Marshall\u27s Theory of Value and the Strong Law of Demand

We show that all the fundamental properties of competitive equilibrium in Marshall’s theory of value, as presented in Note XXI of the mathematical appendix to his Principles of Economics (1890), derive from the Strong Law of Demand. This is, existence, uniqueness, optimality, global stability of equilibrium prices with respect to tantonnement price adjustment and refutability follow from the cyclical monotonicity of the market demand function in the Marshallian general equilibrium model

The Strong Law of Demand

We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.Permanent income hypothesis, Afriat's theorem, Law of demand, Consumer's surplus, Testable restrictions

Rationalizing and Curve-Fitting Demand Data with Quasilinear Utilities

In the empirical and theoretical literature a consumer's utility function is often assumed to be quasilinear. In this paper we provide necessary and sufficient conditions for testing if the consumer acts as if she is maximizing a quasilinear utility function over her budget set. If the consumer's choices are inconsistent with maximizing a quasilinear utility function over her budget set, then we compute the "best" quasilinear rationalization of her choices.Quasilinear utilities, Afriat inequalities, Curve-fitting

Constrained School Choice: An Experimental Study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferentes. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools plays an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.School Choice, Matching, Experiment, Gale-Shapley, Top Trading Cycles, Boston Mechanism, Efficiency, Stability, Truncation, Truthtelling, Safety School

Constrained School Choice: An Experimental Study

The literature on school choice assumes that families can submit a preference list over all the schools they want to be assigned to. However, in many real-life instances families are only allowed to submit a list containing a limited number of schools. Subjects' incentives are drastically affected, as more individuals manipulate their preferences. Including a safety school in the constrained list explains most manipulations. Competitiveness across schools play an important role. Constraining choices increases segregation and affects the stability and efficiency of the final allocation. Remarkably, the constraint reduces significantly the proportion of subjects playing a dominated strategy.school choice, matching, experiment

Grading on a curve: When having good peers is not good

Student access to education levels, tracks or majors is usually determined by their previous performance, measured either by internal exams, designed and graded by teachers in school, or external exams, designed and graded by central authorities. We say teachers grade on a curve whenever having better peers harms the evaluation obtained by a given student. We use rich administrative records from public schools in Catalonia to provide evidence that teachers indeed grade on a curve, leading to negative peer effects. This puts forth a source of distortion that may arise in any system that uses internal grades to compare students across schools and classes. We find suggestive evidence that school choice is impacted only the year when internal grades matter for future prospects

Maturity and school outcomes in an inflexible system : evidence from Catalonia

The existence of a rigid cutoff date which determines when children start primary school creates a large heterogeneity in students' level of maturity within the classroom. We use rich administrative data of the universe of public schools in Catalonia to show that: (1) relatively younger children do significantly worse both in tests administered at the school level and at the regional level, and they experience greater retention. (2) These effects are homogeneous across SES and significant across the whole distribution of performance. (3) Younger children in our data exhibit higher dropout rates and choose the academic track in secondary school less often. (4) Younger children are more frequently diagnosed with learning disorders

The Nonparametric Approach to Applied Welfare Analysis

Changes in total surplus and deadweight loss are traditional measures of economic welfare. We propose necessary and sufficient conditions for rationalizing consumer demand data with a quasilinear utility function. Under these conditions, consumer surplus is a valid measure of consumer welfare. For nonmarketed goods, we propose necessary and sufficient conditions on market data for efficient production , i.e., production at minimum cost. Under these conditions we derive a cost function for the nonmarketed good, where producer surplus is the area above the marginal cost curve