In this chapter the marginal contribution of each input to the resultant output is estimated with the help of the Cobb-Douglas production function. Such estimates will enable us to evaluate the performance of inputs vis-a-vis land productivity7 as well as to total output. The Cobb-Douglas function undoubtedly has its limits. The lack of knowledge of the precise nature of the input-output relationships and the difficulty of accurately measuring all inputs somewhat erode the results obtained from the assumed Cobb-Douglas function. Moreover, there can exist inter-correlationships among inputs, whereas the function assumes a unilateral causal relation between input and output. Despite its shortcomings, the Cobb-Douglas function may still yield the best possible estimates of marginal contributions of various inputs to the output.

Contribution of Inputs to Land Productivity

Table 10 presents the result of applying a Cobb-Douglas production function, taking land productivity as the dependent variable with total fixed capital per acre (including state capital expenditure, tractors, and draught cattle) and total current capital per acre (including state current expenditure, fertilizers, and chemicals) as independent variables. As far as the T-value is concerned, total fixed capital was the only input which is significant here while that of other inputs was less than one — in other words, insignificant. This suggests that at the present technological level, fixed capital is the major determinant towards improving land productivity. Since the sum of the regression coefficients (elasticity coefficients) is greater than one, it indicates an increasing return to inputs on land productivity. Theoretically, the regression coefficient of total fixed capital suggests that a 10 per cent increase in total fixed capital would increase 14 per cent in land productivity while a 10 per cent increase in total current capital could produce an increase of only 0.3 per cent in land productivity. The value of R1 = 0.99 shows that the joint influence of the inputs explained 99 per cent of land productivity.

Contribution of Inputs to Total Net Output

Assuming total agricultural net output as a dependent variable with respect to inputs such as total fixed capital per acre and total current capital per acre, the results from the application of a Cobb-Douglas production function is shown in Table 11.