evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

games with unique mixed strategy equilibria an experimental study abstract the results of an experiment studying the choices of subjects playing mixed extensions of three variants of simple 2 2 non constant sum strictly competitive games of the same form matching pennies are presented subjects exhibited a variety of behavioral adaptive learning strategies this heterogeneity of individual behavior produced aggregate dynamics whose estimated steady states are quite different from those predicted by the nash equilibria of those stage games with asymmetrical payoff functions the observed aggregative dynamics are well accounted for both by a quantal equilibrium model of mckelvey and palfrey and by a learning model of roth and erev journal of economic literature classification number c72

learning behavior and mixed strategy nash equilibria abstract the paper considers whether an adaptive justification like those commonly available for non interactive optimization models can be found for the mixed strategy nash equilibrium although it is known that such a justification is frequently available for pure strategy equilibria it is shown that all members of a wide class of behaviorally plausible learning mechanisms must fail to converge in almost all games in which the equilibrium involves mixed strategies an exact formal analogy is developed which allows these learning mechanisms to be viewed as discrete ta tonnement processes in properly chosen competitive exchange economies in the analogy the instability derives from the independence of excess demand functions except at the boundaries from own prices this independence arises because of the linearity in probabilities of von neumann morgenstern risk preferences and therefore does not extend to pure strategy equilibria in general thus assuming that agents will play equilibrium strategies implicitly assumes more sophistication when the equilibrium involves mixed strategies than when it involves only pure strategies

capital investments and resource extraction from non identical deposits abstract taking account of necessary investments in physical capital we characterize the optimal investment and extraction program for exploiting several non identical deposits of an exhaustible resource under the given technology assumptions capital investments will be concentrated up front if deposits are identical in the case of non identical deposits it may be optimal to have investments spread out over time moreover the smallest deposit is depleted first

a note on mining with investment in capital one of the principal predictions of the theory of the extractive firm is that its rate of output will decline steadily throughout time recently in this journal campbell 1980 presented an interesting analysis suggesting that this behaviour may be altered if one accounts for the fact that firms must invest in some level of fixed capital which is needed in combination with variable inputs to extract the resource in the campbell analysis the fixed capital places a constraint on the maximum rate of extraction it is shown that this constraint is binding and that extraction is therefore constant over some initial period of the mine when the firm behaves optimally this note demonstrates that the campbell result is due to a fixed proportions technology assumption in particular when a neoclassical technology is assumed one finds that the constraint imposed by the level of fixed capital is never binding and that the optimal extraction rate is strictly monotonically declining as a function of time i to demonstrate this an informal argument will suffice let k be the level of fixed capital chosen by the firm let lt be the amount of the variable factor employed in period t assume that the rate of extraction et is given by the production function2

reinforcement learning in the el farol model abstract the paper applies the approach of reinforcement learning to arthur s american economic review 84 1994a 406 el farol problem where repeatedly a population of agents decides to go to a bar or stay home and going is enjoyable if and only if the bar is not crowded the numerical simulations show that the learning process is fairly efficient in that attendances tend to fluctuate around the bar s capacity on the other hand the shape of the long run equilibrium frequency distribution is usually quite distinct from the nash equilibrium solutions and furthermore rather sensitive to some of the model s specification details

learning a mixed strategy equilibrium in the laboratory abstract this paper examines a laboratory game with no pure strategy equilibrium and one mixed strategy equilibrium a simple adaptive model describes players strategy adjustments reasonably well as long as predictable adjustments are not easily exploited by others consistent with theory these adjustments do not lead players to equilibrium when predictable adjustments are made more easily exploited players deviate from adaptive adjustments in order to avoid exploitation and exploit others these deviations cause players to converge more strongly to equilibrium these results confirm both the predictive power of adaptive models in some settings and the instability of mixed strategy equilibria

an experiment to evaluate bayesian learning of nash equilibrium play abstract we report on an experiment designed to evaluate the empirical implications of jordan s model of bayesian learning in games of incomplete information a finite example is constructed in which the model generates unique predictions of subjects choices in nearly all periods when the true game defined by players private information was one with a unique equilibrium in pure strategies the experimental subjects play converged to the equilibrium as jordan s theory predicts even when the subjects had not attained complete information about one another but when there were two pure strategy equilibria the theory s predictions were not consistent with observed behavior journal of economic literature classification numbers d83 c72 c92

evidence on the validity of cross sectional and longitudinal labor market data this article investigates error properties of survey reports of labor market variables we use the panel study of income dynamics psid validation study a two wave panel survey of workers employed by a large firm that shared its detailed payroll records individuals reports of annual earnings are fairly accurate errors are negatively related to true earnings reducing bias due to measurement error when earnings are used as an independent variable biases are moderately larger for changes in earnings earnings per hour are less reliably reported than annual earnings biases in estimating earnings functions are relatively small but those in labor supply functions may be important

