Showing papers in "International Economic Review in 1977"

Sufficient conditions in optimal control theory

Abstract: During the last ten years or so a large number of papers in professional journals in economics dealing with dynamic optimization problems have been employing the modern version of the calculus of variations called optimal control theory. The central result in the theory is the well known Pontryagin maximum principle providing necessary conditions for optimality in very general dynamic optimization problems. These conditions are not, in general, sufficient for optimality. Of course, if an existence theorem can be applied guaranteeing that a solution exists, then by comparing all the candidates for optimality that the necessary conditions produce, we can in principle pick out an optimal solution to the problem. In several cases, however, there is a more convenient method that can be used. Suppose that a solution candidate suggests itself through an application of the necessary conditions, or possibly also by a process of informed guessing. Then, if we can prove that the solution satisfies suLfficiency conditions of the type considered in this paper, then these conditions will ensure the optimality of the solution. In such a case we need not go through the process of finding all the candidates for optimality, comparing them and finally appealing to all existence thieorem. In ordcle to get all idea of what types of conditions might be involved in such sufficiency theorems, it is natural to look at the corresponding problem in static optimization. Here it is well known that the first order calculus or Kulhn-TLcker conditions are sU11ficient for optimality, provided suitable concavity/convexity conditions are imposed on the functions involved. It is natural to expect that similar conditions might secure sufficiency also in dynamic optimization problems. Growth theorists were early aware of this and proofs of sufficienccy in particular problems were constructed; see, e.g., Uzawa's 1964 paper [19]. In the mathematical literature few and only rather special results were available until Mangasarian. in a 1966 paper [10] proved a rather general sufficiency theorem in which he was dealing with a nonlinear system, state and control variable constraints and a fixed time interval. In the maximization case, when there are no state space constraints, his result was, essentially, that the Pontryagin necessary conditions plus concavity of the Hamiltonian function with respect to the state and control variables, were sufficient for optimality. The Mangasarian concavity condition is rather strong and in many economic problems his theorem does not apply. Arrow [1] proposed an interesting partial

A new proof of the existence and uniqueness of the cournot eouilibrium

Abstract: ntime period. Thus s= L xi. It is this variation of commodity market price that causes interaction among producers. It is assumed that producer i must expend kL(x) units of money for the manufacture of x items. Consequently, the profit enjoyed by producer i is given, for any production level xi and total production s, by

The demand for money during hyperinflations under rational expectations: i*

Abstract: paradox that emerged when Cagan used his estimates of x to calculate the sustained rates of inflation associated with the maximum flow of real resources that the creators of money could command by printing money. This "optimal" rate of inflation turns out to be -l/oc. For each of the seven hyperinflations, the reciprocal of Cagan's estimate of -a turned out to be less, and often very much less, than the actual average rate of inflation. The data are shown in

Inter-Fuel Substitution Possibilities: A Translog Application to Intercountry Data

Abstract: One of the pressing issues in current energy policy debates in both the U S and other consuming countries is the feasibility of substantially reducing the use of crude oil In some energy consuming sectors suchl as transportation, the shortrun mechanism to reduce consumption is through lower utilization of energyconsuming equipment while in the long-run, the equipment can be redesigned to achieve greater fuel efficiencies In electricity generation and heatilng uses the primary mechanism to reduce consumption is inter-fuel substitution rather than capital/energy substitution This paper is concernied with estimating the interfuel substitution relationships between fossil fuels (coal, gas, and residual fuel oil) in the generation of electricity It is important to consider fossil fuel substitution possibilities in electricity generation both because considerable technical flexibility exists2 and because electric utilities are large consumers of fossil fuels For example, electric utilities consumed 25% of primary energy inputs in the U S in 1970 Although not as high as the U S, the other developed countries exhibit a similar pattern In the 20 0 E C D coun-tries, electric utilities consumed 50% of the coal, 17% of the gas, and 11% of petroleum products3 High substitution elasticities among fuels in electricity generation indirectly increase subsequenit substitution of electricity for petroleum as a fuel source in residential, commercial, and industrial sectors Thus the nature and extent of inter-fuel substitution possibilities in electricity generation are fundamental to the question of reducing dependency on crude oil There have been several econometric studies of inter-fuel substitution in electricity generation using a variety of estimation procedures and samples MacAvoy [15] used cross sectional data for U S power regions to examine substitution between nuclear fuel and fossil fuel Griffin [10] estimated dynamic price and cross price elasticities among fuels utilizing annual time series data More recently, Joskow and Mishkin [13] used individual plant data to analyze fuel choice in a logit model framework But probably the approach capturing the most attention is the application of

