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Luigi BRIGHI

Professore Associato
Dipartimento di Economia "Marco Biagi"

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Pubblicazioni

2022 - Limit Pricing and Strategic Investment [Working paper]
Brighi, L.; D'Amato, M.
abstract

We study an entry model where an incumbent privately informed about costs can make a cost-reducing investment choice, along with a pricing decision, in order to prevent a competing rm from entering the market. We show that if limit pricing per se can not deter pro table entry, the opportunity to undertake a strategic investment does not provide an additional instrument for the achievement of this goal to the incumbent.

2022 - Limit pricing and strategic investment [Articolo su rivista]
Brighi, L.; D'Amato, M.
abstract

We study an entry model where an incumbent privately informed about costs can make a cost-reducing investment choice, along with a pricing decision, in order to prevent a competing firm from entering the market. We show that if limit pricing per se can not deter profitable entry, the opportunity to undertake a strategic investment does not provide an additional instrument for the achievement of this goal to the incumbent

2020 - Investment in early education and job market signaling [Working paper]
Brighi, L.; D'Amato, M.
abstract

We consider a signaling model of the job market in which workers, before choosing their level of education, have the opportunity to undertake an unobservable investment in activities aimed at saving on future education costs. Suciently high levels of investments allow a low productivity worker to cut the marginal costs of signaling below the high productivity worker's. In contrast to standard results, we nd that the equilibrium outcome will depend on the relative magnitude of workers' average productivity. If average productivity exceeds a certain threshold the most plausible solution is a rened pooling equilibrium in which all workers attain the same level of over-education and are paid the same wage. Otherwise, the most plausible outcome is the standard least cost separating equilibrium in which only high ability workers are over-educated.

2019 - Inefficiency in Childcare Production: Evidence from Italian Microdata [Articolo su rivista]
Brighi, Luigi; Silvestri, Paolo
abstract

The paper provides an empirical analysis of production technology in the childcare sector and offers a comparative analysis of inefficiency between public and private day-care centres. Estimates of multi-output production technology and technical inefficiency are obtained in a stochastic frontier model by using cross-section micro-data from a region of northern Italy over the period 2007/8. We find that production exhibits increasing returns to scale and that separability between inputs and outputs is rejected. The average estimate of technical inefficiency is about 10% and public centres are more inefficient than private centres by 4.1% points.

2018 - Private Information and the Commitment Value of Unobservable Investment [Working paper]
Brighi, L.; D'Amato, M.
abstract

The commitment value of unobservable investment with cost-reducing effects is examined in an entry model where the incumbent is privately informed about his costs of production. We show that when the price signals incumbent's costs, unobservable investment can not have any commitment value and the limit price does not limit entry. By contrast, if the price does not reveal costs, which is the more likely outcome, unobservable investment has a magnified value of commitment and a less aggressive limit price deters profitable entry.

2018 - Private Information and the Commitment Value of Unobservable Investment [Working paper]
Brighi, L.; D'Amato, M.
abstract

The commitment value of unobservable investment with cost-reducing effects is examined in an entry model where the incumbent is privately informed about his costs of production. We show that when the price signals incumbent’s costs, unobservable investment can not have any commitment value and the limit price does not limit entry. By contrast, if the price does not reveal costs, which is the more likely outcome, unobservable investment has a magnified value of commitment and a less aggressive limit price deters profitable entry.

2017 - Strategic Effects of Investment and Private Information: The Incumbent's Curse [Working paper]
Brighi, L.; D'Amato, M.
abstract

We study a two-period entry model where the incumbent, privately informed about his cost of production, makes a long run investment choice along with a pricing decision. Investment is cost-reducing and its effects are assumed to differ across incumbent's types, as a result investment plays a double role as a commitment variable and, along with price, as a signal. We ask whether and how investment decisions allow the incumbent to limit entry into the market. We find that the incumbent will never undertake strategic investment to deter profitable entry, because when incumbent's costs are private information the signaling role of investment cancels out its value of commitment.