capital adjustment costs a nonrenewable resource industry the exploitation of a nonrenewable resource by a monopolist or by competitive firms has been studied extensively since hotelling 2 one focal point has been the investigation of markets characterized by a cartel competing with a group of smaller firms as in the oil industry salant 7 and gilbert 1 conclude that the opec cartel will increase its market share and attain monopoly status the industry s history from 1980 through 1986 however suggests that this is not the case the price set by the cartel has encouraged expansion by other firms pushing opec to the point of near collapse further the structure of the nickel and other resource industries has changed from monopoly into competition the fact that existing models fail to track observed trends in market structure implies that important economic elements have been omitted from the analysis as the present study will show including limitations on the ability of firms to expand production quickly yields a more general model of the evolution of market structure

an investment model of natural resource markets over the last decade there has been an increasing interest in natural resource economics to some extent this can be ascribed to a general concern with the environment but an important cause was the large price increases for resources in the early 1970s the observed price jumps can be understood as a belated recognition of the scarcity of resources but they can also be viewed as shortor medium term phenomena arising from demand shocks and in the case of petroleum cartelization in markets with slow supply responses a jump in demand or a drop in foreign supplies would result in a sharp immediate price increase even in the absence of any long term resource scarcity the purpose of the present analysis is to try and assess the absolute and relative importance of these two potentially distinctive features of resource markets depletability and slow supply adjustment most of the empirical analysis in the literature examines resource markets from the hotelling 1939 asset market perspective by comparing observed price paths to the equilibrium price path in its simplest form the hotelling model leads to the rule of equality between interest rates and rates of resource price growth however the seminal empirical study by barnett and morse 1963 was not supportive of the hotelling rule and later studies by heal and barrow 1980 1981 smith 1981 and feige and geweke 1979 have provided only limited support the current study provides an alternative approach to testing for depletability in a formulation that also allows for consideration of the inelasticity of supply in the short and intermediate term we do this by concentrating upon the production side of the market and using an adjustment cost1 or investment model of resource production the resulting model seems fairly successful in describing the behaviour of at least three of the metals considered with evidence for both the adjustment cost hypothesis and for depletability there is however also evidence for a technological progress effect that has in the past outweighed the depletability effect and can explain the failure of resource prices to follow the hotelling path section i of the paper develops the adjustment cost model and section ii presents the empirical analysis section iii considers the policy implications of the depletability and adjustment factors

three problems in learning mixed strategy nash equilibria this paper discusses three problems that can prevent the convergence of learning mechanisms to mixed strategy nash equilibria first while players expectations may converge to a mixed equilibrium the strategies played typically fail to converge second even in 2 2 games fictitious play can produce a sequence of frequency distributions in which the marginal frequencies converge to equilibrium mixed strategies but the joint frequencies violate independence third in a three player matching pennies game with a unique equilibrium it is shown that if players learn as bayesian statisticians then the equilibrium is locally unstable journal of economic literature classification numbers c72 c73 d83

adjustment costs uncertainty and the behavior of the firm this paper examines the effects of demand and cost uncertainty on a firm s investment output and pricing decisions but unlike most earlier studies in which demand and cost are simply not known at the time an output or pricing decision is made here i consider uncertainties over future demand and costs it will be seen that the effects of such uncertainties depend critically on the characteristics of the firm s adjustment costs i treat demand uncertainty in a dynamic context by letting the market demand function shift randomly but continuously through time according to a stochastic process this means that today s demand is known exactly but future demand may be larger or smaller and has a variance that increases with the time horizon likewise uncertainty over factor costs is characterized by treating those variables as stochastic processes i combine this characterization of uncertainty with a dynamic model of the firm in which some factor inputs can be adjusted freely in response to stochastic demand changes but other factors are quasi fixed in that adjustment costs are incurred when they are changed in this model the firm s price and output are random processes but we can examine the firm s behavior in expected value terms of interest is whether the presence of uncertainty should cause competitive or monopolistic firms to invest and produce more or less than they would otherwise how the effects of uncertainty are influenced by the presence of risk aversion and how the use of inventories can alter the impact of uncertainty on capacity and sales of course these questions have been addressed by others in the past among the earliest studies of demand uncertainty are those of edwin mills 1959 1962 and samuel karlin and charles carr 1962 mills examined a single period monopolistic firm that sets both output and price and showed that additive demand uncertainty i e the demand function is of the form q q p u where u is a random variable leads to a lower price if marginal cost is constant so that the firm reduces the expected loss from discarding unsold production karlin and carr confirmed for both the static case and the multiperiod case with inventory carryover that additive uncertainty tends to reduce the price and increase the output of a risk neutral firm while multiplicative uncertainty does the opposite other papers have been concerned with the way in which the error term enters the demand function additively multiplicatively or nonlinearly the implications of choosing price ex ante instead of output the implications of risk aversion and the use of inventories for example agnar sandmo 1971 and david baron 1970 showed that a risk averse competitive firm will produce less when the price is a random variable or subject to an additive error term but a riskneutral firm will not alter its production hayne leland 1972 extended these results to a monopolistic firm whose demand can depend in a general way on a random error term for example q q p u and showed that uncertainty reduces the production of a

