Review - Pareto E¢ ciency and Welfare Analysis Shih En Lu
... Pareto E¢ ciency in a Market Consider a perfectly competitive market, like you had in ECON 201. Would it be Pareto e¢ cient if the quantity were lower? What if the quantity were higher? What if the quantity were equal to the competitive quantity, but transactions are forced to occur (e.g. by a dict ...
... Pareto E¢ ciency in a Market Consider a perfectly competitive market, like you had in ECON 201. Would it be Pareto e¢ cient if the quantity were lower? What if the quantity were higher? What if the quantity were equal to the competitive quantity, but transactions are forced to occur (e.g. by a dict ...
The Compactness Theorem 1 The Compactness Theorem
... formulation: if a set of formulas S is unsatisfiable then some finite subset of S is already unsatisfiable. This suggests a procedure by which we can show that an infinite set of formulas S is unsatisfiable. Suppose that S can be enumerated by some algorithm as S = {F1 , F2 , F3 , . . .} Then for ea ...
... formulation: if a set of formulas S is unsatisfiable then some finite subset of S is already unsatisfiable. This suggests a procedure by which we can show that an infinite set of formulas S is unsatisfiable. Suppose that S can be enumerated by some algorithm as S = {F1 , F2 , F3 , . . .} Then for ea ...
Expected Utility Theory with Probability Grids and Preferential
... Then, Lemma 2.2 shows that these sets are connected from coarser to finer ones, which facilitates mathematical induction. Finally, a preference relation is defined. Let ` be an integer with ` ≥ 2. This ` is the base for describing probability values; we take ` = 10 in all examples in this paper. The ...
... Then, Lemma 2.2 shows that these sets are connected from coarser to finer ones, which facilitates mathematical induction. Finally, a preference relation is defined. Let ` be an integer with ` ≥ 2. This ` is the base for describing probability values; we take ` = 10 in all examples in this paper. The ...
Preferences, Binary Relations, and Utility Functions
... Rl , and if n = 2 then they are curves, and these indifference curves slope downward. In fact, the indifference sets are surfaces (but do not necessarily slope downward) for a much broader class of preferences than just the increasing ones: (6) A preference % on X ⊆ Rl is locally nonsatiated (LNS) i ...
... Rl , and if n = 2 then they are curves, and these indifference curves slope downward. In fact, the indifference sets are surfaces (but do not necessarily slope downward) for a much broader class of preferences than just the increasing ones: (6) A preference % on X ⊆ Rl is locally nonsatiated (LNS) i ...
PDF
... from the language Lc of PLc under this system. In Li , the logical connectives consist of →, ¬, ∧, ∨, whereas in Lc , only → is used. The other connectives are introduced as abbreviational devices: ¬A is A →⊥, A ∨ B is ¬A → B, and A ∧ B is ¬(A → ¬B). So it doesn’t make much sense to say that PLi < P ...
... from the language Lc of PLc under this system. In Li , the logical connectives consist of →, ¬, ∧, ∨, whereas in Lc , only → is used. The other connectives are introduced as abbreviational devices: ¬A is A →⊥, A ∨ B is ¬A → B, and A ∧ B is ¬(A → ¬B). So it doesn’t make much sense to say that PLi < P ...
1. Axioms and rules of inference for propositional logic. Suppose T
... For Ass, Ex, Contr and Cut this amounts to the so called “generalized rules of inference” on stated and proved on pp. 91-93 of the coursepack. The rest are a straightforward exercise for the reader making use of associativity. ...
... For Ass, Ex, Contr and Cut this amounts to the so called “generalized rules of inference” on stated and proved on pp. 91-93 of the coursepack. The rest are a straightforward exercise for the reader making use of associativity. ...
Prof. Blume's notes
... measures how risk-averse the decision-maker is. Optimization: We want to find optimal elements of orders on feasible sets. Sometimes these are more easily computed with utility functions. For instance, if U is C 1 and B is of the form {x : F (x) ≤ 0}, then optima can be found with the calculus. So w ...
... measures how risk-averse the decision-maker is. Optimization: We want to find optimal elements of orders on feasible sets. Sometimes these are more easily computed with utility functions. For instance, if U is C 1 and B is of the form {x : F (x) ≤ 0}, then optima can be found with the calculus. So w ...
Multilingual Ballots: How much do they cost?
... Multilingual Ballots: How much do they cost? The Federal Voting Rights Act (42 U.S.C., Section 1973 aa-6) states: "Any voter who requires assistance to vote by reason of blindness, disability or inability to read or write may be given assistance by a person of the voter's choice, other than the vote ...
... Multilingual Ballots: How much do they cost? The Federal Voting Rights Act (42 U.S.C., Section 1973 aa-6) states: "Any voter who requires assistance to vote by reason of blindness, disability or inability to read or write may be given assistance by a person of the voter's choice, other than the vote ...
1 (Robust) Expected Utility
... For the rest of this section, we assume that the preference ordering admits a vNM representation with a utility function u. If µ ̸= δm(µ) then there exists x, y ∈ S such that u(x) < U (µ) < u(y). Hence an application of the intermediate-value theorem to the strictly increasing function u : S → R yi ...
... For the rest of this section, we assume that the preference ordering admits a vNM representation with a utility function u. If µ ̸= δm(µ) then there exists x, y ∈ S such that u(x) < U (µ) < u(y). Hence an application of the intermediate-value theorem to the strictly increasing function u : S → R yi ...
