Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model*

In a standard exhaustible resource model, it is known that if, along a competitive path, investment in the augmentable capital good equals the rents on the exhaustible resource (known as Hartwick's rule), then the path is equitable in the sense that the consumption level is constant over time. In this paper, we show the converse of this result: if a competitive path is equitable, then it must satisfy Hartwick's rule.     

On the Welfare Significance of National Product for Economic Growth and Sustainable Development

This paper formulates an investment value transversality condition in a continuous-time growth model, which characterizes competitive paths along which current net national product measures the welfare achieved along the path. This transversality condition requires that the present value of net investment goes to zero asymptotically. An example provided shows that, in general, competitive paths do not necessarily satisfy this condition. It is also shown that, in a standard growth model including an exhaustible resource as an essential factor of production, competitive paths always satisfy this condition. Implications regarding national income accounting procedures and sustainable development policies are discussed.
JEL Classification Numbers: D90; O11; O41; Q32.     

A step beside the maximin path: Can we sustain the economy by following Hartwick's investment rule?

If sustainability is interpreted as the requirement to sustain consumption or utility at an optimal level, a maximin objective appears to be relevant. The sustained economy is characterized by an optimal investment following Hartwick's investment rule. This paper examines how the sustainability of a production-consumption economy with a non-renewable resource is modified in the neighborhood of the maximin path, i.e. when the consumption and the resource price are not optimal. A Sustainable Consumption Indicator is introduced in order to characterize the sustainability of constant consumption paths, defined as deviations from the maximin path. We describe how an over-consumption jeopardizes future sustainability.     

On industry equilibrium under uncertainty

The paper considers an industry consisting of numerous firms that produce a homogeneous output, the demand for which is a random variable. Each firm belongs to one of K possible types, and each type is characterized by a U-shaped average cost curve. It is shown that: (i) the first-order necessary conditions for efficient investment and output are sufficient; accordingly, the set of competitive equilibria is non-empty and coincides with the set of efficient allocations; (ii) a dynamic process of free entry and exit of firms, guided by expected profits, is quasistable and every limit point is a competitive equilibrium. The paper also defines a sufficient condition for uniqueness of the competitive equilibrium, in which case it is stable.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

One Cow,One Vote?

We study investment decisions in a farmers' cooperative. Farmers sell their products through the cooperative. Before production takes place the cooperative has to decide on an investment. We study whether voting on investment leads to efficient investment decisions. The answer depends on how the number of votes and the cost of the investment are distributed among the farmers. It is shown that in a variety of settings, there is no reason to suppose that voting rules favoring large farmers —"one cow, one vote" rules — are more efficient than simple majority rule.     

Savings growth and the path of utility

Abstract.  We derive an expression relating the change in instantaneous utility to the growth of net (genuine) saving in an economy with multiple stocks and externalities that maximizes welfare in the utilitarian sense. This result is then shown to hold for decentralized competitive efficient economies as well, to yield an extension of the Hartwick rule: instantaneous utility is non-declining along a development path if genuine saving is decreasing. By way of example the rule is applied as a constant genuine saving rate rule in a simple Dasgupta-Heal-Solow-Stiglitz economy. The rule yields a path with unbounded consumption and higher wealth than on the standard Hartwick constant consumption path.     

Investment options and the business cycle

This paper extends [R. Mehra, E.C. Prescott, Recursive competitive equilibrium: The case of homogeneous households, Econometrica 48 (1980) 1365-1380] to a production economy with two capital goods. It is an RBC model in which each unit of investment requires a new idea, an ‘option.’ When options are scarce, new capital is harder to put in place and the value of old capital rises. Thus the stock market and Tobin's Q are negative indexes of intangibles. During a boom, Q rises gradually, as options are used up. Because investment represents an exercise of options, it has an intertemporal substitution tradeoff that is absent from the adjustment-cost model. Equilibrium may be efficient even without markets for knowledge; the stock market may suffice.     

Public Investment and Income Taxation: Redistribution vs. Productive Performance

This paper deals with government investment in a static two-type self-selection model of optimum income taxation. It is shown that the second-best investment rule is consistent with efficient production, provided that public investment has no influence on relative factor prices. Otherwise, however, redistributive income taxation implies that optimal investment expenditures exceed (or fall below) the efficient level as long as they raise (or decrease) the wage rate of the unskilled individuals relative to the wage rate of the skilled individuals.     

On decomposable exchange rules

We study an exchange rule decomposability property requiring that if a fraction only of a recommended exchange takes place, then the remaining exchange be also recommended when including already exchanged quantities in individual endowments. We obtain justifications for the Walrasian exchange rule although this rule is not the only efficient, decomposable and equitable exchange rule.     

