On capital accumulation paths in a neoclassical stochastic growth model

Summary. Boldrin and Montrucchio [2] showed that any twice continuously differentiable function could be obtained as the optimal policy function for some value of the discount parameter in a deterministic neoclassical growth model. I extend their result to the stochastic growth model with non-degenerate shocks to preferences or technology. This indicates that one can obtain complex dynamics endogenously in a wide variety of economic models, both under certainty and uncertainty. Further, this result motivates the analysis of convergence of adaptive learning mechanisms to rational expectations in economic models with (potentially) complicated dynamics. Received: June 21, 1996; revised version: October 31, 1996     

Characterization of optimal plans for stochastic dynamic programs

This paper provides general techniques for the characterization of optimal plans resulting from stochastic dynamic programming. We show that under standard assumptions the optimal plans in both finite and infinite horizon problems can be obtained by an application of the Implicit Function Theorem to first order conditions. Further, we show that under certain checkable conditions, optimal plans and value functions are p-times differentiable for any integer p ? 0. Finally, we apply our technique to obtain a C^p plan and value function in a one sector infinite horizon growth problem under uncertainty.     

Quantifying the Subjective Value of Certainty

Traditional measures of risk preference require that an agent's utility function be twice differentiable and that the risk be miniscule. We introduce a discrete index that requires no assumptions regarding the functional form of utility or the magnitude of the risk. The index quantifies the value of certainty by contrasting the relief that one experiences from the absence of a loss to the regret that (s)he feels at a foregone opportunity for gain. It exhibits a consistent range across different data types, and signals any economically irrational behavior. Empirical estimates are made with reservation price data and reservation probability data.     

WELFARE ECONOMICS AND THE MEASUREMENT OF NNP*

Some relationships between NNP and economic welfare are explored in the confines of a simple, static welfare maximization model. Various assumptions concerning both the measurement of NNP and the economic system underlying this model are dropped seriatem and the implications for the correspondence between NNP and economic welfare are examined. The following conclusions emerge. There are several classes of resource reorganization in which NNP and welfare move in the same direction, so that NNP can serve as an ordinal proxy for welfare. These include changes in taxes or competitive imperfections which result in product substitution and movements along the transformation function. With a general qualification, NNP-welfare correspondence is preserved for allocative changes which affect the real costs and prices of goods included in NNP or of non-included goods in inelastic demand; changes in involuntary unemployment; and changes in technological externalities affecting producers. There are other cases where changes in NNP and welfare are not positively correlated. Included here are changes in real costs of non-included goods for which demand is elastic and changes in technological externalities imposed on consumers.     

A complete characterization of optimal growth paths in an aggregated model with a non-concave production function

We use the Principle of Optimality in addition to the Euler equation in order to provide a characterization of optimal one-sector growth for all ranges of interest rates when the technology is not convex. Our key result is that the sequence of capital stocks is necessarily monotonic. For certain interest rates we show that the optimal path converges to a steady state only if the initial capital stock is above a critical level, otherwise it converges to zero. Finally, we demonstrate that the set of points for which the value function is differentiable is precisely the set of initial capital stocks from which there is a unique optimal path.     

Recursive utility and optimal capital accumulation II: sensitivity and duality theory

Summary This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we find the value function is differentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sufficient for an optimum.Robert Becker acknowledges the research support of National Science Foundation Grant SES 85-20180. We also thank Gerhard Sorger and the participants at the Northwestern Summer Workshop in Capital Theory and Monetary Economics for their helpful comments and suggestions.     

An economic reappraisal of the Melamchi water supply project - Kathmandu,Nepal

This paper examines whether the benefits of the Melamchi water supply project in Nepal are likely to exceed its costs, assuming that high-quality municipal water services can be delivered to households and firms in the urbanized part of the Kathmandu Valley. Monte Carlo simulations are used to explore the sensitivity of the net present value and economic internal rate of return calculations to a wide range of assumptions and input parameters. We find that extreme assumptions are not required to generate large differences in economic feasibility; quite plausible differences in the values of some key parameters can lead to large differences in the economic attractiveness of the project. The results reveal that the three most important influences on net present value and economic internal rate of return are: (i) the discount rate and discounting procedure; (ii) the magnitude of monthly benefits for households connected to the new water system; and (iii) the annual growth rate in monthly benefits of connected households after the project comes on line. Our contribution lies in illustrating, with an actual case study in a developing country, the degree to which cost-benefit calculations of large infrastructure projects are influenced by key economic modeling assumptions and input parameters.JEL Classification: H42, H43, H54, Q25, Q56 Correspondence to: Dale WhittingtonWe would especially like to thank Keiichi Tamaki (ADB) and Ian Hill (Acres International) for their guidance and assistance with this project. We would also like to thank the following individuals for their help during our mission to Kathmandu in May, 2003: Richard W. A. Vokes, Kathie M. Julian, Raj Kumar Malla, Madan Shankar Shrestha, Suman Prasad Sharma and Noor Kumar Tamrakar.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Econometric estimation of a variable rate of depreciation of the capital stock

Measuring the capital stock is crucial in some fields of economic research. Capital stock is not observable, though, and its estimation requires the knowledge of its rate of depreciation. In most cases, econometric regressions are not used for this task. However, this methodology could be used to estimate capital stock values which are consistent with the technology of the economy. If we assume that the depreciation rate is not constant, its estimation poses some additional technical difficulties. In this paper we suggest a method to estimate a variable rate of depreciation which is shown to have wide empirical applicability and some computational advantages. Also, this method is easily implementable in standard packages by means of NLS or ML. The formalization of this method, and empirical evidence and simulation exercises based on its implementation are presented.First version received: October 2002/Final version received: May 2004All correspondence to José A. Hernandez. We would like to thank to the University of Las Palmas project uni2002/14 for financial support and two anonymous referees for helpful comments.     

