Maximum Principle for Linear-Convex Boundary Control Problems applied to Optimal Investment with Vintage Capital

The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author, or by Faggian and Gozzi. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital

Equilibrium points for Optimal Investment with Vintage Capital

The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run

Optimal investment in age-structured goodwill

Segmentation is a core strategy in modern marketing and age-specific segmentation, which is based on the age of the consumers, is very common in practice. A characteristic of age-specific segmentation is the change of the segments composition during time, which may be studied only using dynamic advertising models. Here, we assume that a firm wants to promote and sell a single product in an age segmented market and we model the awareness of this product using an infinite dimensional Nerlove- Arrow goodwill as a state variable. Assuming an infinite time horizon, we use some dynamic programming techniques to solve the problem and to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market due to the time evolution of the segmentation.Segmentation; infinite dimensional Nerlove-Arrow goodwill.

Measuring Regional Multipliers: A Comparison between Two Different Methodologies for the Case Of The Italian Regions

This paper focuses on theory and methodology in estimating Keynesian regional multipliers. After introducing the concept of Keynesian multipliers at both national and regional level and describe the database used, two methodologies are compared and applied to the case of the Italian regions: the "Marginal propensities method" (MPM) and the "Aggregate leakages method" (ALM). The higher multipliers values in Southern Italy, resulting from the application of both methodologies, are consistent with similar previous findings and appear to be related to the degree of openness of the local economy, the availability of resources and their marginal productivity, the level of wealth, income distribution and the consequent different consumption patterns. Keywords: Keynesian multipliers, Italian regions, regional disparities JEL-classification: R10, E12, R15

Knowledge, innovation and collective learning: theory and evidence from three different productive areas in Italy

Innovative capacity of firms has traditionally been explained through intra-firm characteristics, being firms size the most important. A wave of empirical studies identifies small firms as the engines of technological change and innovative activity, at least in certain industries. This statement and these empirical findings constrast the well known observation that, since R&D expenditure is concentrated in large firms, and that innovative output strongly depends on R&D inputs, large firms are expected to drive the technological process. These contrasting results have pushed industrial economists to look for other explanatory variables. In the recent literature much emphasis has been put to determinats which are external to the firm; these external factors are called knowledge spillovers, and refer to the positive externalities that firms receive in terms of knowledge from the environment in which it operates. Both industrial and regional economists underline the importance of knowledge spillovers. As this paper underlines, the main difference between the two groups is that regional economists identify in a clear way the channels through which knowledge spills over a local area. The concept of relational capital is fundamental in this respect. Relation capital is in fact defined as the set of all relationships - market relationships, power relationships, co-operation - established between firms, institutions and people, which stem from a strong sense of belonging and a highly developed capacity of cooperation typical of culturally similar people and institutions. The existence of high relational capital in an area generates stable cooperation between firms and their local suppliers and customers, an efficient local labour market with a high internal mobility of employees and spin-offs from local firms, which are considered as the main channels through which knowledge spreads over a local area. Thus regional economists provide a new insight in the way knowledge develops over space; from the empirical point of view, some qualitative case studies exist which stress collective learning mechanisms, but a real need exists for solid quantitative empirical analyses. The main aims of the present paper are twofold. The first aim is o underline the main differences between industrial and regional economists. The second aim is to provide a quantitative empirical approach using econometric techniques to verify the existence and importance of relational capital on the innovation activity of firms. Proxies are found to represent the channels of collective knowledge and therefore indirectly of relational capital. The different regional, sectoral and firms' characteristics will also be analysed, in order to understand whether they influence the role relational capital has on firms' innovation. It is, indeed, reasonable to expect that relational capital will play a different role in different regional, sectoral and firm's contexts.

Equilibrium Points for Optimal Investment with Vintage Capital

The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.Linear convex control, Boundary control, Hamilton–Jacobi–Bellman equations, Optimal investment problems, Vintage capital

Mobility, education and labor market outcomes for U.S. graduates: Is selectivity important?

The literature on human capital, and its positive effects on individuals and regional economies, is now vast. The linkages between human capital and migration have also found a fertile ground in recent years especially in Europe where many studies have focused on interregional migration of graduates and highly skilled individuals. However, the literature on this phenomenon in the USA is less developed. Using the SESTAT database from NSF, this paper aims at contributing to the understanding of inter-state migration behavior of graduates in the USA and its effects on their career outcomes. It builds on the existing literature not only by focusing specifically on the US context, but also incorporating into the empirical model a correction for the possible selection bias that arises from the dual relationship between migration propensity and human capital endowment. Our estimated Mincerian earning equations, corrected for migrant self-selectivity, show that indeed repeat migration is associated with higher average salaries, while late migration is associated with a salary penalty. As for the other control variables, our results are consistent with what has been found in the labor economics literature. Female workers suffer from a salary penalty, while experience, level of education and employer size are all associated with higher average salaries. The labor market also rewards different fields of study differently

On the Dynamic Programming approach to economic models governed by DDE's

In this paper a family of optimal control problems for economic models is considered, whose state variables are driven by Delay Differential Equations (DDE's). Two main examples are illustrated: an AK model with vintage capital and an advertising model with delay e ect. These problems are very di cult to treat for three main reasons: the presence of the DDE's, that makes them ifinite dimensional; the presence of state constraints; the presence of delay in the control. The purpose here is to develop, at a first stage, the Dynamic Programming approach for this family of problems. The Dynamic Programming approach has been already used for similar problems in cases when it is possible to write explicitly the value function V (Fabbri and Gozzi, 2006). The cases when the explicit form of V cannot be found, as most often occurs, are those treated here. The basic setting is carefully described and some first results on the solution of the Hamilton-Jacobi-Bellman (HJB) equation are given, regarding them as a first step to nd optimal strategies in closed loop form.

Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital

The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.Linear convex control, Boundary control, Hamilton–Jacobi–Bellman equations, Optimal investment problems, Vintage capital