Why Sunk Costs Matter for Bargaining Outcomes: An Evolutionary Approach

Two bargaining parties play the Nash Demand Game to share a pie whose size is determined by one party's investment decision. Various investment levels are subgame-perfect. Adding the investment decision to Young's evolutionary bargaining model yields the following long-run outcome: efficient investment prevails and the investor's share of the pie approximates die maximum of (i) the smallest share that induces efficient investment, even if the investor expects to appropriate the available pie from every inefficient investment, and (ii) half of the pie. The result favors forward induction to subgame consistency and equity theory to hold-ups. Journal of Economic Literature Classification Numbers: C78, L14.     

OVERLAPPING GENERATIONS MODEL,INVESTMENT FUNCTION AND DYNAMIC EFFICIENCY OF RESOURCE ALLOCATION*

This paper suggests that the possibility of dynamically inefficient resource allocation as pointed out by Diamond (1965) is due to the neoclassical property of that model where no investment instalment cost, and hence no investment function in the proper sense, may exist. If one introduces, instead, Tobin's q-theory type investment function, competitive equilibrium is shown to be consistent only with the dynamically efficient use of resources.     

Risk-aversely efficient random variables: Characterization and an application to growth under uncertainty

Consider a problem of choice from a set R of multivariate random variables. Let us examine only efficient elements of R which are optimal choices of risk averse decision-makers (whose aim is to maximize expected utility over R). We obtain a price characteristic of all risk-aversely efficient random variables in R. This result has been applied to multi-sector optimal growth model to obtain a characterization by competitive prices of all risk-aversely efficient stationary consumption programs.     

Consumption Externalities,Habit Formation and Equilibrium Efficiency*

We analyze the welfare properties of the competitive equilibrium in a capital accumulation model where individual preferences are subject to both habit formation and consumption spillovers. Using an additive specification for preferences, according to which the argument in the utility function is a linear combination of present and past values of own consumption and consumption spillovers, we analyze the circumstances under which these spillovers are a source of inefficiency. It is shown that consumption externalities have to interact with habits in order to generate an inefficient dynamic equilibrium. Finally, we characterize optimal tax policies aimed at restoring efficient decentralized paths.     

Financial Markets and Stochastic Growth

The authors study the effect of financial markets on the investment of a two-good two-country economy with stochastic production in a dynamic framework. Each country produces and invests only one good and, therefore, makes decisions as a central planner in an optimal growth model. Trade between consumers of both countries, however, takes place on competitive (spot or financial) markets. The authors compare the investment–consumption decisions of both "market" models with the benchmark case of an integrated world-equilibrium. In the log-linear case, it is possible to uniquely characterize the state-dependent preferences of consumers that lead to dynamically efficient investment decisions. It is shown that the investment decisions in both "market" models are, in general, inefficient compared with the efficient, or integrated world economy, case.     

Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics

The replicator dynamics are generalized to allow for strategy-specific barriers to learning. The resulting dynamics satisfy neither payoff monotonicity nor payoff positivity, but do satisfy weak payoff positivity. It is shown that initial states from which trajectories converge to a rest point under the replicator dynamics may yield trajectories which approach a stable limit cycle under the generalized replicator dynamics. Furthermore, strategies which are strictly dominated by other pure strategies may survive indefinitely along such nonconvergent paths.Journal of Economic LiteratureClassification Numbers: C73.     

Bank structure, capital accumulation and growth: a simple macroeconomic model

Summary. This paper analyzes the equilibrium growth paths of two economies that are identical in all respects, except for the organization of their financial systems: in particular, one has a competitive banking system and the other has a monopolistic banking system. In addition, the sources of inefficiencies, as a result of monopoly banking, and their relationship to the existence of credit rationing are explored. Monopoly in banking tends to depress the equilibrium law of motion for the capital stock for either of two reasons. When credit rationing exists, monopoly banks ration credit more heavily than competitive banks. When credit is not rationed, the existence of monopoly banking leads to excessive monitoring of credit financed investment. Both of these have adverse consequences for capital accumulation. In addition, monopoly banking is more likely to lead to credit rationing than is competitive banking. Finally, the scope for development trap phenomena to arise is considered under both a competitive and a monopolistic banking system. Received: September 20, 1999; revised version: December 3, 1999     

Investment criteria for production processes of non-storable goods with periodic demand and constant production constraints

Following Pareto's principles a general economic optimum is worked out for the producer of a non-storable good who has to satisfy a periodic demand with a constant production capacity. It is found that the marginal cost pricing rule applies, with some accommodations when the production capability of the plant is inelastic.A general investment criterion is also obtained, and it is shown that this general criterion can take simplified forms when applied to some well-defined classes of actual production functions.These results should find a broad application in peak-load pricing and in investment policies for such industries as electricity production, railways, telephone, etc.,…, i.e., for producers of non-storable commodities subject to seasonal demand variations.