Lecture Notes in Economics and Mathematical Systems, 1986
In the previous chapters, we have explored how the presence of income taxation may alter several ... more In the previous chapters, we have explored how the presence of income taxation may alter several of the neoclassical properties of consumer demand functions and labor supply functions. As of yet, however, we have not discussed how one may empirically estimate the demand and supply functions when consumers face nonlinear budget sets While the literature is now quite extensive, the interested reader may find the recent work of Hausman (1985) a most useful review of the labor supply literature.
Lecture Notes in Economics and Mathematical Systems, 1986
We now consider the implications of allowing taxes to be a function of the income earned by indiv... more We now consider the implications of allowing taxes to be a function of the income earned by individuals. If the government wishes to, redistribute income by its tax policy, government may decide to use a nonlinear tax, taxing wealthy individuals more than poorer individual s. This leads to the question; how should government define how wealthy an individual is? Perhaps ideally government could base the income tax on the individual’s full income, F. This would allow government to base taxes on the market spending potential of each individual, and to construct a tax bill that really redistributes utility.
Lecture Notes in Economics and Mathematical Systems, 1986
Throughout this monograph we have focused on behavioral and index concepts that view government s... more Throughout this monograph we have focused on behavioral and index concepts that view government services and the tax system as fixed. In practice, the consumer may receive benefits from taxes (eg., public goods), and the government may from time to time change the tax code. This chapter provides a brief look at these issues, and shows how earlier results may be extended to deal with the issues. We consider first the issue of government goods, and then the issue of tax code changes. Finally, some preliminary results concerning the indexation of tax codes are presented.
Lecture Notes in Economics and Mathematical Systems, 1986
As a means of introducing the concept of an income-based measure of the cost of living, it is use... more As a means of introducing the concept of an income-based measure of the cost of living, it is useful to note that in the absence of taxes, the expenditure function and the full income compensation function correspond. That is, \({\text{e}}\left( {{\text{P, u}}} \right) \equiv \mu \left( {{\text{P, u; T}}} \right)\) where e(•) in the expenditure function defined in Chapter Three, and μ(•) is the income-compensation function defined in Chapter Four.
Lecture Notes in Economics and Mathematical Systems, 1986
In Chapter Seven we examined the construction of an income based cost of living index in the pres... more In Chapter Seven we examined the construction of an income based cost of living index in the presence of an income tax, but where the consumer’s income was solely exogenous. This chapter considers the concept of income based cost of living indices when the consumer’s income depends upon an endogenously determined labor supply. Recall that \({\text{P}} = \left( {{\text{P}}_0 ,\bar P} \right)\)) and \(X = ({X_0},\bar X)\)).
Lecture Notes in Economics and Mathematical Systems, 1986
In order to solidify important concepts, we shall first present some index concepts in the absenc... more In order to solidify important concepts, we shall first present some index concepts in the absence of an income tax. The key to constructing an expenditure-based cost of living index is the expenditure function examined in Chapter Three, namely \({\text{e}}\left( {{\text{P,u}}} \right) \equiv \frac{{\min }}{{\text{X}}}\left\{ {{\text{P}} \bullet {\text{X}}\left| {{\text{U}}\left( {\text{X}} \right) \geqslant {\text{u}}} \right.} \right\}\). This function defines the minimum expenditures on goods and leisure necessary to purchase the standard of living corresponding to u.
We show that the total cost of production index and the marginal cost of production index may be ... more We show that the total cost of production index and the marginal cost of production index may be used to illuminate the course of an industry's evolution. Each of these summary statistics conveys different bits of information about the industry. Theoretical properties of the indices are compared, and then the indices are applied to data from the steel industry to
... I.7. Baye and DA Black, On the Theory qf~zncome-based cost-of-living indiees 87 leisure. Assu... more ... I.7. Baye and DA Black, On the Theory qf~zncome-based cost-of-living indiees 87 leisure. Assuming that P and vary over tune, we differentiate eq. (4) with respect to time to obtain - F where dots over .-ariables denote their time derivatives. ...
