quasi concavity, and after the presentation in Lecture Note 3 of the A Revealed Preference Test of Quasi-Linear Preferences Marco Castillo Mikhail Freery August 2016 Abstract We provide criteria for a set of observed choices to be generated by a quasi-linear preference relation. Norton & Company. Concave functions of two variables While we will not provide a proof here, the following three definitions are equivalent if the function f is differentiable. The consumer is born with these attitudes, i. 1. chose it in 30% of the triples, suggesting strictly quasi-concave preferences. Basket Good Good A 2 8 B 10 2 C 6 5 If Basket A and Basket B are on the same indifference curve, preferences satisfy the usual assumptions, and the indifference curves have a diminishing marginal rate of substitution, Our main result is a quasi-concave numerical representation for a class of preferences wide enough to accommodate Ellsberg as well as Allais-type behavior. If preferences of each type are convex, than any competitive equilibrium is equivalent to a type-i-identical equilibrium. then. Preferences are risk averse if for all y,e(y) ≤E[y]. GS/ECON 5010 Answers to Assignment 1 February 2005 1. A characteristic feature of quasi-linear preferences is that they are not strictly Single-Peaked and Single-Crossing Preferences The classic median voter theorem is formulated under single-peaked (quasi-concave) preferences. There is a similar characterization for quasi-concavity. • We make the assumptions about preferences that utility functions . d. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter?s preference is strictly quasi-concave. Increasing-ness and quasi-concavity are ordinal properties of U. with “taste for variety”) have quasi-concave indifference curves, which in A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set. Instead of being concave, then, it's generally concave but not perfectly so at every point in the graph, which may have minor sections of convexity. For any two bundles xand x0, the following equivalence holds, x x0,u(x) u(x0). preferences are a ‘primitive’ in classical consumer theory. According to duality theory, pro t functions are concave in output price and cost functions are monotonically increasing and concave in input price. R. of preferences in decisions and games under (quasi-)convex/concave The right half of figure 3 shows quasi-concave indifference curves. punch in the face). I. and current resources simply have to be divided into current consumption and savings. W. Show that a. We now look at the properties of the utility representations of convex preferences. These facts allow to treat with utility functions not di erentiable (but however, existing in real contexts) and to obtain a multi-valued demand function, because quasi-concavity is weaker than concavity and than strictly concavity, too. uk Consultation hours: Friday, 2-3pm, Weeks 1,3-8 (MT) 25 October 2011 Macro for Development Class 3 1 Properties of Preferences 1. Paulo Klinger Monteiro. 2) Are Contour Lines Only Of A Linear Utility Function. Concavity 2. E. Previous research has shown that, in case of decisions under uncertainty, the compliance with this property (jointly) depends on the concavity/convexity of the imprecise probabi- listic model with respect to the decision variable and on the attitudes towards imprecision of the decision maker. We say that a consumer has Quasi linear preferences over these two goods if such preferences can be represented by utility function of the form [math]u(x, y) = v(x) + y[/math] Demand function is the soluti Reading: [Simon], Chapter 21, p. Deﬁnition 4. Distributions like about the functional form of the utility functions, and only require standard assumptions that it be quasi-concave, non-decreasing, and strictly increasing in at least one argument. shift when prices change. a computable way), we will usually assume that preferences can be described by a utility function. Among others, Very often, we also assume that preferences are convex. ) • See graph in notes for convex preferences which are not strictly convex [G-2. Convex preferences imply a quasi-concave utility function but not every quasi-concave function is concave. 1 Preferences • Not all preferences can be described by utility functions. Their behavior on antimatroids was studied in (Kempner, Muchnik 2003), where they were applied to constraint clustering. 2. X: set of alternatives (choice set or domain). Not very realistic No attention to psychology EC 701, Fall 2005, Microeconomic Theory September 28, 2005 page 82 • Preference relations % are deﬁned on X ⊂Rn +. g. 1) A) Must every quasi-concave function must be concave? If so, prove it. But, in contrast, a quasi-concave function is not necessarily continuous on the interior of its domain and the sum of quasi-concave functions is not quasi-concave in general. The quasi-concave functions which arise in consumer theory share much in common with concave functions, and quasi-concave programming has a rich duality theory. (c) Quasi-concave, but not strictly quasi-concave and not strictly concave. Indeed since ln(1 )+xj is a strictly concave function, ( )ux is strictly concave and so preferences are strictly convex. D. 28 This video introduces widely used concepts of quasiconcavity and quasiconvexity in economics through a mathematical as well as graphical explanation. Quasi−linear peferences with Auspitz−Lieben−Pareto complementarity Christian Weber Seattle University Abstract I show that if preferences are quasi−linear (non−linear in goods x1, …, xn but linear in xn+1) and the sub−utility function defined over [x1, …, xn] is strongly concave and exhibits OPTIMAL TAXES AND THE STRUCTURE OF PREFERENCES BY ANGUS DEATON1 If optimal tax theory is to be the basis for calculating tax rates, a close understanding is required of the relationship between the structure of preferences and the configuration of optimal tax rates. indifference curves in a probability simplex, i. Par ailleurs, on suppose que : 1. Q Are the preferences represented by the following utility function strictly monotonic? Convex? u(x 1,x 2) = (x 1) 2 +(x 2) 2 In each case, explain brieﬂy. When this is not true, consumer demand functions are not continuous: a small change in price will lead to big jumps in quantity demanded. This utility function is concave, therefore, quasiconcave. Then, indirect utility function U (p;a i) The preferred policy or the (political) bliss point of (preferences) dx dy MRS The SOC (sufficient condition) is that is diminishing throughout the indifference curve (strictly convex indifference curve, strictly quasi-concave utility function). 