The analytics of seasonal migration

A framework that yields different possible patterns of migration as optimal solutions to a simple utility maximization problem is presented and explored. It is shown that seasonal migration arises as an optimal endogenous response to a comparison of costs (of living and of separation) and returns (to work) over a set of three alternative options, even if a year-long migration is feasible.     

Forest Value and Optimal Rotations in Continuous Cover Forestry

The Faustmann forest rotation model is a celebrated contribution in economics. The model provides a forest value expression and allows a solution to the optimal rotation problem valid for perpetual rotations of even-aged forest stands. However, continuous forest cover forest management systems imply uneven-aged dynamics, and while a number of numerical studies have analysed specific continuous cover forest ecosystems in search of optimal management regimes, no one has tried to capture key dynamics of continuous cover forestry in simple mathematical models. In this paper we develop a simple, but rigorous mathematical model of the continuous cover forest, which strictly focuses on the area use dynamics that such an uneven-aged forest must have in equilibrium. This implies explicitly accounting for area reallocation and for weighting the productivity of each age class by the area occupied. We present results for unrestricted as well as area-restricted versions of the models. We find that land values are unambiguously higher in the continuous cover forest models compared with the even-aged models. Under area restrictions, the optimal rotation age in a continuous cover forest model is unambiguously lower than the corresponding area restricted Faustmann solution, while the result for the area unrestricted model is ambiguous.     

On the theory of the competitive firm with a utility function defined on profits and regret

In this paper we analyze the optimal output determined by a competitive firm facing uncertain demand. We analyze the effect of introducing uncertainty and the effect of increasing uncertainty on the optimal output, under the assumption that the utility function of the firm depends both on profits and on regret. We show that if the firm is more risk averse to profits than to regret (in a sense described below), both effects tend to decrease the optimal output. Similar effects of introducing uncertainty and of increased uncertainty were previously shown by Sandmo (1971) to exist in the case where utility is defined on profits only. Thus, this paper provides conditions under which the above results hold true, even when utility is defined on regret and on profits.     

Uncertainty and sustainability in the management of rangelands

We analyze a dynamic and stochastic ecological-economic model of grazing management in semi-arid rangelands. The ecosystem is driven by stochastic precipitation. A risk averse farmer chooses a grazing management strategy under uncertainty such as to maximize expected utility from farming income. Grazing management strategies are rules about which share of the rangeland is given rest depending on the actual rainfall in that year. In a first step we determine a myopic farmer's optimal grazing management strategy and show that a risk averse farmer chooses a strategy such as to obtain insurance from the ecosystem: the optimal strategy reduces income variability, but yields less mean income than possible. In a second step we analyze the long-run ecological and economic impact of different strategies. We conclude that a myopic farmer, if he is sufficiently risk averse, will choose a sustainable grazing management strategy, even if he does not take into account long-term ecological and economic benefits of conservative strategies.     

Biological capital theory: a question and a conjecture

A community possesses an empty tract of land, good only for growing trees of a particular type. What is the optimal pattern of planting and harvesting? If utility is convex in consumption it is optimal to plant and harvest periodically. If the utility function is strictly concave our numerical analyses suggest that the forest approaches a balanced state in which the rate of timber production is uniform.     

Decreasing absolute risk aversion and utility indices derived from cake-eating problems

This paper establishes the following characterization of decreasing absolute risk aversion (DARA) utility indices: J exhibits DARA if and only if it is the indirect function corresponding to an infinite horizon cake-eating problem for some nondecreasing and concave utility function of consumption. The characterization is applied to the analysis of resource extraction under uncertainty and to an inverse optimal problem.     

“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which highlight the correct use of the Hamilton-Jacobi-Bellman equation and the change-of-variables formula (sometimes referred to as ``Itô's Lemma'') under Poisson uncertainty.     

The Impact of Regret on Exports

We examine optimal production and export decisions of a firm facing exchange rate uncertainty, where the firm's management is not only risk averse but also regret averse, i.e., is characterized by a utility function that includes disutility from having chosen ex post suboptimal alternatives. Experimental and empirical results support the view that managers tend to be regret averse. Under regret aversion a negative risk premium need not preclude the firm from exporting which would be the case if the firm were only risk averse. Exporting creates an implicit hedge against the possibility of regret when the realized spot exchange rate turns out to be high. The regret‐averse firm as such has a greater ex ante incentive to export than the purely risk averse firm. Finally, we use a two‐state example to illustrate that the firm optimally exports more (less) to the foreign country than in the case of pure risk aversion if the low (high) spot exchange rate is more likely to prevail. Regret aversion as such plays a crucial role in determining the firm's optimal allocation between domestic sales and foreign exports.     

