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In the treatment of water as an input to agricultural production, economists have adhered to one of two schools of

thought, as discussed, for example, by Flinn (1968). One group n seems to be dominated by the idea that water is a vital necessity to crops and that each crop has a unique water requirement.

It also believes that water is an input which is complementary to other physical inputs in the production process. On the other hand, the second group contend that water like any other

input has substitution possibilities and has a production response function.

These two strands of 'thought' have greatly influenced the literature in irrigation economics and its concepts. An explicit distinction is crucial in the evolution of any management strategy. In particular, it will be seen that the concept of

'variable input' is more relevant for small dam situations.

2.4.1 Water: Complementary Input

The concept of 'unique water requirement' has received frequent attention and dominates the literature of irrigation economics. Very often it is a basic assumption in irrigation

development planning and water resource investments. Steiner (1964) assumes unique water requirements for crops in water resource

investment evaluations.

In the economics of irrigation of agricultural production, it has been a convenient concept. Clark (1970) reviewed the

economics of irrigation of alternative crops with 'unique water requirement' estimates. However, this concept becomes sterile when it confronts the economics of irrigation of a single crop.

Generally in the irrigation of a single crop, the 'economics' of irrigation usually means little more than the attainment of greater efficiency in water use by the reduction of waste. The popular proposition is that more sparing and less wasteful use of available water resources enables the community to increase the extent of cultivation. Following this line of reasoning, the benefits accruable to economic (or efficient) use of water is derived in terms of either additional land brought under cultivation or an

increase in the cropping intensity of the land already in cultivation, or both. Chambers (1976; 1978) adopted this kind of reasoning for optimal management of water resources for rice production in the Dry Zone of Sri Lanka.

The complementary role of water becomes evident in the discussions of a rainfed production system. Additional benefits accruing to the application of irrigation water to hitherto purely rainfed systems is very often viewed in terms of increases of

marginal value products (MVPs) or productivity of the other inputs. Such a postulate implies an upward shift in the production function on the provision of irrigation. Notably water is not a variable input in such a production function. Yet, this constitutes the core for many studies which attempt to assess the impact of irrigation. The framework for such an analysis is either a 'cost-benefit'

approach or a production function. A production function is adopted by Desai (1973) and Sadeghi (1978). The same approach has also been used, for example, by Levine (1966) to highlight the higher impact of irrigation in the dry season in comparison to that in the wet season in a selected region. However, a fundamental point to bear in mind is that these analyses are not concerned about the supply of the water resource. At best it is assumed as 'free and plenty'.

2.4.2 Water Response Functions

The alternative theory treats water as a variable input in the production process. It emerges from the proposition that crops exhibit differential responses to variation in the quantity of water

made available. This provides the necessary physical basis for analysis within the conventional production function framework.

Empirical studies to estimate the productivity of water simply use planned experiments to vary the quantity of water applied to a crop. At the farm level, there have been many attempts to make such estimates. Two of the noteworthy examples are Hopper (1965) and Naik (1965). These studies have made use of quantity measures of water at the farm 'headgate' of sample farms to specify whole-farm production functions. Such a technique is not relevant in the context of a small dam which concerns only a single

'community farm'. Furthermore, the objective in such dams is not simply to maximise productivity of water in rice production but to ensure the sustenance of a crop of rice.

For the small dam situation, a relevant set of concepts seems to exist in moisture stress-yield functions.

2.4.3 Moisture Stress - Yield Functions

There has been a distinct group of studies which infers the importance of water to crops indirectly. Instead of quantity measures of water, they incorporate a drought index or an index of

stress reduction in the specification of production functions. The relevant agricultural engineering literature is substantial. A few seminal papers on the above are noteworthy. Knetsch (1959) made use of drought days to define critical levels of soil moisture deficit in a production function of corn yield. Similar functions for rice are given by Wickham (1973) and Bhuiyan and Sumayao (1978). The obvious value of irrigation in increasing yield via the reduction of drought days was highlighted by Parks

and Knetsch (1960) and Reutlinger and Seagraves (1962). These studies incorporated into production functions, the number of days of stress reduction via irrigation. Recently, in a study to examine the differential performance of rice within an irrigation system, Asnawi (1981) has considered stress days and field water depths in production functions. A greater insight into such functions has been provided by Beringer (1961). Beringer (1961) drew heavily from the more fundamental soil-plant-water relationships. He also postulated the operation of the law o f diminishing marginal returns between the decreasing soil moisture stress and crop yield.

Nevertheless, the above studies do not give explicit

recognition to the temporal nature of water use. Moore (1961) was, perhaps, the first to identify the problem of allocation of water over time. However, Yaron's (1971) contribution is more valuable in the course of water resource optimisation research. Yaron (1971) distinguished between two types of water-yield relationships; namely:

(i) the yield with the total water input having a fixed intraseasonal distribution; and (ii) the yield with flexible and dated water

input.

The studies of Stewart and Hagan (1969), Hagan and Stewart (1972) and Ellis (1972) adopt the first approach which involves estimation of the relationship between water shortage and yield by regression techniques. The difficulty of estimation of the second type of

function was recognised by Yaron (1971). He advocated the derivation of 'growth rules' by simulation in a dynamic programming framework, with growth stages and states a transition function to update the

yield from period to period. In fact this approach has been predominant in recent water-resource optimisation studies.

2.4.4 Optimal Dam-Water Management

Optimal water allocation issues usually recognize the temporal nature of the water demand. Most of the studies have employed a dynamic programming framework for analysis which allows sequential decision making. Normally the crop growth duration is divided into a number of stages at which irrigations are given. The decision on irrigation quantities at each stage is made

considering the state of the water storage and crop growth towards attaining maximum profit. The optimisation studies'" could be classified, depending on the nature of water supply and demand at each stage, into three groups.