1 Since it is well-understood that the quasi-concavity of an additive social welfare function necessitates, by the theorem of function. Warning: convex preferences are represented by quasi-concave utility functions. Convexity and concavity (and quasi-convexity and quasi-concavity) of functions play an essential role in economics first because they play an essential role . TESTING STRICTLY CONCAVE RATIONALITY'" by Rosa L. Then, inverse demand functions can be obtained by solving the following problem: U(x) = Minimise r {V(r): r'x = 1}. We assume that the consumer operates a technology which has (weakly) decreasing returns in its input, capital (that is, savings from last period). In additlon, he imposed some contlnulty and boundedness condltions on the approximate derivative of Vu to guarantee that the demand function 1s approximately differentiable on the comp1ement of Under our assumptions, m i:ℝ + L →ℝ can be taken to be a continuous, strictly monotone and strictly quasi-concave function. wills@economics. strict convexity. A) If g is a strictly increasing function, then h is a quasi-concave function. (x'y) is a feasible allocation. Decreasing returns leads to “more convexity” rather than less and if uiis (strictly) quasi-concave and fis concave, then euiis (strictly) quasi-concave. In what follows, we shall call anyone who behaves this way a classical agent. ⊳Equivalently,afunction 𝑓:𝑆 continuing education program in behavioral economics, Atlanta, January 5-7. 6, and assume that α 1 = α 2 = 1. Downloadable! The Shafer and Sonnenshein convexity of preferences is a key property in game theory. Problem 4. It is important to note that the condition has to be satisﬁed by the political preference function. It is a property of preferences. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries. Quasi concavity utility function represents the consumer preferences it's how consumer respond to change in good amount or cost. His preferences over bundles in X are represented by the Let f be a multivariate function defined on the set S. Elisabet Rutström† December 2005 Abstract. The quasi bliss point of the social ordering chosen by an Arrovian welfare function for a pro…le of preferences is the outcome of the generalized median rule applied to this pro…le of quasi bliss points. a solution to the first order conditions (7) is that each profit function nH is quasi-concave in pj and locally concave in the neighborhood of the equilibrium price. • We make the assumptions about preferences that utility functions require. -Il. 1) is called quasi–concave. We need to make sure that both x 1 and x 2 are 0 because 1) the p function is not de ned and 2) we do not want to talk about negative Other Properties - never used convexity of preferences (or quasiconcave U(x)) so there are more Differentiable - if we assume strictly concave preferences (U(x) strictly quasiconcave), then V(P,I) is continuous and differentiable hard to prove, but needed for Roy's Identity (a) Quasi-concave, but not strictly quasi-concave and not concave. Logarithmic Quasi-Homothetic Preferences PAOLO BERTOLETTI§ Dipartimento di economia politica e metodi quantitativi¥ University of Pavia Abstract We study a class of symmetric, quasi-homothetic preferences that result in demands logarithmic in own prices when these have a negligible impact on aggregate price organization with lexiographic preferences?) to a quantity f ¡P iz i ¢ of the public good. ∑. We need to show that uis a quasiconcave function if the consumer’s preferences are convex. Consider that the consumption set is X = Rn+1 S. This may n ot be equilibrium ·if ¢1 is continuous and quasi-concave in 8 and quasi-convex in W for each (8 ,w) in a closed convex set in Rn . . Three fundamental axioms are the following: 1. Question: What does the term, quadratic quasi-linear utility, mean? Quasilinear preferences. As is argued in the literature (e. This also means that if a monotonic transformation of f is concave, then f is concave. B. Read "Interactive evolutionary multi-objective optimization for quasi-concave preference functions, European Journal of Operational Research" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. 1: Introduction This chapter is interesting and important. Utility Function for Strictly Convex Indifference Curves: 1. If the answer is affirmative, the methods developed here allow to reconstruct bounds on indifference curves This function is quasi-concave. The twist is that while concavity Differing from existing works in the area, our focus is on quasi-concave choice functions rather than concave functions and this enables us to cover a wide range of utility/risk preference The robust choice function is increasing and quasi-concave but not necessarily translation invariant, a key property of monetary risk measures. Slightly confusingly, a utility function that satisfies (2. Edition. The proof of the first part is an exercise, and the proof of the second part is symmetric with the proof of the first part. Suppose the consumer’s preferences are represented by function u. In microeconomics, quasiconcave utility functions imply that consumers have convex preferences. 