Tom C. Brown

A primer on nonmarket valuation

List of Contributors. Preface P.A. Champ, K.J. Boyle, T.C. Brown. 1. Economic Valuation: What and Why A. Myrick Freeman III. 2. Conceptual Framework for Nonmarket Valuation N.E. Flores. 3. Collecting Survey Data for Nonmarket Valuation P.A. Champ. 4. Introduction to Stated Preference Methods T.C. Brown. 5. Contingent Valuation in Practice K.J. Boyle. 6. Attribute-Based Methods T.P. Holmes, W.L. Adamowicz. 7. Multiple Good Valuation T.C. Brown, G.L. Peterson. 8. Introduction to Revealed Preference Methods K.J. Boyle. 9. The Travel Cost Model G.R. Parsons. 10. The Hedonic Method L.O. Taylor. 11. Defensive Behavior and Damage Cost Methods M. Dickie. 12. Benefit Transfer R.S. Rosenberger, J.B. Loomis. 13. Nonmarket Valuation in Action D.W McCollum. 14. Where to from Here? R.C. Bishop. Index.

Which response format reveals the truth about donations to a public good

Several contingent valuation studies have found that the open-ended format yields lower estimates of willingness to pay (WTP) than does the closed-ended, or dichotomous choice, format. In this study, WTP for a public environmental good was estimated under four conditions: actual payment in response to open-ended and closed-ended requests, and hypothetical payment in response to open-ended and closed-ended requests. The experimental results, showing that the response format mattered far more for hypothetical than for actual payments, support conclusions about the reasons that the dichotomous choice format yields larger estimates of hypothetical WTP, conclusions that hinge on the hypothetical nature of contingent valuation.

Descriptions of the characteristic sequence of an irrational

Let α be a positive irrational real number. (Without loss of generality assume 0 characteristic sequence of α is f(α) =f 1 f 2 ···, where f n = [(n + 1)α] - [nα]. We make some observations on the various descriptions of the characteristic sequence of α which have appeared in the literature. We then refine one of these descriptions in order to obtain a very simple derivation of an arithmetic expression for [nα] which appears in A. S. Fraenkel, J. Levitt, and M. Shimshoni [17]. Some concluding remarks give conditions on n which are equivalent to f n = 1.

A density version of a geometric ramsey theorem

Abstract Let V be an n -dimensional affine space over the field with p d elements, p ≠ 2. Then for every e > 0 there is an n ( e ) such that if n = dim( V ) ⩾ n ( e ) then any subset of V with more than e | V | elements must contain 3 collinear points (i.e., 3 points lying in a one-dimensional affine subspace).

Environmental Damage Schedules: Community Judgments of Importance and Assessments of Losses

Available methods of valuing environmental changes are often limited in their applicability to current issues such as damage assessment and implementing regulatory controls, or may otherwise not provide reliable readings of community preferences. An alternative is to base decisions on predetermined fixed schedules of sanctions, restrictions, damage awards, and other allocative guides and incentives, which are based on community judgments of the relative importance of different environmental resources and particular changes in their availability and quality. Such schedules can offer advantages of cost savings and consistency over current methods, as demonstrated in the case of Thailand coastal resources. (Jel Q20)

Is There a Sequence on Four Symbols in Which No Two Adjacent Segments are Permutations of One Another