learning and communication in sender receiver games an econometric investigation this paper compares the performance of stimulus response sr and belief based learning bbl using data from game theory experiments the environment extensive form games played in a population setting is novel in the empirical literature on learning in games both the sr and bbl models fit the data reasonably well in common interest games with history while the test results accept sr and reject bbl in games with no history and in all but one of the divergent interest games estimation is challenging since the likelihood function is not globally concave and the results may be subject to convergence bias

sectoral supply of minerals of varying quality in this sectoral model of mineral production investment in capacity and variation in orebody grade and volume help explain some stylized facts more than one grade of ore may be exploited simultaneously mine exhaustion but not necessarily entry occurs in declining order of grade the price may rise or fall but is likely to fall initially young industry and must eventually rise at less than the interest rate unless demand expands rapidly these trends exhibit fluctuations due to entry and exhaustion of deposits resource price cyclicality is reinforced because mines keep producing at capacity when the price is falling

returns to scale adjustment costs and the optimal investment of the mining firm abstract this paper analyses the optimal investment programme of a competitive mining firm for two different technologies and capital adjustment costs in the first part the case of a variable proportions technology with decreasing returns to scale is studied and it is concluded that under the assumption of a constant mineral price a first stage in the exploitation period of the deposit will occur in which capital stock is increasing in the second part the optimal investment programme is determined when there are constant returns to scale and hotelling s rule governs the dynamics of the mineral price

unobserved heterogeneity and equilibrium an experimental study of bayesian and adaptive learning in normal form games abstract we describe an experiment based on a simple two person game designed so that different learning models make different predictions econometric analysis of the experimental data reveals clear heterogeneity in the subjects learning behavior but the subjects follow only a few decision rules for basing their play on their information and these rules have simple cognitive interpretations there is a unique equilibrium in pure strategies and many equilibria in mixed strategies we find that the only equilibrium consistent with the data is one of the mixed strategy equilibria this equilibrium is shown surprisingly to be consistent with jordan s bayesian model

production and investment in natural resource industries there has been a recent tendency for economists to view natural resource scarcity as a diminishing threat to man s existence and his ability to produce an abundant supply of worldly goods see john v krutilla this change in view has emanated from the world s experience of the last few decades with technological development and the absence of any evidence that this rapid accumulation of technical knowledge will cease in some respects one might think that modern technology has removed the need for an economic theory of conservation temporal allocation of natural resources on the other hand conservation of natural resources can now be looked upon with less emotion since the dire consequences of too rapid exploitation are no longer a threat the question of conservation is thus a cold economic problem removed from many of its older value connotations there is indeed considerable effort taking place in the economics profession to fill this need for a quantitative economic theory of conservation however with one exception vernon smith focus has been limited to specific resources earlier works by lewis c gray and harold hotelling concerning the theory of the mine have recently been extended in numerous papers see r cummings and 0 burt richard l gordon anthony scott 1967 problems associated with petroleum production are considered in paul davidson and the fishery is considered in j a crutchfield and arnold zellner h scott gordon james quirk and vernon smith anthony scott 1955 and ralph turvey an extensive literature exists on the temporal allocation of groundwater two recent contributions are gardner brown and charles b mcguire and burt a logical problem has been encountered however in efforts to examine the optimum allocation of a natural resource over time without explicitly considering the rate of investment associated with resource use this difficulty stems from the long life of many capital items used in the process of exploiting the natural resource earlier studies have either tacitly or explicitly amortized costs of investment associated with resource use and proceeded as though all costs of production were essentially variable smith was the first to explicitly bring capital investment into a production model for natural resources and his work was followed by the authors where only exhaustible resources were considered more recently quirk and smith have introduced a dynamic model of the fishery in which capital investment is treated explicitly it seems then that there is a need for a comprehensive model for simultaneously optimizing the rate of resource use and investment in natural resource industries

learning mixed equilibria we study learning processes for finite strategic form games in which players use the history of past play to forecast play in the current period in a generalization of fictitious play we assume only that players asymptotically choose best responses to the historical frequencies of opponents past play this implies that if the stage game strategies converge the limit is a nash equilibrium in the basic model plays seems unlikely to converge to a mixed strategy equilibrium but such convergence is natural when the stage game is perturbed in the manner of harsanyi s purification theorem journal of economic literature classification number c72

measurement error and earnings dynamics some estimates from the psid validation study previous empirical work on measurement error in survey earnings data has shown that the variance of the measurement error is roughly constant over time it is negatively correlated with true earnings and it is autocorrelated with previous measurement errors this article proposes a simple model in which the measurement error stems from underreporting of transitory earnings fluctuations and a white noise component the model fits well to data from the panel study of income dynamics validation study the results imply that autocorrelations in the changes of earnings can be estimated relatively accurately despite the presence of measurement error