The bias of instrumental variable estimators of simultaneous equation systems

Abstract: This paper examines the discussion in the econometric literature of the conditioins which instruments should satisfy in order to be used in the single equation Iiistrumental Variable (IV) estimation of structural parameters in a simultaneouIs equation system. The Two Stage Least Squares (TSLS) estimator can be interpreted as an IV estimator. It is consistent and, under normality assumptions for disturbances, asymptotically efficient. A new IV estimator is proposed which is also consistent and asymptotically efficient but whose instruments satisfy a stronger condition than the TSLS instruments. The finite sample bias of the new IV estimator is examined and found to be non-zero but a condition is presented for its bias to be smaller than that of TSLS.

Some Properties of the Optimal Income-Tax

Abstract: This paper explores the properties of optional income taxation when individuals differ in productive ability. Interest in this question can stem from either or both of two considerations. One is the fact that disparities in abilities will lead to inequalities in well-being among individuals. Tax policies can be developed to ameliorate such inequalities. This was the major concern of nineteenth century utilitarians and gave rise to minimum "sacrifice" theories of taxation. A second consideration arises from the fact that income taxation, for whatever purpose, will generally distort the allocation of resources in an economy. Because an individual's innate ability is difficult to measure objectively, taxes must be based upon the manifestation of this ability in the market place, i.e., earned income. As a consequence, individuals have incentives to alter their effective supply of labor, resulting in excess burden. Thus the policy-maker is confronted with the task of designing a tax structure which minimizes excess burden. This aspect of taxation has come under heavy scrutiny by economists in the past decade, giving rise to various optimal tax "rules." With one major exception, however, the literature has restricted its attention to unit taxes on commodities or linear taxes upon income. In a seminal work, Mirrlees [8], examined the question of optimal income taxation without imposing the condition of linearity and within a framework which incorporated both equity and efficiency criteria. His numerical analysis seemed to suggest that an optimal income tax was apt to be far less progressive than utilitarian concepts would lead us to suspect. Indeed, in recent extensions, Phelps [10] and Sadka [11] demonstrated that the optimal marginal tax rate on the highest income bracket is zero!2 Despite the obvious policy significance of Mirrlees' work, it is reasonable to assert that his analysis is not widely understood by most economists. In part this reflects the complexity of the problem, but more importantly it owes to his use of variational techniques. The latter makes the analysis cumbersome and the findings difficult to interpret.

Storage with price uncertainty in international trade

Abstract: The effects of price uncertainty in an international trade model where the possibility of storage is taken into account are investigated. The model's economy comprises two food production sectors where a single factor of production is used to produce both goods. With nonincreasing risk aversion, an increase in price uncertainty leads to an increase in production of both stored and nonstored commodities and a decrease in storage for exporters of the stored commodity; importers of the stored commodity decrease production of both commodities and increase storage; with nonincreasing risk aversion and increased price uncertainty, both importers and exporters of the stored commodity tend to limit their involvement in future trade; with increased future price uncertainty, expected social welfare is reduced for all risk averse importers and exporters; with a rise in expected future price of the stored commodity, all trading countries tend to shift resources into the storage activity and away from production of both stored and nonstored goods; with an increase in current price of the stored commodity, exporters increase planned future production of the stored commodity but reduced storage. 14 references.