2017 - Strategic Effects of Investment andPrivate Information: The Incumbent's Curse [Working paper]
Brighi, L.; D'Amato, M.
abstract

We study a two-period entry model where the incumbent, privately informed about his cost of production, makes a long run investment choice along with a pricing decision. Investment is costreducing and its effects are assumed to differ across incumbent’s types, as a result investment plays a double role as a commitment variable and, along with price, as a signal. We ask whether and how investment decisions allow the incumbent to limit entry into the market. We find that the incumbent will never undertake strategic investment to deter profitable entry, because when incumbent’s costs are private information the signaling role of investment cancels out its value of commitment

2016 - Inefficiency in Childcare Production. Evidence from Italian Microdata [Working paper]
Brighi, L.; Silvestri, P.
abstract

The purpose of the paper is to study inefficiency in the production technology of the childcare service and to carry out a comparative analysis of public and private day-care centres. An empirical analysis on cross-section micro-data from a region of northern Italy has been conducted by using an input-distance function with a translog specification. Estimates of the multi-output production technology and input-oriented technical inefficiency are obtained in a stochastic frontier model with a half-normally distributed one-sided error. Heteroscedasticity has been modelled to investigate the determinants of inefficiency and estimate their marginal effects. We find that production exhibits increasing returns with an estimated elasticity of scale of 1.21. Separability between inputs and outputs is rejected at a 5% level of significance. The average estimate of technical inefficiency is 10% and public centres are more inefficient than private centres by 4.1 percentage points. The proportion of part-time children and the presence of mixed-age classrooms are significant determinants of inefficiency which equally affect both public and private centres.

2016 - Inefficiency in Childcare Production. Evidence from Italian Microdata [Working paper]
Brighi, L.; Silvestri, P.
abstract

The purpose of the paper is to study inefficiency in the production technology of the childcare service and to carry out a comparative analysis of public and private day-care centres. An empirical analysis on cross-section micro-data from a region of northern Italy has been conducted by using an input-distance function with a translog specification. Estimates of the multi-output production technology and input-oriented technical inefficiency are obtained in a stochastic frontier model with a half-normally distributed one-sided error. Heteroscedasticity has been modelled to investigate the determinants of inefficiency and estimate their marginal e ects. We find that production exhibits increasing returns with an estimated elasticity of scale of 1.21. Separability between inputs and outputs is rejected at a 5% level of significance. The average estimate of technical inefficiency is 10% and public centres are more ine cient than private centres by 4.1 percentage points. The proportion of part-time children and the presence of mixed-age classrooms are significant determinants of inefficiency which equally a ect both public and private centres.

2016 - Inefficiency in childcare production. Evidence from italian microdata [Working paper]
Brighi, L.; Silvestri, P.
abstract

The purpose of the paper is to study inefficiency in the production technology of the childcare service and to carry out a comparative analysis of public and private day-care centres. An empirical analysis on cross-section micro-data from a region of northern Italy has been conducted by using an input-distance function with a translog specification. Estimates of the multi-output production technology and input-oriented technical inefficiency are obtained in a stochastic frontier model with a half-normally distributed one-sided error. Heteroscedasticity has been modelled to investigate the determinants of inefficiency and estimate their marginal effects. We find that production exhibits increasing returns with an estimated elasticity of scale of 1.21. Separability between inputs and outputs is rejected at a 5% level of significance. The average estimate of technical inefficiency is 10% and public centres are more inefficient than private centres by 4.1 percentage points. The proportion of part-time children and the presence of mixed-age classrooms are significant determinants of inefficiency which equally affect both public and private centres.

2014 - Limit pricing and secret barriers to entry [Working paper]
Brighi, L.; D'Amato, M.
abstract

We study a two periods entry game where the incumbent rm, who has private information about his own production costs, makes a non observable long run investment choice, along with a pricing decision observed by the entrant. The investment choice aff ects both post-entry competition and fi rst period cost of production, so that the cost of signaling becomes endogenous. The game is solved following Bayes-Nash requirements, the intuitive criterion is used to constrain o -equilibrium beliefs. When investment is publicly observable, it is shown that the unique intuitive equilibrium is the separating equilibrium with limit pricing and no entry deterrence. When investment is not observable, quite remarkably, there exists a unique intuitive pooling equilibrium which is Pareto superior, from the incumbent's point of view, to the unique intuitive separating equilibrium. In the pooling equilibrium no entry takes place and the price is below the low cost monopoly price. Thus, when investment is secret, a limit pricing policy supports entry deterrence. Our model provides an example of secret barriers to entry and their relationship with limit pricing. We also contribute to the analysis of a relatively under-researched class of games where the cost of signaling unobservable characteristics is endogenously determined by unobserved actions.