Abstract This note extends recent work on cost of living index numbers for a population of indivi... more Abstract This note extends recent work on cost of living index numbers for a population of individuals who face imperfect and costly information about prices. It is known that individuals with identical preferences but different incomes will require different cost of living adjustments unless preferences are homothetic. However, this result in based on a model of consumer behavior under costless information. We analyze differences in the cost of living among searchers with different incomes, and show that even if preferences are homothetic, expected cost of living indices will generally vary across searchers with different references standards of living. The reason for the differences is that, under homothetic preferences, reservation prices are a decreasing function of the searcher's standard of living.
... Substituting e(p, w, u) and t, into eq. (1) yields y+y(p, y, u)8=e(p, la (p, y, u), u). (4) D... more ... Substituting e(p, w, u) and t, into eq. (1) yields y+y(p, y, u)8=e(p, la (p, y, u), u). (4) Differentiating eq. (4) with respect to time and applying Shephard's Lemma we have n .Y+A(sh) Lr pixh, i=1 where the dots' denote the time derivatives. ...
... This paper examines the implications of stochastic discount factors for Nash equilibria in re... more ... This paper examines the implications of stochastic discount factors for Nash equilibria in repeatedgames. ... Our results are also relevant for finitely repeated games where the probability that thegame ends (owing to bankruptcy, say) varies stochastically over time. ...
Communications in Statistics - Theory and Methods, 1984
... We concur with Lin and Kmenta (1982) that 'I.. .economic researchers [should] pa... more ... We concur with Lin and Kmenta (1982) that 'I.. .economic researchers [should] pay more attention to ridge regression than has so far been the case." (p. 494). ... PRINCIPAL COMPONENT REGRESSION have u 2 2 2 kjc > - - - - a >O. max a. That is, k* is bounded away from zero. ...
Lecture Notes in Economics and Mathematical Systems, 1986
In the previous chapters, we have explored how the presence of income taxation may alter several ... more In the previous chapters, we have explored how the presence of income taxation may alter several of the neoclassical properties of consumer demand functions and labor supply functions. As of yet, however, we have not discussed how one may empirically estimate the demand and supply functions when consumers face nonlinear budget sets While the literature is now quite extensive, the interested reader may find the recent work of Hausman (1985) a most useful review of the labor supply literature.
Lecture Notes in Economics and Mathematical Systems, 1986
We now consider the implications of allowing taxes to be a function of the income earned by indiv... more We now consider the implications of allowing taxes to be a function of the income earned by individuals. If the government wishes to, redistribute income by its tax policy, government may decide to use a nonlinear tax, taxing wealthy individuals more than poorer individual s. This leads to the question; how should government define how wealthy an individual is? Perhaps ideally government could base the income tax on the individual’s full income, F. This would allow government to base taxes on the market spending potential of each individual, and to construct a tax bill that really redistributes utility.
Lecture Notes in Economics and Mathematical Systems, 1986
Throughout this monograph we have focused on behavioral and index concepts that view government s... more Throughout this monograph we have focused on behavioral and index concepts that view government services and the tax system as fixed. In practice, the consumer may receive benefits from taxes (eg., public goods), and the government may from time to time change the tax code. This chapter provides a brief look at these issues, and shows how earlier results may be extended to deal with the issues. We consider first the issue of government goods, and then the issue of tax code changes. Finally, some preliminary results concerning the indexation of tax codes are presented.
Lecture Notes in Economics and Mathematical Systems, 1986
As a means of introducing the concept of an income-based measure of the cost of living, it is use... more As a means of introducing the concept of an income-based measure of the cost of living, it is useful to note that in the absence of taxes, the expenditure function and the full income compensation function correspond. That is, \({\text{e}}\left( {{\text{P, u}}} \right) \equiv \mu \left( {{\text{P, u; T}}} \right)\) where e(•) in the expenditure function defined in Chapter Three, and μ(•) is the income-compensation function defined in Chapter Four.
Lecture Notes in Economics and Mathematical Systems, 1986
In Chapter Seven we examined the construction of an income based cost of living index in the pres... more In Chapter Seven we examined the construction of an income based cost of living index in the presence of an income tax, but where the consumer’s income was solely exogenous. This chapter considers the concept of income based cost of living indices when the consumer’s income depends upon an endogenously determined labor supply. Recall that \({\text{P}} = \left( {{\text{P}}_0 ,\bar P} \right)\)) and \(X = ({X_0},\bar X)\)).