Fractions
... Fractions which have non-terminating decimal representation are given with the line above the repeating numbers. ...
... Fractions which have non-terminating decimal representation are given with the line above the repeating numbers. ...
four color theorem
... a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program; the Kepler conje ...
... a mathematical theorem. The idea is to use a computer program to perform lengthy computations, and to provide a proof that the result of these computations implies the given theorem. In 1976, the four color theorem was the first major theorem to be verified using a computer program; the Kepler conje ...
Document
... The more fruitful type of definition is a matter of drawing boundary lines that were not previously given at all. What we shall be able to infer from it, cannot be inspected in advance; here, we are not simply taking out of the box again what we have just put into it. The conclusions we draw from i ...
... The more fruitful type of definition is a matter of drawing boundary lines that were not previously given at all. What we shall be able to infer from it, cannot be inspected in advance; here, we are not simply taking out of the box again what we have just put into it. The conclusions we draw from i ...
Shivani Agarwal
... where 1(φ) is 1 if φ is true and 0 otherwise. In order to design a good ranking function f , we need to estimate the error incurred by f on new movies. Under suitable probabilistic assumptions, we would like to find out whether we can use the observed or empirical error of f on the movies for which ...
... where 1(φ) is 1 if φ is true and 0 otherwise. In order to design a good ranking function f , we need to estimate the error incurred by f on new movies. Under suitable probabilistic assumptions, we would like to find out whether we can use the observed or empirical error of f on the movies for which ...
PDF
... remains is the case when A has the form D. We do induction on the number n of ’s in A. The case when n = 0 means that A is a wff of PLc , and has already been proved. Now suppose A has n + 1 ’s. Then D has n ’s, and so by induction, ` D[B/p] ↔ D[C/p], and therefore ` D[B/p] ↔ D[C/p] by 2. This ...
... remains is the case when A has the form D. We do induction on the number n of ’s in A. The case when n = 0 means that A is a wff of PLc , and has already been proved. Now suppose A has n + 1 ’s. Then D has n ’s, and so by induction, ` D[B/p] ↔ D[C/p], and therefore ` D[B/p] ↔ D[C/p] by 2. This ...
Discounting, values, decisions
... • Let T = [ 0, t̄ ]. • Let the probability space with a filtration be (Ω, P, {Ft }t∈T ). • α(t) denotes a discount rate, e.g. α(t) = e−rt . • τ denotes a stopping time w.r.t. the filtration. • u(t) denotes a payoff stream. • G(t) is the termination payoff if the process is stopped at time t. ...
... • Let T = [ 0, t̄ ]. • Let the probability space with a filtration be (Ω, P, {Ft }t∈T ). • α(t) denotes a discount rate, e.g. α(t) = e−rt . • τ denotes a stopping time w.r.t. the filtration. • u(t) denotes a payoff stream. • G(t) is the termination payoff if the process is stopped at time t. ...
Document
... Large Deviation results are applicable for this statistics. It is observed that just like Pitman’s sense, Linear test in intermediate (all three cases) is most efficient as well because it satisfies the above mentioned condition. Key words: Asymptotic Efficiency, Goodness of fit, Spacing, Cramér’s c ...
... Large Deviation results are applicable for this statistics. It is observed that just like Pitman’s sense, Linear test in intermediate (all three cases) is most efficient as well because it satisfies the above mentioned condition. Key words: Asymptotic Efficiency, Goodness of fit, Spacing, Cramér’s c ...
ECON 246 - Meeting #3
... – where X=vector of locational factors, B is a vector of parameters, and e is a disturbance term. – Need to compare location k with all other j locations. ...
... – where X=vector of locational factors, B is a vector of parameters, and e is a disturbance term. – Need to compare location k with all other j locations. ...
Warm-Up: 1. What are the three things that need to be true to apply
... Objective: Students will be able to understand and use Rolle’s Theorem. Rolle’s Theorem: Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). If f(a)=f(b) then there is at least one number c in (a,b) such that f’(c)=0. How does it work? ...
... Objective: Students will be able to understand and use Rolle’s Theorem. Rolle’s Theorem: Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). If f(a)=f(b) then there is at least one number c in (a,b) such that f’(c)=0. How does it work? ...
Practical suggestions for mathematical writing
... (5) If a section contains several theorems, propositions, and lemmas, but only one of them is needed in subsequent sections, mention this. (Again, this can free up memory in the reader’s brain!) (6) Make quantifiers unambiguous: instead of writing We have x2 + 1 ∈ S for x ∈ R. or worse We have x2 + ...
... (5) If a section contains several theorems, propositions, and lemmas, but only one of them is needed in subsequent sections, mention this. (Again, this can free up memory in the reader’s brain!) (6) Make quantifiers unambiguous: instead of writing We have x2 + 1 ∈ S for x ∈ R. or worse We have x2 + ...
SBOE Policy Regarding Access to Public Records
... The North Carolina State Board of Elections release of public records policy is to be as open as possible while protecting legal privacy and ensuring confidentiality, when required by law. ...
... The North Carolina State Board of Elections release of public records policy is to be as open as possible while protecting legal privacy and ensuring confidentiality, when required by law. ...
12.2 Reteaching
... In this problem, x is the radius. To find its value draw radius BD , which becomes the hypotenuse of right ∆BED. Then use the Pythagorean Theorem to solve. ED = CE = 3 ...
... In this problem, x is the radius. To find its value draw radius BD , which becomes the hypotenuse of right ∆BED. Then use the Pythagorean Theorem to solve. ED = CE = 3 ...