2014 - Limit pricing and secret barriers to entry [Working paper]
Brighi, L.; D'Amato, M.
abstract

We study a two periods entry game where the incumbent firm, who has private information about his own production costs, makes a non observable long run investment choice, along with a pricing decision observed by the entrant. The investment choice affects both post-entry competition and first period cost of production, so that the cost of signaling becomes endogenous. The game is solved following Bayes-Nash requirements, the intuitive criterion is used to constrain off-equilibrium beliefs. When investment is publicly observable, it is shown that the unique intuitive equilibrium is the separating equilibrium with limit pricing and no entry deterrence. When investment is not observable, quite remarkably, there exists a unique intuitive pooling equilibrium which is Pareto superior, from the incumbent’s point of view, to the unique intuitive separating equilibrium. In the pooling equilibrium no entry takes place and the price is below the low cost monopoly price. Thus, when investment is secret, a limit pricing policy supports entry deterrence. Our model provides an example of secret barriers to entry and their relationship with limit pricing. We also contribute to the analysis of a relatively under-researched class of games where the cost of signaling unobservable characteristics is endogenously determined by unobserved actions.

2005 - A Hypothesis Guaranteeing the Weak Weak Axiom [Working paper]
Brighi, Luigi; R., John
abstract

The Weak Weak Axiom (WWA) for the aggregate excess demand function ensures uniqueness of equilibrium in regular economies. Jerison (1999) shows that the WWA holds if the excess demand satisfies the hypothesis of Nondecreasing Dispersion of Excess Demand (NDED). This note offers a new hypothesis guaranteeing that the WWA holds and suggests a new way for obtaining supporting empirical evidence.

2005 - An Extension Theorem for Non-Transitive Preferences [Working paper]
Brighi, Luigi
abstract

In his classical contribution Szpilrajn (1930) shows that any quasi-ordering (a reflexive and transitive binary relation) can be extended to an ordering (a complete quasi-ordering). The purpose of this paper is to provide an analogous extension result for non-transitive preferences. The case of quasi-transitivity (transitivity of the strict preference) is trivial since it suffices to `complete' the original preference by putting indifference for all pairs of alternatives that are non-comparable. The focus of our analysis is a different notion of non-transitivity called $sigma$-transitivity and put forward bySen (1970).Our main result is an extension theorem which shows that any $sigma$-transitive preference can be extended to a complete preference preserving$sigma$-transitivity. We also provide the dual result in terms of a strict preference approach.Finally, we show an application to the theory of choice by providing a new characterization of the Weak Axiom of Revealed Preference.

2005 - Entry deterrence with unobservable investment. Revisiting LimitPricing [Working paper]
Brighi, Luigi; M., D'Amato; S., Piccolo
abstract

We study a standard entry game where the incumbent makes a long runinvestment choice and a pricing decision facing the threat of entry. Whenthe investment decision is not observed by the potential entrant and theincumbent has private information on costs we show that an aggressivepricing strategy restores the commitment value of investment in a separatingequilibrium and affects the probability of entry.

2005 - Three-Types Models of Multidimensional Screening [Working paper]
Brighi, Luigi; M., D'Amato
abstract

This paper analyzes the variety of optimal screening contracts in a relatively simple multidimensional framework a la Armstrong and Rochet (1999), when only three types of agents are present. It is shown, among other things, that the well known principle in optimal contract theory of `no distortion at the top' does not carry over to the multidimensional case.