Lecture Notes in Economics and Mathematical Systems, 1986
In order to solidify important concepts, we shall first present some index concepts in the absenc... more In order to solidify important concepts, we shall first present some index concepts in the absence of an income tax. The key to constructing an expenditure-based cost of living index is the expenditure function examined in Chapter Three, namely \({\text{e}}\left( {{\text{P,u}}} \right) \equiv \frac{{\min }}{{\text{X}}}\left\{ {{\text{P}} \bullet {\text{X}}\left| {{\text{U}}\left( {\text{X}} \right) \geqslant {\text{u}}} \right.} \right\}\). This function defines the minimum expenditures on goods and leisure necessary to purchase the standard of living corresponding to u.
We show that the total cost of production index and the marginal cost of production index may be ... more We show that the total cost of production index and the marginal cost of production index may be used to illuminate the course of an industry's evolution. Each of these summary statistics conveys different bits of information about the industry. Theoretical properties of the indices are compared, and then the indices are applied to data from the steel industry to
... I.7. Baye and DA Black, On the Theory qf~zncome-based cost-of-living indiees 87 leisure. Assu... more ... I.7. Baye and DA Black, On the Theory qf~zncome-based cost-of-living indiees 87 leisure. Assuming that P and vary over tune, we differentiate eq. (4) with respect to time to obtain - F where dots over .-ariables denote their time derivatives. ...
Abstract This note extends recent work on cost of living index numbers for a population of indivi... more Abstract This note extends recent work on cost of living index numbers for a population of individuals who face imperfect and costly information about prices. It is known that individuals with identical preferences but different incomes will require different cost of living adjustments unless preferences are homothetic. However, this result in based on a model of consumer behavior under costless information. We analyze differences in the cost of living among searchers with different incomes, and show that even if preferences are homothetic, expected cost of living indices will generally vary across searchers with different references standards of living. The reason for the differences is that, under homothetic preferences, reservation prices are a decreasing function of the searcher's standard of living.
... Substituting e(p, w, u) and t, into eq. (1) yields y+y(p, y, u)8=e(p, la (p, y, u), u). (4) D... more ... Substituting e(p, w, u) and t, into eq. (1) yields y+y(p, y, u)8=e(p, la (p, y, u), u). (4) Differentiating eq. (4) with respect to time and applying Shephard's Lemma we have n .Y+A(sh) Lr pixh, i=1 where the dots' denote the time derivatives. ...
... This paper examines the implications of stochastic discount factors for Nash equilibria in re... more ... This paper examines the implications of stochastic discount factors for Nash equilibria in repeatedgames. ... Our results are also relevant for finitely repeated games where the probability that thegame ends (owing to bankruptcy, say) varies stochastically over time. ...
Communications in Statistics - Theory and Methods, 1984
... We concur with Lin and Kmenta (1982) that 'I.. .economic researchers [should] pa... more ... We concur with Lin and Kmenta (1982) that 'I.. .economic researchers [should] pay more attention to ridge regression than has so far been the case." (p. 494). ... PRINCIPAL COMPONENT REGRESSION have u 2 2 2 kjc > - - - - a >O. max a. That is, k* is bounded away from zero. ...
We exploit a unique dataset from a price comparison site to estimate the determinants of clicks r... more We exploit a unique dataset from a price comparison site to estimate the determinants of clicks received by online retailers. We find that a firm enjoys a 60% jump in its clicks when it offers the lowest price at the site and failure to account for discontinuities distorts parameter estimates by nearly 100%. This discontinuity is consistent with a variety of models that have been used to rationalize online price dispersion. Finally, we show that one may use estimates of the determinants of a firm’s clicks to obtain bounds on its underlying demand parameters, including standard elasticities of demand.
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This discontinuity is consistent with a variety of models that have been used to rationalize online price dispersion. Finally, we show that one may use estimates of the determinants of a firm’s clicks to obtain bounds on its underlying demand parameters, including standard elasticities of demand.