15 Mar 2017 of the involved quasiconvex and semicontinuous functions. Exercise: quasi-concavity a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. The latter implies that the payoﬀ functions of the take the conﬂicting preferences of the members of a group and arrive individual objective functions are strictly quasi-concave so that each functions, some of which are not quasi-concave. It also helps to answer a question you may well have been asking ever since we studied quasi-linear preferences right at the beginning of the book. not only the log-concave ones, but ultimately the class of all quasi-concave densities. are convex if the utility function is quasi-concave. . are contour lines only of a linear utility function. Necessary and sufficient conditions are presented. The duality theorem we proved above guarantees that W is increasing and quasi-concave. Rationality . Rationality of preferences is suﬃcient to keep indiﬀerence curves from crossing. 1 Consumer Choice Theory Four building blocks 1. Functional form, aggregation, and separability 3. The property of convexity of preferences, on the other hand, implies that t/(x 1, x 2) is quasi-concave (and, similarly, strict convexity of preferences implies strict quasi-concavity of U). CONSUMER THEORY & DEMAND 1. JENSEN Department of Economics, University of Leicester, Leicester LE1 7RH, UK. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voters preference is strictly quasi-concave. Adjective . For the finite number of agents and the finite dimensional strategy MSc in Economics for Development Macroeconomics for Development Week 3 Class Sam Wills Department of Economics, University of Oxford samuel. quasi-concave functions is not necessarily quasi-concave. of type q has strictly quasi-concave preferences represented by the utility function Up(c0,c1;q), where Up is increasing, strictly concave and twice differentiable in (c0,c1;q). ) August 14, 2014 Christopher Connell and Eric B. Otherwise hypotheses chosen by the econometrician for practical Un exemple d’une fonction d’utilité quasi-linéaire est : où b et sont des constantes positives et . 1 Handout on Consumer Theory Susan Athey, Fall 1998 I. Instead of assuming the usual monotonicity we suppose that our preferences are monotone with respect to first order stochastic dominance. quasiconvex; Related terms . Preferences and Utility. If (x, y) is a Pareto optimal allocation, then there exists λ ∈ RI. 3. Utility is time-additive with quasi-geometric discounting, and the period utility function is strictly concave. 505-522. So, can we say that an utillity function is quasi-concave if the indifference curve is convex (and vice-versa)? concave. find evidence in favor of consumers' preferences being time inconsistent. ANSWER: c POINTS: 1 2. In addition it will be strictly pseudo convex. Strict quasi-concavity for v(. But a quasi-concave function cannot be concave, for some quasi-concave functions, like F’BG’DH’, may lie below the line segment joining the points on the function at x = x 1 and x = x 2, which a concave function cannot. (b) Strictly quasi-concave, but not concave. g and its alternatives. They are meant to be supplements for those attending the lectures (and listening to the clarifications, caveats, and discussion), not as stand-alone documents. During the campaign, parties choose simultaneously their dis-tributive policies to maximize the expected vote share, but they care also about voters’ other-regarding preferences. quasi concave and differentiable and assuming an interior solution for optimal from ECONOMICS 211 at University of Waterloo Microeconomics Summary Rebecca Sela October 19, 2005 Microeconomics is based on the decisions of individual agents. Hazen (1983) provides a rigorous analysis of this concept. Nash equilibrium exists, possibly in mixed strategies, but if prefer- ences are quasiconvex in Exhibiting the (quasi-)concavity of utility and production function. Continuous Preference Relation =⇒ UCS and LCS are Closed (contain their boundries. Pour démontrer que c’est une fonction d’utilité quasi-linéaire comme décrite ci-dessus, nous devons montrer que la fonction v est croissante et concave. To represent them formally, we use the at least as good as binary relation %on X; and for any two bundles x1 and x2, we say that, 1. A utility function is strictly quasi–concave if and only if the preferences represented by that utility function are strictly convex. (In all answers where you provide a counterexample, you must show that your example is really a counterexample. The theory that people behave towards quasi-(“ to some degree ”) + concave. Individual utility is allowed to vary depending on individual, household, and dynasty specific welfare function is quasi-concave in the overall trade barrier when that barrier takes a symmetric value for each direction of trade. biguity preferences are thus represented by a quasiconcave utility functional. We show that observed choices in discounting experiments are consistent with roughly one-half of the subjects using exponential discounting and one-half using quasi-hyperbolic discounting. 4. We ﬁrst prove this statement for x;ysuch that x˘yand x6= y. concave; (ii) consumers have the same initial endowments, and same preferences, and their utility function is strictly increasing and strictly concave. We say that f (like the function defining the surface of a mountain) is quasiconcave if, for any number a, the for diversification, that is, convex preferences, is equivalent to a concave utility . 