A note on equivalence of consistency and bilateral consistency through converse consistency

In the framework of (set-valued or single-valued) solutions for coalitional games with transferable utility, the three notions of consistency, bilateral consistency, and converse consistency are frequently used to provide axiomatic characterizations of a particular solution (like the core, prekernel, prenucleolus, Shapley value). Our main equivalence theorem claims that a solution satisfies consistency (with respect to an arbitrary reduced game) if and only if the solution satisfies both bilateral consistency and converse consistency (with respect to the same reduced game). The equivalence theorem presumes transitivity of the reduced game technique as well as difference independence on payoff vectors for two-person reduced games.     

Timber harvesting versus forest reserves—producer prices for open-use areas in German beech forests (Fagus sylvatica L.)

A strong demand for nature conservation can be ascertained in Germany. Several nature conservation groups argue that in order to provide nature conservation in considerable parts of the forest area forestry should sacrifice timber harvesting. For example, the abandoning of harvesting altogether is supposed to enhance and protect the species richness. This fact and the very low profitability of forestry in Germany motivated the writing of this paper. The paper explains a methodology for deriving producer prices involved in forest reserves, where harvest benefits are sacrificed totally. Such methodology can be useful to form a basis for private contracts between forest owners and nature conservationists, who demand forest reserves. The results of this methodology can also be integrated in financial programs for species and habitat conservation.In a basic theoretical consideration, it is demonstrated that a stand-by-stand evaluation approach may only serve as an initial step in deriving compensation prices for forest reserves. Due to the stochastic character of forest management, a nonlinear programming approach (NLP) was adopted to find an optimal operational plan for a hypothetical beech (Fagus sylvatica L.) forest. In both the constraints and the objective function, the nonlinearity is considered by integrating stochastic components. Additionally, only virtual homogenous forest reserves are considered. Firstly, a basic NLP solution for the hypothetical forest with the objective “maximise the net present value (NPV) of timber harvests adjusted to risk” was obtained when considering several constraints subject to stochastic variation of net revenues and timber harvests without considering forest reserves. Secondly, other solutions allowing for forest reserves were computed. The decrease of the objective function when forest reserves were increased in periodic increments seemed well suited to mirror the opportunity costs of forest reserves.The results showed that a stand-by-stand approach gave much greater compensation prices than the NLP approach. The reason for this lay in the consideration of a nonlinear objective function as well as the nonlinear constraints in the case of NLP. The first 42-ha forest reserve was priced at 11,494 Euro/ha or, 483 Euro/ha/year expressed in infinite yearly compensation. The yearly compensation price for the last forest reserve had an increase up to 607 Euro/ha/year. A stand-by-stand approach, however, resulted with compensation prices from minimally 609 up to maximally 709 Euro/ha/year.Various interest rates (3.2% and 5.2%) caused different compensation price curves. The slope of the curves increased when the interest rate decreased.The limits of the approach, the problem of deriving a demand for forest reserves and the opportunities for applying the presented approach to state forests are discussed.     

Trade policy with asset markets: The role of financial structure for time consistency

The present study uses a two-country, two-good, stochastic general equilibrium trade model to analyze the implications of optimal trade policy under uncertainty in the presence of financial markets. Using such a framework, I demonstrate that the policy-active home government, acting to maximize domestic welfare, will always have incentive to revise the previously announced import tariff policy once an asset position is taken by the representative agent in each country engaged in trade. The resulting time-consistent solution will be sensitive to the composition of asset income. Since the fiancial contracts can be combined in an infinite number of ways to yield the same optimal level of asset income, there will exist multiple time-consistent solutions, one for each financial structure. Using a specific log utility function, I also show that for certain financial structures, precommitment solutions will be replicated by time-consistent solutions, a result which marks a significant departure from the standard deterministic framework.     

Economies of scale and the optimality of rotational dynamics in forestry

Forest harvesting is traditionally analyzed in terms of the Faustmann rotation model. This paper considers the identification of optimal forest harvest regimes using jump controls. This approach enables the structural assumptions of clear-cut technology and identical cycles in perpetuity which are imposed in a Faustmann model to be relaxed. Jump control models permit investigation of the biological and economic conditions which favour continuous growth management regimes as opposed to clear-cut harvest regimes. A numerical solution approach to the jump control model is presented. The link between the harvest cost function and the optimal biomass path is analyzed. Economies of scale are shown to generate rotational harvest as optimal policies.      

