Scrap Value Functions in Dynamic Decision Problems

We introduce an accurate, easily implementable, and fast algorithm to compute optimal decisions in discrete-time long-horizon welfaremaximizing problems. The algorithm is useful when interest is only in the decisions up to period T, where T is small. It relies on a flexible parametrization of the relationship between state variables and optimal total time-discounted welfare through scrap value functions. We demonstrate that this relationship depends on the boundedness, half-boundedness, or unboundedness of the utility function, and on whether a state variable increases or decreases welfare. We propose functional forms for this relationship for large classes of utility functions and explain how to identify the parameters.Scrap value function;Dynamic optimization;Computation;Short horizon.

Burr Utility

This note proposes the Burr utility function. Burr utility is a flexible two-parameter family that behaves approximately power-like (CRRA) remote from the origin, while exhibiting exponential-like (CARA) features near the origin. It thus avoids the extreme behavior of the power family near the origin. We show how to characterize Burr utility as a special case in the general class of utility functions with non-increasing and convex absolute risk aversion, and non-decreasing and concave relative risk aversion. We further show its connection to the Burr probability distribution. A related class of generalized exponential utility functions is also studied.Cardinal scale;Utility function;Harmonic absolute risk aversion (HARA);Exponential utility;Power utility

The economic impact of the Green Certificate market through the Macro Multiplier approach

In the last decade, as many other European countries, the Italian Government adopted several reforms in order to increase the use of Renewable Energy Sources (RES). The liberalization of the electricity market that represent one of these reforms aims to reach environmental benefits from the substitution of fossil fuel with renewable sources.The Italian Green Certificate market was introduced in 2002 in order to accomplish this objective and represents a mechanism where a quota of renewable electricity is imposed to suppliers in proportion to their sales. The electricity industries are obliged to meet this condition by producing the quantity of renewable electricity by means of a change in their production process, otherwise they must buy a number of certificates corresponding to the quota. This mechanism changes the importance of the electricity industry first in promoting climate protection, than in terms of the impact in the economy as a whole. A policy aimed to develop the market of green certificates may lead to environmental improvement by switching the energy production process to renewable resources. But above all an increase in demand for green certificates, resultant from a reform on the quota of renewable electricity, can generate positive change in all components of the industrial production. For this purpose, the paper aims to quantify the economic impact of a reform on Green Certificate market for the Italian system by means of the Macro Multiplier (MM) approach. The analysis is performed through the Hybrid Input-Output (I-O) model that allows expressing the energy flows in physical terms (GWh) while all other flows are expressed in monetary terms (e). Moreover, through the singular value decomposition of the inverse matrix of the model, which reveals the set of key structures of the exogenous change of final demand, we identify the appropriate key structure able to obtain both the expected positive total output change and the increase of electricity production from RES

Marketing Via Friends: Strategic Diffusion of Information in Social Networks with Homophily

The paper studies the impact of homophily on the optimal strategies of a monopolist, whose marketing campaign of new product relies on a word of mouth communication. Homophily is a tendency of people to interact more with those who are similar to them. In the model there are two types of consumers embedded into a social network, which differ in friendship preferences and desirable design of product. Consumers can learn about the product directly from an advertisement or from their neighbors. The monopolist chooses the product design and price to influence a pattern of communication among consumers. We find a number of results: (i) for low levels of homophily the product attractive to both types of consumers is preferred to specialized products; (ii) the price elasticity is increasing in homophily; (iii) an increase in the homophily benefits both the monopolist and consumers; and (iv) the product attractive to both types may be optimal even if the monopolist obtains profits only from sales to one type of consumers