Luigi Filippini

Two Theorems on Joint Production

The aim of this note is to present some new results in joint production models represented by linear equations.1 Necessary and sufficient conditions are derived for the existence of a semi-positive (positive) price vector and for a decreasing relation between profit and wage rates.2 As a corollary the presence of negative labour values and positive prices is explained and the scrap age of a machine determined.

Price and quantity adjustment in a dynamic closed model: The dual stability theorem☆

Abstract The paper analyzes dual instability in a dynamic input-output framework. It is divided into three parts: the first gives an informal introduction, the second discusses the similarity with the knife edge, and the last suggests a new interpretation, which guarantees nonnegative solutions and relative stability. It has been assumed that the producers adjust their prices following an adaptive expectation mechanism, and the current level of investment to the expected value defined by a golden rule approach.

Strategic Choice between Process and Product Innovation under Different Competitive Regimes

This paper investigates the strategic choice between introducing a process or a product innovation in a duopoly model with vertical differentiation, comparing the outcomes in case of Bertrand and Cournot competition. It is shown that under both competitive regimes three equilibria in innovation adoption may arise: two symmetric equilibria, where firms select the same innovation type, and one asymmetric equilibrium. The competitive regime has an impact on the features of the asymmetric equilibrium, since in case of Bertrand competition, the high (low) quality firm chooses a product (process) innovation, while firms make the opposite choices in case of Cournot competition. The presence of a leapfrogging effect (only in the Cournot competitors tend to favor the introduction of a new product in comparison with the Bertrand competitors.

A note on the diffusion of innovation

Abstract The paper deals with the process of substitution between technologies in a framework of increasing returns to scale. The approach stresses the interaction between capacity expansion and market demand as explanations of the diffusion of technologies into their niches. The demand and supply sides of the diffusion process are therefore brought together to determine simultaneously patterns of output and prices. It analyzes the dynamics of the substitution path, where a logistic diffusion process for the new technology is assumed, and determines the substitution curve between the old technology and the new one.

Cost Reduction, Licensing and Incentive to Innovate: A Note

In this Note we consider an economy composed by two firms; a leader and a follower, that invest in R&D for process innovations. Competition to innovate is usually modelled as a two stage game. In the first stage of the game both firms simultaneously reduces their production costs. In the second stage the firms compete la Stackelberg and it is possible to prove that the profits of one of the two firms (and total profits) might decrease in a range of parameters. Then we consider the possibility of technology transfer from the leader that has the most productive technology to the follower under licensing by means of a fixed fee and of a royalty. It is possible to prove that under licensing total profits will increase in some range of parameters above mentioned in comparison to the pre-innovation case.

Towards a Linear Model of Non-homogeneous Labour

Leontief’s scheme and Sraffa’s model are significant examples in the field of linear models of analyses based on the hypothesis of heterogeneous capital goods and homogeneous labour. This paper, instead, sets out to present the case of a non-homogeneous labour force within the framework of the same models and to examine some of the first implications.1

Vertical Integration Smooths Innovation Diffusion

Abstract Does vertical integration of an input innovator with a downstream firm entail innovation foreclosure? We study the licensing incentives of an independent input producer owning a patented product innovation which allows the downstream firms to improve the quality of their final goods. We consider two-part tariff contracts for both outside and incumbent innovators. We find that the incumbent innovator has always the incentive to license its innovation to the rival firm so that under vertical integration complete technology diffusion takes place. In contrast, the external patent holder may prefer exclusive licensing depending on the innovation size as well as on the set of allowed contracts. As a result vertical integration does not entail innovation foreclosure, rather it facilitates innovation diffusion with respect to vertical separation. As for the profitability, the vertical integration with either downstream firm is always privately profitable and it is welfare improving for large innovations: this implies that not all profitable mergers should be rejected.

Product innovation in a vertically differentiated model

We study the licensing incentives of an independent input producer owning a patented product innovation which allows the downstream firms to improve the quality of their final goods. We consider a general two-part tariff contract for both outside and incumbent innovators. We find that technology diffusion critically depends on the nature of market competition (Cournot vs. Bertrand). Moreover, the vertical merger with either downstream firm is always privately profitable and it is welfare improving for large innovations: this implies that not all profitable mergers should be rejected.

Wage differentials among workers in input-output models

Abstract A human capital approach is assumed to explain wage differentials among workers in an input-output framework, where skilled workers are produced by means of goods and labor of different kinds. The first part discusses the solution of the input-output system; wage differentials are analyzed in terms of the rate of profit. In the second part, on the basis of an education matrix compiled ad hoc, hypothetical wage differentials are calculated according to education costs and the changes of skill prices at various levels of nonwage incomes derived.