“The winner takes it all” or a story of the optimal allocation of the European Cohesion Fund

This paper aims to determine an optimal allocation of the European Cohesion Fund (ECF) and compares it with the observed allocation. This optimal allocation is the solution of a donor optimization problem which maximizes recipient countries' GDP per capita to achieve economic convergence in the European Union. Compared to the observed allocation, our solution can identify the recipient countries that can benefit from higher ECF transfers than the observed levels, as those having low relative GDP per capita, large population size and where the ECF has a strong capacity to support economic growth. Result is robust to changes in the specification of the donor's utility function.     

Stochastic continuous time growth models that allow for closed form solutions

We find a closed form solution that maximises the expected utility of an agent’s inter-temporal consumption subject to a stochastic technology, which is a linear combination of AK and Cobb–Douglas technologies. Additionally, we consider two cases of agent preferences: (i) Constant Relative Risk Aversion (CRRA) preferences, which treat optimal consumption as a linear function of capital, and (ii) Hyperbolic Absolute Risk Aversion (HARA) preferences, which treat optimal consumption as an affine function of capital. By establishing a minimum (subsistence) level of consumption in the HARA model, we are able to create a framework that more accurately represents real-world circumstances than previous studies have done. Furthermore, for both the CRRA and HARA cases we show the suitable, consistent stochastic differential equation which describes the capital dynamics. Finally, we perform a numerical simulation based on the CRRA case and calibrate US data for the HARA case.     

Risk preference and indirect utility in portfolio-choice problems

We consider a portfolio-choice problem with one risky and one safe asset, where the utility function exhibits decreasing absolute risk aversion (DARA). We show that the indirect utility function of the portfolio-choice problem need not exhibit DARA. However, if the (optimal) marginal propensity to invest is positive for both assets, which is true when the utility function exhibits nondecreasing relative risk aversion, then the DARA property is carried over from the direct to the indirect utility function.     

The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case

We consider a multiperiod, additive utility, optimal consumption model with a riskless investment and a stochastic labor income. The main result is that for utility functions belonging to the set F, consumption decreases when we go from any sequence of distribution functions representing labor income to a more risky sequence. A concave utility function belongs to F if its first derivative exists everywhere and is convex.     

A closed-form solution to the Ramsey model with logistic population growth

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb–Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.     

Disutility of pollution and endogenous growth

Endogenous growth is generally built on a positive externality hypothesis which is the opposite of a negative externality caused by pollution. We study a linear technology with simple assumption: an aggregate capital stock which represents a learning by doing effect and a pollution flow proportional to production. In this framework, we analyse the precise effects on growth of the disutility of pollution and its interaction with the utility of consumption in an economy without abatement technology. The decentralized equilibrium always leads to unlimited growth, but optimal growth is often limited (the negative effect of pollution dominating the positive effect of learning by doing). In this case, the optimal policy which leads the decentralized economy to follow the optimal growth path is to tax capital; in contrast with the optimal subsidy policy in an economy without pollution. When an abatement technology is introduced, the optimal solution can lead the economy to unlimited growth, whatever the form of the utility function.     

Unemployment insurance with hidden savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini (1997) [1]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.     

Optimal Design of Forest Taxation with Multiple-Use Characteristics of Forest Stands

The paper studies optimal forest taxation under uncertainty about future timber price when private forest owners value amenity services of forest stands and forest stands have public goods characteristics. It is assumed that preferences of forest owners can be described by a quasi-linear, intertemporal utility function which reflects risk aversion in terms of consumption and constant marginal utility in terms of amenity services. The comparative statics of current and future harvesting in terms of timber price risk, site productivity tax and yield tax are first developed. It is shown that, given the optimal site productivity tax, which is independent of the timber harvested and thus non-distortionary, it is desirable to introduce the yield tax at the margin; it both corrects externality due to the public goods characteristic of forest stands and serves as a social insurance device. The optimal yield tax is less than 100% and depends on the social value of forest stands, timber price risk and properties of compensated timber supply. In the general case the 'inverse elasticity rule – according to which the optimal yield tax is negatively related to the size of the substitution effects – may not hold. Under certainty, the desirability of the yield tax, given the optimal site productivity tax, depends only on the existence of public goods characteristic and is thus a pure Pigouvian tax.