Ricerche Economiche最新文献

In this study, we investigate optimal dynamics in a two-sector model in which the capital good is a public good. We obtain a sufficient condition under which optimal dynamics in fact follows non-linear dynamics, involving period-2 cycles and a tentshaped transition function.

We consider discrete time optimal growth models in the reduced form. The maintained assumptions are that the production technology set is convex and that preferences are additively separable with a continuous and strictly concave (reduced form) utility function. Using the dynamic programming approach we derive two new optimality conditions for models of this class. The first one is an inequality which has to be satisfied by the optimal value function and the optimal policy function of any strictly concave optimal growth model. As an application of this condition we derive Hölder continuity and Lipschitz continuity, respectively, of the optimal policy functions in strongly concave optimal growth models. (These properties were originally proven by Luigi Montrucchio using a completely different approach.) The second optimality condition is a condition that has to be satisfied by a continuous mapping h from a convex set X into itself if this mapping is the optimal policy function of any strictly concave optimal growth model with a given discount factor p and the state space X. This condition is stated in terms of a dominance relation between two probability measures on X. We also derive a reformulation of this condition for the special case of probability measures with finite support and illustrate its application by showing that the tent map (one of the most famous examples from chaos theory) cannot be an optimal policy function unless the discount factor is smaller than $\text{1}\text{√6}$.

Conditions for saddle point property, and the loss of it, have been widely studied. Generally these properties are established by means of a Hamiltonian formalism; we propose here to work without reference to any Hamiltonian system, and to use only the Lagrangian.

Our study is local; it may seem that no new result can be obtained in this setting; nevertheless we establish sufficient conditions for the loss of saddle point property and for the existence of periodic orbits which, to our knowledge, are not found in the literature.

We take the standard assumption that the Lagrangian is concave. It is well known that the cross derivatives of the Hamiltonian (i.e. H_xp(x, p)) are important in these problems, but the concavity-convexity property of the Hamiltonian does not easily give any information on these derivatives. On the other hand, we obtain such information directly in the Lagrangian version, because the Lagrangian is concave on its two arguments.

We give here a self-contained version of our results and we do not hesitate to re-establish some well-known results, because we believe it is interesting to underline the straightforward aspect of the Lagrangian approach.

The purpose of this paper is to investigate the (theoretical) importance of chaos as a phenomenon occurring in dynamic optimization problems. The intertemporal models we focus on are specified by a standard aggregative production function, an immediate return function depending on current consumption, capital input and a taste parameter, and a discount factor.

We interpret “chaos” as a situation in which the Liapounov exponent of the relevant dynamical system is positive. This notion of chaos is related to the concept of “unpredictability” as measured by the Kolmogorov-Sinai entropy.

In the family of intertemporal models, indexed by the taste parameter (with values lying in a closed interval), chaos is considered to be an “unimportant” phenomenon, if the set of parameter values for which chaos occurs is of Lebesgue measure zero.

We identify a family of dynamic optimization models, for which the optimal transition functions are represented by the quadratic family of maps. Relying on the mathematical literature on the robustness of chaos for this family of maps, we conclude that chaos cannot be considered to be an unimportant phenomenon in dynamic optimization models.

This paper uses the dynamic duality approach to build a closed-form factor demand equation system which is consistent with the intertemporal problem faced by the representative firm, aiming at minimizing the present value of its expected future costs. The technology is characterized by convex internal costs in adjusting the quasi-fixed capital input with no constraints on the degree of returns to scale. A model imposing long-run constant returns is also estimated. The two models are non-nested because of the functional form used to specify the underlying technology. In both models the hypotheses of existence and separability of adjustment costs are tested. Non-nested tests are used to discriminate between the assumptions of non-constant and constant returns to scale. Finally, the production structure for the Italian total manufacturing sector over the period 1954–1983 is analysed.

The paper develops an endogenous growth model which is based on lexicographical consumer preferences. The central variable determining the long-run rate of growth is personal income distribution. Its role in the process of growth depends crucially on the assumption about productivity growth. If productivity grows proportionally to product diversity, then an unequal distribution of incomes, measured by the rate of proportion of top to average incomes, has a positive effect on growth. However, under alternative assumptions, for instance, if productivity is a function of average income, inequality turns out to be harmful for economic growth.

This paper provides some evidence against the rational expectations—permanent income model of consumption behaviour and the Ricardian Equivalence proposition by testing the responsiveness of spending to the implementation of pre-announced changes in income taxes. A long series of recurrent episodes of this kind for the United Kingdom (1960–1990) is examined. It is found that consumption expenditure strongly reacts to (pre-announced) fiscally-induced changes in current disposable income. This effect is attributable to the semi-durable and durable component of spending.

A model of private provision of a public good under conjectural variations is discussed and the rule for a symmetric consistent conjectures equilibrium (CCE) derived. It is shown that in a number of reasonable cases symmetric CCEs fail to exist in economies with identical individuals, while there may exist asymmetric ones. The relevance of these results for the use of the conjectural variations approach in public good theory is then discussed together with some suggestions for further research.