[Changes in asset prices are shown to produce only substitution effects in a broad class of portfolio-choice models. Wealth effects are identically zero unless the individual's stocks of assets are subject to unanticipated changes.]
Zellner [11], and Chow [3], is to deal with the uncertainty by treating the model parameters as independent, identically distributed random variables in each period,' yielding what Zellner calls rules. Although the sequential updating rules do capture the uncertainty, they ignore the possibility of ongoing estimation in the formulation of decision rules. The purpose of this paper is to develop an adaptive learning decision rule for the multiperiod problem. This rule incorporates the effect of policy variables on the learning which is expected to occur throughout the remainder of the planning period. It is a generalization of the rules described above in the sense that both of them can be derived as special cases of this rule. Finally, this decision rule yields to economic analysis in terms of the stock and value of information, a feature which is not found in previous work. Section 2 of the paper describes the multiperiod decision problem with unknown parameters, discusses the assumptions associated with the certainty equivalence and sequential updating rules, and then presents the assumptions employed in this paper. Adaptive learning decision rules are derived in Section 3 and a mathe
[A preference ordering R is called "self-dual" by Samuelson if and only if there exists a direct utility function U representing R such that U(Z) = - U*(Z) is any non-negative n-vector and U* is the indirect utility function corresponding to U. Samuelson showed that the Cobb-Douglas preference ordering is self-dual and asked the open question as to the existence of any other self-dual case. If a preference ordering R is both self-dual and homothetic, then for the two-good case Samuelson claims to have proved that R is Cobb-Douglasian and conjectures the same to be true in the three-or-more good-case. Swamy has claimed that the Cobb-Douglas case is the only example of a preference ordering which is self-dual and either homothetic or additive. In this paper, we give two non Cobb-Douglasian examples of self-duality, one additive and the other homothetic, in order to answer the open question and refute the claims.]
A method for optimization in nonlinear stochastic models is proposed in this paper, and applied to study monetary and fiscal policy in the St. Louis econometric model. Essentially, the method is to simulate the model in a number of stochastic simulations in which the coefficients of the model are treated as random, to use the results of the stochastic simulations to find parsimonious representations of the time form of the policy multipliers by estimating autoregressive moving-average regressions for the effects of policy on the relevant endogenous variables, and then to use these equations in computing optimal policy. The method is applied to the study of monetary and fiscal policy for the St. Louis model over a 60-period horizon with encouraging and sensible results.
This paper deals with the relationship between the monopoly price and the socially optimal price in the presence of consumption diseconomies. The above relationship is derived from characteristics of the utility function. THE THEORY of external diseconomies asserts that the socially optimal price of a good causing a diseconomy should be above its marginal cost. We also know that a monopolist will charge a price above its marginal cost. The purpose of this paper is to determine the relationship between these two prices. In addition, we demonstrate that knowledge of consumer preferences permits one to infer whether the monopoly price would be higher or lower than the socially optimal price. This relationship is of both theoretical and applied interest. Baumol and Oates [1] suggested some practical ways to measure the marginal harm to the environment in the presence of external diseconomies, using certain environmental standards. In general, the determination of the socially optimal price is impossible because the elements determining the price are unobserved. We will prove a theorem based on elasticity characteristics of the utility function, which yields policy information necessary to achieve a social optimum. We shall also prove that a large class of utility functions will yield the same optimal prices; in particular, the socially optimal price is equal to the monopoly price. In the past, it has been commonly asserted that the monopolistic price would be higher than the socially optimal price in the presence of consumption diseconomies. This view is illustrated by Naor [8], and in a more general case by Knudsen [7]. They do not deal with a general model of external diseconomies, but rather with a specific case of a queuing model with a waiting line. Within this context, including some restrictions on the utility function, they derive the above relationship between the monopolistic and the socially optimal prices. Buchanan [2] also discusses the possibility of having a socially optimal price higher than the monopolistic price. Examples of such possibilities in the context of diseconomies arising from congestion are supplied by Edelson [6].2 Similar problems were discussed by Diamond and Mirrlees [5] in dealing with the relationship between the Pareto optimal situation and the competitive equilibrium. In addition, a general discussion of optimal surcharge in cases of consumption externalities is given in Diamond [4]. ' Research for this paper was done while I. Luski was Visiting Assistant Professor of Economics, University of Florida. We are indebted to Milton Z. Kafoglis and David Levhari for helpful comments and suggestions. 2 It can be shown that the results of his examples can be inferred from our theorem.