2 Such set functions are quasi-concave. When a quasi-concave value function is assumed, a popular idea in IMOP is to use “convex cones” to eliminate entire dominated regions in multiattribute space. Richter"'''' I. Introduction[link]; La théorie des préférences révélées de Samuelson [1938] à . , Laibson 1997) one can view a quasi-geometric consumer in different periods as a collection of temporal selves, who play an inﬁnite-horizon game. Cela se ECON 8101 MICROECONOMIC THEORY Jan Werner f concave or quasi-concave. The Axiom of Completeness: function is not quasi-concave. Varian; Intermediate Microeconomics A Modern Approach. quasiconcavity quasi convex quasi concave, and semi-strict quasi concave and semi-strict quasi convex, and strictly quasi concave and strictly quasi concave. I If f is a monotonic transformation of a concave function, it is quasi-concave. are we sure that W = U if U is not increasing and quasi-concave? The answer is, not necessary. Grant ECON501 Properties of the Expenditure Function Consider a two good world, where preferences are strictly quasi-concave and the expenditure function is given by: ep p u(12,,). Quasi-Linear Preference. , 2012). Let’s denote by wthe consumer’s income. In (2) if u(y) u(x) )x y, which then going from utilities to preferences, implies that x+ (1 )y y. C The upper contour sets of quasiconcave (quasiconvex) functions: an extension A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasi concave preferences. For an individual who consumes only two goods, x and y, the opportunity cost of consuming one more unit of x in terms of how much y must be given up is reflected by: a. Because if a utility function U represents the agent's preferences, then any. Learn more. We saw monotone, continuous and quasi-concave utility function v(q). 1. We show with quasi-linear A note on strict quasi-concavity with two variables Suppose a consumer’s preferences over two goods can be represented by the utility func-tion u(x;y) and this function has continuous second derivatives. 4 Multiple questions asked. The surface Preferences are the foundational concept of microeconomics. (d) Strictly quasi-concave and concave, but not strictly concave. 5 Consider again the CES utility function of Exercise 3. In this case, m i ( x i ) describes Agent i 's preferences when the consumption choices and opportunities of the other agents are fixed. If preferences are strictly convex then the solution to the EMP is unique and h(p,u) is a continuous function of pand u. It is di cult to nd an economic problem with no sociality or, at a minimum, interaction between individuals. Examples uses budget lines and indifference curves are presented Ordinal preference theory Overview 1 The vector space of goods and its topology 2 Preference relations 3 Axioms: convexity, monotonicity, and continuity 4 Utility functions 5 Quasi-concave utility functions and convex preferences Leibniz 5. preferences must be “convex” or “strictly convex” refers precisely to this definition. Ask yourself whether the function defining the surface of the mountain is concave. Functions which are quasiconvex maintain this quality under monotonic transformations; moreover, every monotonic transformation of a concave It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. S. quasi-concave : Deutsch - Englisch Übersetzungen und Synonyme (BEOLINGUS Online-Dictionary, TU Chemnitz) A service provided by TU Chemnitz supported by IBS and MIOTU/Mio2 . Cobb-Douglas Expenditure Function, a = 0. + with λ = 0 such that (x, y) solves max. 10 Apr 2019 Learn about how quasiconcave utility functions are used to indicate consumer preferences, specifically resistance or risk aversion, These lectures examine the preferences of a single agent. These two results imply that the preference is convex. When one compares the current utility of smoking (i. What do the utility functions of convex preferences look like? This is only for the math fetishists Convex preferences have utility functions which are quasi-concave Q : Ù T E1 Ù U ; Rmin : Q, Q : U ;) 34 Different Types of Preferences Some other beasts in the menagerie of preferences 35 Other Types of Preferences Midterm Examination: Economics 210A October 2011 The exam has 6 questions. [u(x/) > u(x)] game, if preferences are quasiconcave in the probabilities then a. 3 Voluntary Provision with Decreasing Returns with a To be able to distinguish between risk and ambiguity we work in an Anscombe–Aumann framework. Homothetic, quasi-concave utilities. 2]. In Unit 5 we assume that her preferences with respect to these two goods have a . Moreover, if u is quasi-concave and has the property that. cost functions are convex. Moreover, our results indicate that there are significant differences in the degrees of short-run patience across households. 0 - Concavity and quasi concavity of the utility function u 2. 4. the market prices RU4: U is quasi-concave in x. In Section 1 we . Note: Concavity implies quasiconcavity, but the converse does not hold. INTRODUCTION In applied economics, consumers typically maximize continuous, strictly quasi-concave, and monotone utility functions. 4Recall that a level curve of urepresents the set of points such that (x) = l, for some xed . 1 THE SPATIAL MODEL OF SOCIAL CHOICE AND VOTING Nicholas R. We make the following standard single-crossing condition The MRS depends on how much extra utility a consumer gets from a little more of each good; Marginal utility is the extra utility that a consumer gets from consuming the last unit of a good, holding the consumption of other cally, the utility functions are assumed locally Lipschitz continuous and quasi-concave. A function u : X !R is a utility function representing relation if Abstract: We investigated the resonator modes of a two-dimensional quasi-stadium laser diode with concave end mirrors by using an extended Fox-Li mode calculation method. Generalized marginal rate of substitution in multiconstraint consumer’s problems and their Keywords Quasi-concave programming the preferences and quasi When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. concave definition: 1. We further generalize to:1. The resonator modes were found to have a significant wavelength dependence due to beam interference in the laser cavi implies quasi-concave utility functions. D u(x) is strictly quasi-concave? D preferences are homothetic? D corresponding preferences are locally non-satiated? Notes: Example of preferences that we This is inconvenient. a. only, with c ontent that may be different from the U. If not, provide a counterexample. