Irrigation production functions with water-capital substitution

The dynamics of biomass growth implies that the yield of irrigated crops depends, in addition to the total amount of water applied, on irrigation scheduling during the growing period. Advanced irrigation technologies relax constraints on irrigation rates and timing, allowing us to better adjust irrigation scheduling to the varying needs of the plants along the growing period. Irrigation production functions, then, should include capital (or expenditures on irrigation equipment) in addition to aggregate water. We derive such functions and study their water-capital substitution properties. Implications for water demand and adoption of irrigation technologies are investigated. A numerical example illustrates these properties.     

Preparing for catastrophic climate change

We study optimal adaptation to climate change when the harmful consequences of global warming are associated with uncertain occurrence of abrupt changes. The adaptation policy entails the accumulation of a particular sort of capital that will eliminate or reduce the catastrophic damage of an abrupt climate change when (and if) it occurs. The occurrence date is uncertain. The policy problem involves balancing the tradeoffs between the (certain) investment cost prior to occurrence and the benefit (in reduced damage) that will be realized after the (uncertain) occurrence date. For stationary economies the optimal adaptation capital converges monotonically to a steady state. In most cases, investment begins immediately. However, if the initial adaptation capital exceeds a pre-specified threshold level, which lies above the optimal steady state, investment is delayed while the capital stock decreases (due to depreciation) and commences only when it reaches this threshold level. For growing economies the optimal adaptation capital stock approaches the maximal economic level above which further accumulation is ineffective.     

Measuring the Recreational Value of Open Space

We develop aggregate measures of the recreational value of types of open space when data on individual site visitation are not available. Our procedure accounts for both the allocation (between the different types of open space) and participation (total number of trips) decisions. The procedure is applied to estimate the recreational value of three types of open spaces (beaches, urban parks and national parks) in Israel.     

Perennial crops under stochastic water supply

Perennial crops require substantial initial investment in groundwork and planting, as well as a multiyear gestation period without commercial yield. Therefore, a crop's cycle (from planting to felling) should be long enough in order to cover the fixed cost and become profitable. The problem becomes involved when the cycle's duration is stochastic due to occurrence of uncertain event that terminates the cycle prematurely. Studying orchard management under stochastic drought events, we show that to each perennial crop that is profitable without drought hazard, there exists a critical drought hazard above which the crop turns loss making. We refer to this critical drought hazard as the crop's drought vulnerability index and show that it increases with the length of the gestation period, the ratio of fixed cost to average annual profit and the interest rate, and decreases with the natural (uninterrupted) cycle length. We then investigate the economic value of a stable water source, such as recycled water, that stabilizes the water supply and diminishes the drought hazard. An empirical application in northern Israel reveals that the stabilization value of recycled water due to its role in eliminating the drought hazard far exceeds its supply cost.     

Endogenous Discounting and Climate Policy

Under risk of abrupt climate change, the occurrence hazard is added to the social discount rate. As a result, the social discount rate (1) increases and (2) turns endogenous to the global warming policy. The second effect bears profound policy implications that are magnified by economic growth. In particular, we find that greenhouse gases (GHG) emission should be terminated at a finite time so that the ensuing occurrence risk will vanish in the long run. Due to the public bad nature of the catastrophic risk, the second effect is ignored in a competitive allocation and unregulated economic growth will give rise to excessive emissions. In the long term, the GHG emission paths under the optimal and competitive growth regimes lie at the extreme ends of the range of feasible emissions.     

Trademark infringement and optimal monitoring policy

The paper addresses a trademark infringer who seeks to capitalize on the reputation of a trademark owner, sells an identical product under a trademark which is confusingly similar to that of the owner, charges the same price and competes with him in the same market. We show that the welfare-maximizing monitoring intensity is zero, hence the government is not likely to engage in monitoring infringement. Recognizing this, the trademark owner may consider monitoring the market himself, discovering, however, that this is worth his while only if the penalty for infringement, which he fully collects, is sufficiently high. Given the entry condition, an increase in the penalty may either raise or lower the optimal monitoring intensity. In the former case it will counter-intuitively increase the infringer's expected profit, apparently because a higher penalty will also lead to a raise in price. While monitoring enables the trademark owner to maintain a positive profit level, it reduces social welfare. The government may intervene to eliminate the private incentive for monitoring through taxing the collected penalty.     

Agricultural Landscape Value and Irrigation Water Policy

Water is a limiting factor of agricultural production in an increasing number of regions. There is also ample empirical evidence to suggest that the economic value of agricultural landscape is substantial, which has been used to justify agricultural support programs in developed economies. We investigate the link between the environmental amenity of agricultural landscape and the value of water in crop production. We find that the environmental externality gives rise to a social derived demand for water which differs from the market‐based (private) derived demand for water. Policy implications regarding irrigation water allocation and pricing are drawn. An empirical example illustrates the methodology and main findings.     

The Amenity Value of Agricultural Landscape and Rural–Urban Land Allocation

We analyse rural–urban land allocation in the light of the increasing environmental role of agricultural landscapes. The landscape amenity value of farmland varies across crops and as a result affects the optimal crop mix in addition to its effect on rural–urban land allocation. Investigating the effects of population and income growth processes, we find that, contrary to market outcomes, the socially optimal allocation may call for more farmland preservation under both processes. In an empirical application to a region in Israel, we find that the extent of market under‐supply of farmland is substantial and that population growth calls for more farmland preservation at the expense of urban land.     

Steady state properties of multi‐state economic models

A simple method to derive optimal steady states of multi‐state dynamic economic systems with minimal assumptions on the underlying processes is developed. This is accomplished by an n‐dimensional function defined over the n‐dimensional state space in terms of the model's primitives. The location and stability properties of optimal steady state candidates are characterized by the roots and derivatives of this function. A resource management example illustrates the simplicity and applicability of the method.     

Risk Management for E-Cash Systems with Partial Real-Time Audit

We analyze coin-wallet and balance-wallet under partial real-time audit, and compute upper bounds on theft due to the fact that not all the transactions are audited in real time, assuming that everything else is perfect. In particular, we assume that the audit regime holds for innocent payees. Let v be the maximum allowed balance in a wallet, and 01 be the fraction of transactions that are audited in real time in an audit round. Assume one unit transactions. We show that the upper bound on expected theft for coin-wallet is lim₀^–2, while for plausible (similar) parameter choice the bound for a balance-wallet is O(exp(mv)), where 1<m. The former is nicely bounded for small transactions, however, the bound for balance-wallet can become huge in those cases where we require very small false alarm probability. We conclude that partial audit, may be suitable for coin-wallets with low denomination coins, and possibly for balance-wallet, when we may tolerate a relatively high false alarm rate, but it may be too risky for balance-wallet, where very low false alarm rate is required.