utility-maximizing choices|we only care about ordinal comparisons.) Problem 2 (Well-Behaved Preferences) (a) Instead of using utility function U(x 1;x 2) = x3 1 x 1 2, we can use a monotonic trans-formation instead: U(x 1;x 2) = 3lnx 1 + lnx 2. (To get this, let f(u) = ln(u). Then f(u) = ln(x3 1 x 2) = 3lnx 1 + lnx 2. Again, even though these ... Jun 19, 2008 · We demonstrate that a well-behaved utility function can generate Giffen behavior, where “well-behaved” means that its indifference curves are smooth, convex, and closed in a commodity space; the resulting demand function of each good is differentiable with respect to prices and income. Moreover, we show that Giffen behavior is compatible with any level of utility and an arbitrarily low ... (well-behaved utility function, simple straight budget line, indifference curves don't cross the axes) the optimal consumption bundle will be the point along the budget line where the consumer's MRS is equal to the price ratio. However, if those conditions are not met, we need to apply logic: always compare MRS and price ratio!!! Any such function is called a utility function for the preference relation in question.u 3. Constructing the Utility Function This section makes the intuitive argument from the introduction precise: given a binary preference relation on a set of alternatives, the “better” an alternative is, the “larger” is its set of worse alternatives. Lecture3 - Axioms of ConsumerPreference and theTheory of Choice DavidTAutor,MI Economicsand NBER 14.03/14.003 Microeconomic Theoryand PublicPolicy, F all2016 Moreover, you have probably heard of the concept of a ‘utility function’ Reports how ‘happy’ a particular bundle of goods makes someone So why can’t we work with utility functions? 29 Where are the Numbers? Okay, so we are going to work with utility functions But first I want you to understand how utility functions are used I can see twice-differentiable as a reasonable requirement for a utility function to be 'well-behaved' is because the derivative of the utility function is marginal utility, and economists often care about the derivative of marginal utility. For example, if the second derivative of utility is negative, this means that the marginal utility has a ... The utility function u in (4) is usc in the D-lower order topology. Corollary 1. If is a complete, transitive, usc binary relation over a topological space X with countable base, the utility function in (4) represents and is usc. Also Rader [12] establishes existence of a usc utility function under the conditions of Corollary 1. Additionally, tangency can only be achieved when preferences are well-behaved/strictly convex. This is because of the linear nature of a budget constraint. It is only possible for a linear indifference curve to touch a linear budget constraint at one point, and usually this results in only one of the goods being consumed. Cobb-Douglas preferences are treated as standard examples of well-behaved indifference curves because a monotonic transformation of the Cobb-Douglas utility function will represent exactly the same preferences. After discussing the consumer’s preferences, we will turn to her utility function. A utility function is a numerical representation of how a consumer feels about alternative consumption bundles: if she likes the ﬁrst bundle better than the second, then the utility function assigns a higher number to the ﬁrst than to the second, and if she likes them equally well, then the utility The utility function u in (4) is usc in the D-lower order topology. Corollary 1. If is a complete, transitive, usc binary relation over a topological space X with countable base, the utility function in (4) represents and is usc. Also Rader [12] establishes existence of a usc utility function under the conditions of Corollary 1. Starting from an intuitive and constructive approach for countable domains, and combining this with elementary measure theory, we obtain an upper semi-continuous utility function based on outer measure. Whenever preferences over an arbitrary domain can at all be represented by a utility function, our function does the job. utility-maximizing choices|we only care about ordinal comparisons.) Problem 2 (Well-Behaved Preferences) (a) Instead of using utility function U(x 1;x 2) = x3 1 x 1 2, we can use a monotonic trans-formation instead: U(x 1;x 2) = 3lnx 1 + lnx 2. (To get this, let f(u) = ln(u). Then f(u) = ln(x3 1 x 2) = 3lnx 1 + lnx 2. Again, even though these ... What is a "well-behaved function"? I keep hearing this in my econ classes, but still don't understand it. I know it has some relationship with "preferences" and "utility". wealth in the utility function generates well-behaved zero-lower-bound steady states. These results are not directly portable to the New Keynesian model, however, because these results require strong forms of wage or price rigidity: inOno and Yamadawages are constrained to follow an are consistent and well-behaved. Firstly, since the utility function assigns a unique real number to every possible bundle, this ensures that preferences are complete, reﬂexive