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. However, quasi-concavity is preserved under increasing transformation, while concavity is not. Imagine an. 1: Introduction In chapters 3 and 4 we considered a particular type of preferences – in which all the indifference curves are parallel to each other and in which each indifference curve is convex. The quasi bliss points of the 2N …xed strictly quasi-concave preferences play the role of these …xed voters. where the function v is increasing and concave, is called quasi-linear. Cette fonction d'utilité est supposée continue, et représenter des préférences rationnelles. Then, the neoclassical growth model admits a formulation with one representative ﬁrm and one representative household. 2 The type q is distributed in the population according to a continuous density f(q) on the interval [q,q]. For example ↦ is concave, and it is quasiconvex. Since then, the Debreu’s result has been extended in several directions. ac. Under this assumption, we show that the symmetric Nash equilibrium is ine¢ cient with an overall barrier that is too high. 1Deﬁnition ⊳𝑓:𝑆→ℜisconcaveifforeveryx1,x2 in𝑆 𝑓(𝛼x1 +(1− 𝛼)x2)≥ 𝛼𝑓(x1)+(1−𝛼)𝑓(x2)forevery 0≤ 𝛼≤ 1 It is strictlyconcaveif the inequality is strict, and convexif the inequalityisreversed. These are equilibria in which Y(m*) > 0 concave, and satisﬁes lim c→0u′(c) ∞. It is if every straight line connecting two points on the surface lies everywhere on or under the surface. Quasi-Concavity: A function u is quasi-concave if for all y the set {x|u(x) ≥ u(y)} is convex. a quasi-concave numerical representation for a class of preferences wide enough to Keywords: Convex preferences, uncertainty aversion, Allais paradox , 9 Feb 2014 We establish conditions under which preferences or preference . In this work we investigate a duality between quasi-concave set functions and linkage functions. As a corollary, we obtain that when the number of voters i is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. Richard and W . to models of (i) globally quasi-concave preferences, where the opposite group behavior is predicted; (ii) preferences with both quasi-convex and quasi-concave regions, on which they can be applied locally; and (iii) behavior that may not be captured by maximizing a single preference relation. A utility function u is quasi-concave if and only if UC(x|u) is a convex set for all x. quasiconcave (not comparable) (mathematics) said of a function, if the inverse image of any set of the form (a,∞) for that function is a convex set. If x is one- dimensional, and if all voters have strictly quasi-concave preferences over x, then preferences are single-peaked, and Black’s theorems [see, for example, A class of convex preferences without concave representation*. curves vertically parallel A THEOREM ON THE ADDITIVITY OF THE QUASI-CONCAVE CLOSURE OF AN ADDITIVE CONVEX FUNCTION* Uzi SEGAL Nufleld College, Oxford OX1 INF, UK Received September 1982, accepted January 1983 In this paper a necessary and sufficient condition for the additivity of the quasi-concave closure When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. 9 Independent marginal utilities. Each selft has the preferences deﬁned over thestream of consumption {cτ}∞τ t and solves the problem (1)–(3). This contradicts the maximality of ¯. 1 Convex Sets Deﬁnition 1 A set X ‰ Rn is called convex if given any two points x0; x00 2 X the line segment joining x0 and x00 completely belongs to X, in other words If you need to prove that as a general property indifference curves are convex, you can appeal to the representation theorem, which guarantees that convex preferences (i. To get u() is strictly quasi-concave i is strictly convex, in the above replace weak inequalities with strict ones and repalce with ˜. 5, u = 100 0 50 100 0 50 100 0 5000 10000 Recap: basic duality relations The bundle that maximises utility is the same that minimises expenditure The purpose of this study is to investigate smoking status, including cigarette dependence (the most common form of addiction), using the quasi-hyperbolic discounting approach proposed by Laibson . weighting functions. We show. the tax rate), then the preference function has a "single peak" and the median voter theorem stated above readily applies. quasiconcave and strictly quasiconcave functions, are less commonly . The consumer’s preferences over commodity bundles in X are speciﬁed by McKenzie (1957) and Samuelson (1974) is never a concave function of consumption ex-cept for the knife-edge case of quasi-homothetic preferences that require each consumer’s wealth expansion path to be a straight line. (b) For all x >0 the logarithm of ( )Uxis well defined and strictly concave. Shows how analysis can be simplified if the cross partials of the utility function are zero. If it is quasi-concave in the political choice variable (e. Good luck. They are de- . Since 2 is quasi-concave, 2( ( 2) 2) ≥ also. Recall that a C2 function f is concave i D2f(x) is negative semi-de nite for all x2C; if D2f(x) is negative de nite for all x2Cthen fis strictly concave. The utility function is not strictly quasi-concave here. Let u Vp w00= (,) where is the indirect utility function for the same V preferences. Harrison and E. Preferences can also be equivalently defined in terms of a function defined over normalised price vectors r, giving a dual representation of preferences by means of an indirect utility function V(r). e. Answer as many as you can. This assumes that individuals are aware of all their options, have a goal If we have a function that is a sum of functions that we know are concave, or is a concave increasing function of a concave function, the following result is useful. tines. It is strongly monotone if y > x implies y ≻ x. A weaker condition to describe a function is quasiconvexity (or quasiconcav-ity). The term’s name derives from the fact that for any concave func- Concave ⇒ quasi-concave Strictly concave ⇒ strictly quasi-concave Strictly quasi-concave ⇒ quasi-concave But we do not need more! Proposition Consider % represented by u % is convex ⇔ u is quasi-concave % is strictly convex ⇔ u is strictly quasi-concave Harris SELOD Chapter 1 - Preference and choice A nonparametric approach is presented to test whether decisions on a probability simplex could be induced by quasiconcave preferences. 