2004 - A Stronger Criterion for the Weak Weak Axiom [Articolo su rivista]
Brighi, Luigi
abstract

The Weak Weak Axiom (WWA) is a milder version of the Weak Axiom of Revealed Preference (WA) and is equivalent to pseudomonotonicity of the excess demand function.Since the WWA guarantees uniqueness of the equilibrium in a broad class of general equilibrium models, it is important to have criteria to check when the WWA holds.In this paper a new and more general characterization ofpseudomonotonicity for $C^1$ maps is provided. Using this result we obtain a stronger criterion for the WWA than those available in the literature.A complete characterization of the WA for excess demand functions is also offered and other important existing results are obtained in a straightforward fashion.

2003 - Characterizations of Pseudomonotone Maps and Economic Equilibrium [Capitolo/Saggio]
Brighi, Luigi; John, R.
abstract

The paper surveys some recent contributions to the analysis ofpseudomonotone maps and their application to economics. It is shown that the concept ofpseudomonotonicity is strongly related to a notion of rationalityof consumer's behaviour which is well known in economics as a weakversion of the Weak Axiom of Revealed Preference. In economic models of general equilibrium, a pseudomonotone aggregate excess demand function is seen to guaranteeconvexity of the set of price equilibria and, in the case of so-called regular economies,even the uniqueness of equilibrium. Some generalcharacterizations of differentiable pseudomonotone maps, which reduce to necessary and sufficient first order conditions under the assumption of regularity, are provided.These conditions are employed in order to prove pseudomonotonicity ofaggregate excess demand in economies displaying a particular kind ofheterogeneous consumer behaviour.

2002 - Two-Dimensional Screening: A case of Monopoly Regulation [Articolo su rivista]
Brighi, Luigi; D'Amato, M.
abstract

This paper deals with the optimal regulatory policy of a monopolist producing two goods and with two-dimensional private information about costs. The case of perfectly and negatively correlated cost's parameters is analyzed and a complete characterization of the optimal mechanism by means of easily interpretable conditions is obtained.

2001 - A Stronger Criterion for the Weak Weak Axiom [Working paper]
Brighi, L.
abstract

2001 - Characterizations of Pseudomonotone Maps and Economie Equilibrium [Working paper]
Brighi, L.; John, R.
abstract

2001 - The Weak Axiom, the ð-Axiom and Complete Non-Transitive Rationality [Working paper]
Brighi, L.
abstract

2001 - Two-Dimensional Screening: A Case of Monopoly Regulation [Working paper]
Brighi, L.; D’Amato, M.
abstract

1998 - Demand and generalized monotonicity [Working paper]
Brighi, L.
abstract

1998 - Optimal Procurement in Multiproduct Monopoly [Articolo su rivista]
Brighi, Luigi; D'Amato, M.
abstract

In this paper we characterize the optimal procurement policy for a multiproduct monopoly with multidimensional private information about its costs. We show that, unless correlation between costs is positive and large, the optimal procurement contract should regulate jointly the production of the various goods even when these goods are not linked by any technological or demand factor.The economic intuition behind this resultis similar to the rent-extracting argument used to justify the optimal sellingstrategy of a multiproduct monopolist. In both cases a bundlingstrategy allows the principal to reduce the informational rents of `mixed type' agents when they are more likely. The results arealso applied to the case where, for each good, a verifiable quality as well asa quantity index can be contracted upon.

1998 - Optimal Procurement in Multiproduct Monopoly [Working paper]
Brighi, Luigi; D'Amato, Marcello
abstract

1996 - Microeconomia - Teoria ed esercizi svolti [Monografia/Trattato scientifico]
Brighi, Luigi
abstract

Manuale di microeconomia di livello intermedio con esercizi svolti

1995 - Monotonicity and the demand theory of the weak axioms,  pp. 20 [Working paper]
Brighi, L.
abstract

1991 - Aggregation Across Agents in Demand Ssystems [Articolo su rivista]
Brighi, Luigi; Forni, Mario
abstract

In this survey we present the main results on the problem of aggregation across agents in demand systems, when no restrictions are placed on income distribution. The focus is on the theoretical aspects of the results. The implications for empirical work are made explicit, but not dealt with in detail.