and transitive, because real numbers have these pro-perties. Secondly, because MU X and MU Y are always positive, this shows Lecture3 - Axioms of ConsumerPreference and theTheory of Choice DavidTAutor,MI Economicsand NBER 14.03/14.003 Microeconomic Theoryand PublicPolicy, F all2016 The answer is something very important about utility functions, which is that if preferences are well-behaved, almost anything that satisfies those rules could be part of a utility function! (In fact, a near infinite number of possible, consistent, utility functions could satisfy those rules. Cobb-Douglas preferences are treated as standard examples of well-behaved indifference curves because a monotonic transformation of the Cobb-Douglas utility function will represent exactly the same preferences. The direct utility function (DUF) is a function whose arguments are the quantities consumed of different goods and two of its basic properties are (increasing) monotonicity and quasi-concavity. An indirect utility function (IUF) is a function whose arguments are the normalized prices of the goods. The last assumption of well-behaved indifference curves is continuity, which means that small changes in the quantity of the goods can not induce big changes in utility. Were indifference curves not continuous, it would be quite hard to analyse preferences. wealth in the utility function generates well-behaved zero-lower-bound steady states. These results are not directly portable to the New Keynesian model, however, because these results require strong forms of wage or price rigidity: inOno and Yamadawages are constrained to follow an Generating well-behaved utility functions for compromise programming Article (PDF Available) in Journal of Optimization Theory and Applications 91(3):643-649 · January 1996 with 35 Reads We want to find preferences that order the bundles. Utility is ordinal, so we only care about which is greater, not by how much. Conditions . There are several Conditions on preferences to produce a continuous (well-behaved) utility function. Additionally, tangency can only be achieved when preferences are well-behaved/strictly convex. This is because of the linear nature of a budget constraint. It is only possible for a linear indifference curve to touch a linear budget constraint at one point, and usually this results in only one of the goods being consumed. The direct utility function (DUF) is a function whose arguments are the quantities consumed of different goods and two of its basic properties are (increasing) monotonicity and quasi-concavity. An indirect utility function (IUF) is a function whose arguments are the normalized prices of the goods. a. Check that they are well behaved (U' > 0, U″ < 0) or state restrictions on the parameters so that they are [utility functions (1) – (6)]. For utility function (6), take positive α and β, and give the range of wealth over which the utility function is well behaved. b. Compute the absolute and relative risk-aversion coefficients. c. The answer is something very important about utility functions, which is that if preferences are well-behaved, almost anything that satisfies those rules could be part of a utility function! (In fact, a near infinite number of possible, consistent, utility functions could satisfy those rules. And it turns out that with this property it is impossible to define a well-behaved utility function! Therefore it seems natural to distinguish being rational with a concave utility function, on the one hand, from, on the other hand, being risk-averse and not being able to have a well-behaved utility function at all. The utility function u in (4) is usc in the D-lower order topology. Corollary 1. If is a complete, transitive, usc binary relation over a topological space X with countable base, the utility function in (4) represents and is usc. Also Rader [12] establishes existence of a usc utility function under the conditions of Corollary 1. wealth in the utility function generates well-behaved zero-lower-bound steady states. These results are not directly portable to the New Keynesian model, however, because these results require strong forms of wage or price rigidity: inOno and Yamadawages are constrained to follow an curves are well behaved) and convexity (so the optima can be characterised by tangency ... utility. 3. The expenditure function is concave in prices (p1;p2). There is an individual with a well-behaved utility function, and initial wealth Y. Let a lottery offer a payoff of G with probability π and a payoff of B with probability 1-π. However, we rarely find a well-behaved supply function of pollution when the system is estimated for multiple pollutants. If reconstruction of the contentive part is mandatory, (2) is a well-behaved example. These effects are like well-behaved children: they are seen, not heard.

(well-behaved utility function, simple straight budget line, indifference curves don't cross the axes) the optimal consumption bundle will be the point along the budget line where the consumer's MRS is equal to the price ratio -- i.e., "bang for their buck" is equalized .