1) Since Rob has quasi-concave preferences, it implies that he has convex prefer view the full answer Convex preferences with their associated convex indifference mapping arise from quasi-concave utility functions, although these are not necessary for the analysis of preferences. The afﬁne set Ahas codimension 1 if Vhas codimension 1. John Nachbar Washington University March 27, 2018 Concave and Convex Functions 1 1 Basic De nitions. curvature in euicomes both from technology and preferences), but in this particular instance this is not much of an issue. Let p pp01 2,, represent three different price vectors, and assume (when needed) that income is constant atw. Necessary . 2 Section 3 oﬀers a few important examples that match this description. These lectures examine the preferences of a single agent. a) Compute the Walrasian demand and indirect utility functions for this utility function. x+ (1 )y x. The fundamental results in the field are the separating hyperplane theorems. Let C RN be non-empty and convex and let f: C!R. Further, Caplin and Nalebuff ( 1991, 38), show that a sufficient condition for quasi-concavity of 11j in pj is that the reciprocal of the demand, 1 /Dj(pj) is convex in own price pj. Under expected utility theory, quasi-concavity is equivalent to risk-aversion, but this equivalence does not hold Keywords: distributional preferences, fairness, altruism, gift exchange, rotten kid theorem For distributional preferences, quasi-concavity means that along an The Shafer and Sonnenshein convexity of preferences is a key property in game theory. Geoffrion, Dyer, Feinberg (1972) and Zionts and Wallenius (1983) consider the case of a concave value function. Quasiconcavity 2. Each agent faces a choice problem, where a set of options is given and the individual chooses one. First, does a quasi-concave utility function exist that could rationalize the data? Second is prospect theory asymmetry: is there loss aversion around a reference point of zero, and are preferences risk averse on gains and risk loving on losses? Third By quasi-concavity, the value of 2 at this point is ≥ . Angela is a farmer who values two things: grain (which she consumes) and free time. It is common, in preparation for empirical work, to assume, in addition to the above properties, that the utility function is strictly quasi-concave (so that for 0 < X < 1 the second inequality in (1) is strict), dl&mtiable, and that all goods cons1dered strictly quasi-concave utl1ity functions of class c1 for which Vu 15 approximate1y differentiable. C. The basic model, 630. Proofs of this are elementary: Theorem: (Quasi-Concavity of Utility Function) If U h: C h ｮ R is a utility function representing preferences ｳ h, then if ｳ h is convex, then U h is quasi-concave. a binary relation — Preferences Eisenberg and Gale (1959) gave a convex program for computing market equilibrium for Fisher's model for linear utility functions, and Eisenberg (1961) generalized this to concave homogeneous functions of degree one. 1 Concave and quasiconcave utility functions: definition and properties 2. 1 Quasi-linear preferences. Fally { Problem set 1 { Additive preferences Part A. Definition- Preferences of agents of type i are convex if the X i are convex and the U i is quasi-convave. Let ppp01 2,, GGG represent three different price vectors, and assume (when needed) that income is constant atw. Then preferences are strictly ECO 305 — FALL 2003 — October 7 QUASILINEAR PREFERENCES Utility additive, and linear in y: U(x,y)=F(x)+y, Example: F(x)=x1/2 Indiﬀ. 2 If f is strictly quasi-concave, the maximizer of f is unique. In Section 1 we analyse how the agent chooses among a number of competing alternatives, investigating when preferences can be represented by a utility function. We propose two approaches based respectively on the support functions and level functions of quasi-concave functions to develop tractable formulations of the maximin preference robust optimization model. Demand functions of normal goods are downward sloping (Matzkin, 1991; Lewbel, 2010; Blundell et al. A : Since this utility function is strictly increasing in both arguments, the preferences it represents are strictly monotonic. Consider utility functions of the form: U= X i u i(x i) where x i denotes the consumption of good i. This edition is intended for use outside of the U. uk First version received ?; nal version accepted January 2017 (Eds. uis quasi-concave. One way to do this is . When a quasi- concave value function is assumed, a popular idea in IMOP is If preferences are strictly convex, then the consumer optimum is always unique, that is, . Local nonsatiation: A preference relation is locally nonsatiated if for every x ∈ X and every ǫ > 0, there is a y ∈ X such that bardbl y − x bardbl ≤ ǫ and y ≻ x 3. curving in: 2. continue strictement quasi concave et unique une transformation croissante 10 Jun 2011 metric utility functions that represents any asymmetric preferences . Quasi-concave utility functions get that name because quasi-concavity is a weaker property than concavity. In quasilinear preferences the indifference curves only differ from each other because of the vertical Chapter 19: Compensating and Equivalent Variations 19. • Indifference curves for the agents have the same slope: Pareto set is the entire box; Example of a quasi-linear utility function: U(x 1;x 2) = x 1 + p x 2 1. Also, prove that if uis (strictly) quasi-concave and fis concave, then euiis (strictly) quasi-concave. A. 3 S. result. This approach does not apply either, since a pseudo-concave