On high-order differentiability of the policy function

Summary This note presents some results concerning high-order differentiability of the policy function. It is shown that simple examples of cubic return functions may yield optimal policies which under standard conditions are not differentiable to high order. The loss of differentiability, however, is not robust to small perturbations of the model. For instance, monotone policy functions are almost always high-order differentiable.     

The scope of satisfactory mechanisms for the provision of public goods

This paper establishes the existence of satisfactory public-good provision mechanisms when utilities are nonseparable. The assumptions used to obtain this result are: (1) that the public good is continuously variable; (2) that utility functions are parametrically representable and twice continuously differentiable; and (3) that the provision rule is a strictly increasing function of the reported marginal rates of substitution between the public good and the private good. The satisfactory mechanisms derived are all augmented Groves mechanisms and are equivalent to Groves mechanisms if, and only if, each consumer's utility function is additive in income.     

Profit Maximizing in Auctions of Public Goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and we find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.     

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.     

The impact of home production on economic inequality in Germany

Using representative income and time-use data from the German Socio-Economic Panel, we estimate non-monetary income advantages arising from home production and analyze their impact on economic inequality. As an alternative to existing measures, we propose a predicted wage approach that relaxes some of the strong assumptions underlying both the standard opportunity cost approach and the housekeeper wage approach. We also propose a method of adjusting the number of hours spent on home production to reduce the bias arising from multi-tasking and joint production in time-use data. Sensitivity analyses comparing results among different approaches provide indications of method effects. Although this study supports the evidence that considering home production leads to a reduction in inequality, we show that the size of this effect differs according to the variations in the mean and distribution of the estimated monetary value of home production across the three approaches. This finding underscores the need for a harmonized approach in cross-national comparative research.     

More on economies with a finite set of Walrasian equilibria

Proposition. The graph of the Walrasian equilibrium correspondence is a piecewise continuously differentiable manifold. Furthermore, there exists an open dense set of economies, Ω, such that for all w in Ω (a) the number of equilibria of the economy w is finite; and (b) there exists a neighborhood V(w) on which the set of equilibria is represented by a finite family of piecewise continously differentiable functions.     

Quasi-option value under strategic interactions

We consider a simple two-period model of irreversible investment under strategic interactions between two players. In this setup, we show that the quasi-option value may cause some conceptual difficulties. In case of asymmetric information, decentralized investment decisions fail to induce first-best allocations. Therefore a regulator may not be able to exercise the option to delay the decision to develop. We also show that information-induced inefficiency may arise in a game situation and that under certain assumptions inefficiency can be eliminated by sending asymmetric information to the players, even when the regulator faces informational constraints. Our model is potentially applicable to various global environmental problems.     

Wealth accumulation and economic progress

In an evolutionary dynamic economic theory the accumulation of durable goods (i.e., wealth) is a key feature. Here we show that the wealth of individual economic agents can be measured by the progress function (PF). PF is a function of goods and money under straightforward assumptions, notably the ‘no-loss’ rule for transactions. We derive explicit formulae for wealth from the PF. We also show how the compatibility of the PF and the neoclassical economics deriving the conventional utility functions from the PF.     

论经济学中的价值理论

价值理论在经济学中占有核心地位.本文简要回顾了经济思想史上价值理论的发展过程,梳理了几种主要价值理论——劳动价值论、生产要素价值论、边际效用价值论、均衡价格理论一之间的对立和传承关系,逐一分析了这几种价值理论的基本内容,重点关注每种理论的前提假设是否合理,逻辑推演过程是否正确,尽力避免意识形态角度的评断.主要结论是:马...     

Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach

We consider a general equilibrium model of a private ownership economy with consumption and production externalities. Utility functions and production technologies may be affected by the consumption and production activities of all other agents in the economy. We use homotopy techniques to show that the set of competitive equilibria is non-empty and compact. Fixing the externalities, the assumptions on utility functions and production technologies are standard in a differentiable framework. Competitive equilibria are written in terms of first order conditions associated with agents’ behavior and market clearing conditions, following the seminal paper of Smale (J Math Econ 1:1–14, 1974). The work of adapting the homotopy approach to economies with externalities on the production side is non-trivial and it requires some ingenious adjustments, because the production technologies are not required to be convex with respect to the consumption and production activities of all agents.     

Dynamic legislative policy making

We prove existence of stationary Markov perfect equilibria in an infinite-horizon model of legislative policy making in which the policy outcome in one period determines the status quo for the next. We allow for a multidimensional policy space and arbitrary smooth stage utilities, and we assume preferences and the status quo are subject to arbitrarily small shocks. We prove that equilibrium continuation values are differentiable and that proposal strategies are continuous almost everywhere. We establish upper hemicontinuity of the equilibrium correspondence, and we provide weak conditions under which each equilibrium of our model determines an aperiodic transition probability over policies. We establish a convergence theorem giving conditions under which the invariant distributions generated by stationary equilibria must be close to the core in a canonical spatial model. Finally, we extend the analysis to sequential move stochastic games and to a version of the model in which the proposer and voting rule are determined by play of a finite, perfect information game.