It has long been known (see [1–3, 5, 6, 10–12, 15, 16]) that there exist sequences on 3 symbols which contain no 2 identically equal consecutive segments, and sequences on 2 symbols which contain no 3 identically equal consecutive segments. Indeed, Axel Thue obtained these results around 1906. See [6] for a brief account of the contexts of the various independent rediscoveries of these results, and see [7,14] for an account of other properties of these sequences. Let X be a set and let s = x1x2x3 be a sequence on X . Then for i+1 k, s[i+1;k] = xi+1xi+2 xk is a segment of s, and the segments s[i+ 1; j];s[ j + 1;k] are consecutive. The segments s[i+ 1; j] and s[p+ 1;q] are identically equal if k i = q p and xi+1 = xp+1;xi+2 = xp+2; : : : ;xk = xq or, in other words, if s[i+1;k] = s[p+1;q] in X , the free semigroup generated by the set X . An interesting situation arises when we allow the symbols within a segment to commute with each other. It will be convenient to use the following terminology. Given a set X and a sequence s on X , we regard segments of s as elements of X . (Thus the results mentioned above say that there exist sequences on 3 symbols without 2nd powers as segments, and sequences on 2 symbols without 3rd powers.) Now let X denote the free commutative semigroup generated by X , and let α : X 7! X be the natural homomorphism (α(x) = x for x 2 X). If s has k consecutive segments f1; : : : ; fk such that α( f1) = = α( fk), then we say that s has a kth power mod α . In this language, the question of the title is: Does there exist a sequence on four symbols without 2nd powers mod α? It is an easy matter to verify that every sequence on 3 symbols contains 2nd powers mod α , and that every sequence on 2 symbols has 3rd powers mod α . For example, if X = fx;yg, one can show by examining all cases that the longest elements of X which do not contain a 3rd power mod α are xxyyxyyxx;xxyyxyyxy; and a few others. Evdomikov [4] constructed a sequence on 25 symbols without 2nd powers mod α , and conjectured that perhaps 5 symbols would suffice. Justin [8], with a remarkable half-page proof, constructed a sequence on 2 symbols without 5th powers mod α . This sequence is obtained by successive iterations of the transformation x 7! xxxxy and y 7! xyyyy, starting with x. Thus the first few iterations give x;xxxxy;(xxxxy)4xyyyy; [(xxxxy)4xyyyy]4xxxxy(xyyyy)4. Then in 1970 a paper appeared [13] in which P. A. B. Pleasants gave a construction of a sequence on 5 symbols without 2nd powers mod α . Pleasants’ sequence, which extends to infinity in both directions, is constructed by

Arithmetic progressions in lacunary sets

We make some observations concerning the conjecture of Erd˝ os that if the sum of the reciprocals of a set A of positive integers diverges, then A contains arbitrarily long arithmetic progressions. We show, for example, that one can assume without loss of generality that A is lacunary. We also show that several special cases of the conjecture are true.

A characterization of the quadratic irrationals

Let α be a positive irrational real number, and let fα (n) = [(n+1)α] [nα] [α], n 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain ‘substitution property’ if and only if α is the root of a quadratic equation over the rationals.

Valuing Risks to the Environment

Increasing awareness of exposure to environmental risks has focused attention on measures that would give greater assurance that such risks are effectively managed and that the adverse consequences of risky activities are mitigated. Implementing such actions is made more difficult by the uncertainties of environmental changes, their often delayed impacts, the great importance attached to extremely small risks, and the lack of clear measures of the values of environmental losses. Findings from recent behavioral studies of peoples time preferences, valuations of losses relative to gains, and risk perceptions are providing information that should lead to more effective risk management strategies.

Quantitative Forms of a Theorem of Hilbert

Hilbert needed this lemma in connection with certain results on the irreducibility of rational functions and, as far as is known, never pursued the combinatorial directions to which it pointed. Others did, however, beginning with Schur, who in 1916 showed that for any r, there is an s(r) so that in any partition of f1;2; : : : ;s(r)g into r classes, some class contains a projective 2-cube, i.e., Q 2(a1;a2) = Q2(a;a1;a2) f0g with a = 0. (This combinatorial result actually arose in Schur’s investigations [11] of a modular version of Fermat’s conjecture.) This was later extended by Rado [9] (who was Schur’s student) who (implicitly) proved that any partition of a sufficiently long interval of integers into r classes must have at least one class which contains a projective m-cube. This was also proved independently later by Folkman (see [4]) and Sanders [10]. Finally, in 1974, Hindman [8] proved the much stronger result that in any partition of all the positive integers into finitely many classes, some class must contain an infinite projective cube, i.e., for positive integers a1;a2; : : : a set ( ∞ ∑ k=1 ekak : ek = 0 or 1 with 0 < ∞ ∑ k=1 ek < ∞ )