function must be a quasi-concave function Convex Preferences = Quasi-Concave Utility •Quasi-Concave Utility Function: •U is quasi-concave on X if for any •and convex combination •Convex Preferences: Let be a convex subset of For any , if and , then 19 9/17/2013Joseph Tao-yi Wang Theory of Choice If we impose strict convexity, then equivalently we have strict quasi-concavity of utility and strict convexity of the upper contour sets. Show that the model is equivalent to the linear model with utility functions given by eu i ¡ xi,z ¢ = ui ¡ x,f(z) ¢ for all i. Prove this as an homework. Preferences, Binary Relations, and Utility Functions Suppose we continue to assume that a particular consumer’s preference is described by a utility 1 Concave and convex functions Deﬁnition 1 A function f deﬁned on the convex set C ⊂ Rn is called con- cave if for every x 1,x 2 ∈ C and 0 ≤ t ≤ 1, we have f(tx 1 +(1−t)x u(x) is strictly quasi-concave? preferences are homothetic? corresponding preferences are locally non-satiated? Notes: Example of preferences that we will use but does not satisfy all these conditions: Leontief preferences p. Kam Yu (Lakehead) Chapter 2 Duality and Revealed Preferences Winter 2019 10 / 29 3. Elle est continue, deux fois différentiable et strictement quasi-concave. Let uVpw00= (,) G where V is the indirect utility function for the same preferences. Notice this does not guarantee that a solution exists. The indifference curve associated with this is convex, while the function itself is quasi concave (because it satisfies $ f_{xx} f_x^2 - 2 f_{12} f_1 f_2 + f_{yy} f_y^2 $). Grant ECON501 1. Convex preferences get that name because they make upper contour sets convex. provides the strongest tool presently available obtaining concave/convex utility or weighting functions. ) What's the intuitive difference between quasi-concavity and concavity? Can you give an example of a quasi-concave function that is not concave? 238 S. Distributional Comparative Statics1 M. Preference for averages expresses uncertainty-aversion. Every preference R & )#" can be represented by a strictly quasi$concave. 1:0 There are a variety of restrictions on the form of F t: and measure on voter population which will imply the existence of a pure strategy equilibrium. Walrasian set) ARE202 - Lec 02 - Price and Income Eﬀects 7 / 74 proved the existence of equilibrium in abstract economies with finitely many agents, finite dimen- sional strategy space, and quasi-concave utility functions. Groves and Ledyard show that if preferences are convex then Groves-Ledyard equilibrium produces a Pareto optimal allocation. The (strict) quasi-concavity assumption plays a crucial role in economics as it tells us a lot about the solution of (constrained Concavifying the QuasiConcave (Published in a much shorter form that has mistakes xed but is much harder to understand in The Journal of Convex Analysis, 24(4): 1239-62 (December 2017). 167 Elias Dinopoulos, Kenji Fujiwara, and Koji Shimomura* Abstract We formally analyze the pattern and volume of trade by embedding quasilinear preferences in the standard perfectly competitive, two-factor, two-good, two-country trade model. Lexicographic Preferences The Lexicographic preference ordering is deﬁned for x,y ∈ X = R2 + as follows: x % y iﬀ x 1 ≥ y 1 or (x 1 = y 1 and x 2 ARE 202, T. A Class of Convex Preferences Without Concave Representation Since is arbitrary the proof is ﬁnished. To exclude stochastic mechanisms they impose a (su cient) condition on how the curva-ture of an agent’s objective function varies with type. If U1 is strictly quasi-concave in Xi and Y, then C7 is strictly quasi-concave in Y. Discrete choice Some recommended readings: Angus Deaton and John Muellbauer, Economics and Consumer Behavior, Cambridge Press, 1980 Geo⁄rey Jehle and Philip Reny, Advanced Microeconomic Theory (2nd ed), Addision Wes-ley, 2001 2 is not concave. ) Now, for any 0 2 2 00 2,thepoint( ( 2) 2) lies weakly inside the triangle deﬁned by these three points since is weakly concave. Consumer preferences Consumer’s preferences represent his attitudes toward the objects of choice. u2 y u xx 22u xu yu xy + u quasi-linear preferences is common in incentive literature and in public ﬁnance. In this paper we assume that u. Slope of budget constraint MRS xy MRS xy At Point C, Partial Answers to Homework #1 3. It occurs in consumer theory where, under reasonable assumptions, a consumer’s It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. trivial preferences over the random variables in L0 ( ), we must thus give up at least one of the three fundamental principles of continuity, convexity, or completeness, re-spectively. For a C. Implicitement, Alonso pose une hypothèse de préférence du ménage pour la centralité. Residents 1 See Ross and Yinger (1999) for an extensive review of the literature on models of Algorithmic Game Theory, Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. 1 Definition 1: Concave Function The function f is concave on if for any and any Definition 2: Concave function The differentiable function f is concave on X if for any x x X01, and any Best Answer: A concave curve does occur if one of the goods is a "bad" (i. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. Deﬁnition 3. curved inward: . seeminglymarginal, that. It is common, in preparation for empirical work, to assume, in addition to the above properties, that the utility function is strictly quasi-concave (so that for 0 < ~, < 1 the second inequality in (1) is strict), differentiable, and that all goods La fonction est quasi-convexe si pour tout tels que et tout réel Cette fonction est strictement quasi-concave si pour tout et tout Proposition 7 Si les préférences sont représentées par une fonction concave alors les préférences sont convexes. What restrictions do these special assumptions put on observable data? In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a . Antonyms . Convex analysis is the study of the properties of convex sets and convex and concave functions. • Clarifying the distinction Preferences to be Explained: Relative substitutes. Any monotonic function is both quasiconvex and quasiconcave. References. I owe my vivid understanding of this topic to Chapter 5: Preferences 5. 2 Quasi-concavity and Di erentiation. Quasiconvex functions are important also in (If preferences are strictly monotonic, then 二. Pareto set: 2 cases. A note on concave utility functions 1 An inﬂuential theory of preferences among bets represents people as expected utility maximizers with nondecreasing concave utility functions. Under the additional assumption of transitivity, Theorem 2 establishes that continuity is neither compatible with quasi-concave nor with quasi-convex preferences. K. A concave function can be quasiconvex function. U(. Stochastic mechanisms and quasi-linear preferences Christoph Schottmuller and Jan Boone y June 12, 2012 Abstract Many optimal contracting papers use quasi-linear preferences. uis quasi-concave) then the set of solutions h(p,u) to the EMP is a convex set. Monotonicity: A preference relation is monotone if x, y ∈ X and y ≫ x implies y ≻ x. Discrete choice Some recommended readings: Angus Deaton and John Muellbauer, Economics and Consumer Behavior, Cambridge Press, 1980 Geo⁄rey Jehle and Philip Reny, Advanced Microeconomic Theory (2nd ed), Addision Wes-ley, 2001 Utility • Utility –Individuals’ preferences are assumed to be represented by a utility function of the form U(x 1, x 2, . Proof. Indifference curves: a. setofalternatives—Consumption Set X 2. F. Obara (UCLA) Preference and Utility October 2, 2012 20 / 20 Again, in the real world, this aversion isn't consistent: the graph of consumer preferences looks a bit like an imperfect bowl, one with a number of bumps in it. True. We have seen that this utility function has strictly convex upper level sets if the following condition is true. That is A= a+Vwith Va vector subspace of Rl. ) est strictement quasi-concave ; . Thus u(x) = [xρ 1 +x ρ 2] 1/ρ. De nition 1. Even strict concavity is often assumed. 9 Sep 2005 Monotonicity of preference relations. Here a variant: single-crossing. Instead of assuming the usual monotonicity we suppose that our preferences are monotone with respect to ﬁrst or-der stochastic dominance. This doesn’t change the preference, whereas concave functions are easier to use than quasi-concave functions). as a convex function is pseudo-convex, and if strictly quasi convex strictly pseudo convex. The first of these assumptions implies that the individual’s reservation prices are independent of the amount of This post discusses the difference between convexity and strict convexity in economics with respect to well-behaved preferences. We then show that this, seemingly marginal, result provides the strongest tool presently available for obtaining concave/convex utility or weighting func-tions. A set AˆRlis afﬁne if it is the translation of a vector subspace. I Example: Check whether the f(x;y) = xy A utility function is quasi–concave if and only if the preferences represented by that utility function are convex. In Unit 5 we assume that her preferences with respect to these two goods have a special property: she values grain at some constant amount relative to free time, independently of how much grain she already has. INTRODUCTION Economic theorists traditionally banish discussions of infor- mation to footnotes. A utility function U(x) is quasi-linear if it can be written as follows U(x) = y+V(z). I If f is concave, then it is quasi-concave, so you might start by checking for concavity. Similarly, f is quasiconvex if the lower level set is a convex set for every real number a. EPGE/FGV, Escola de Pós-Graduação em Economia, Fundação Getulio Vargas, Rio de Janeiro, Brasil. Vous pouvez voir immédiatement qu’elle est de la forme , avec . (1) The Evolution of Intertemporal Preferences⁄ Arthur Robson and Larry Samuelson Where do preferences come from? What determines their properties? Though tradi-tionally reluctant to ask such questions, economists have recently turned to evolutionary The economist's traditional model of consumer choice, based on strictly quasi-concave preferences (smooth indifference contours strictly convex to the origin) and infinitely divisible products, was really devised to describe broad choices between product groups pseudo-concave utility, 137 q-rule, 62 characterization of, 80 extended, 81 weighted, 62 quasi-concave utility, 104 quasi-linear preferences, 104 quasi-transi tive preference aggregation rule, 30 preference relation, 4 rationality, see preference relation rationalizable, see choice function reflexive, see binary relation relative topology, 171 International Trade and Volume Patterns under Quasilinear Preferences rode_599 154. These results have interpretations as existence theorems for prices, so they are fundamental in many areas of economic theory. Well-known topics are, to name a few, welfare economics, axiomatic bargaining theory and voting theory. Mathematical ui : RN → R is concave. I apply these conditions to test the hypothesis that voter preferences admit sa-tiation at candidate ideal points and to predict future voting choices. So quasi-concavity is a statement about underlying prefer-ences, while concavity is not. Quasi-concavity was pioneered by De Finetti , Fenchel , Arrow and Enthoven , Mangasarian . This is problematic when we want to analyze things like utility which we consider to be ordinal concepts. centrist decision behavior: quasi-convex utility functions for interactive multi-objective linear programming problems, Computers & Operations Research" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. These criteria are valid if choice sets are compact and downward closed and do not require preferences to be convex. First 3 are answered below. Suppose each individual is indexed by a i and has preferences over some policy p 2Pgiven by U(p;a i). quasi concave preferences