In the present study, compound growth rates of area, production and yield for vegetables/ vegetable groups were estimated to study the growth in area, production and yield of these crops. However, compound growth rates were used for the study. Compound growth rates were estimated with the following exponential model. Y=abtlog⁡y=log⁡a+tlog⁡bCGR(%)=( Anti log⁡b−1)∗100 where, CGR = Compound growth rate, t = Time period in year, y = Area or production or productivity, a & b = Regression parameters. The ‘t’ test is be applied to test the significance of ‘b’.

To measure the relative contribution of area and yield to the total output change for the major crops, the decomposition analysis model as given below is used. Sharma and Subramanyam (1984) redeveloped the model and several researchers (Kalamkar, 2002) used this model to study growth performance of crops. The method states that, if A₀, P₀ and Y₀, respectively represent area, production and productivity in base year and A_n, P_n and Y_n are values of the respective variable in n^th year item. (1)P0=A0∗Y0 and Pn=An∗Yn

Where, A₀ and A_n represent the area and Y₀ and Y_n represents the yield in the base year and n^th year, respectively, (2)Pn−P0=ΔPAn−A0=ΔA

From equation (1) and (2) we can write, P0+ΔP=(A0+ΔP)(Y0+ΔY)

Hence, P=A0ΔY∗100ΔP+Y0ΔA∗100ΔP+ΔYΔA∗100ΔP

Production = Yield effect + area effect + interaction effect

Thus, the total change in production can be decomposed into three components viz., yield effect, area effect and the interaction effect due to change in yield and area.

Area, production and yield of vegetables in Karnataka from 1998-99 to 2017-18 have been presented in Fig. 1. The total area showed an increasing trend over the period with about 40 per cent increase in a span of two decades. Diversification of agriculture towards high-value crops, especially fruits and vegetables are the contributing factor to this increase (Birthal et al. 2007 and Vanitha et al. 2013). However, figures for increased production were more appealing than its area, as it has shown 60 per cent increase. Yield per unit area under vegetables has increased by 14 per cent in 20 years. Improvement in yield of varieties and/ or hybrids, better farm management practices and increased area under irrigation could be the reasons for enhancement in yield levels.

Area under vegetables for periods between 1998-99 to 2017-18 is depicted in table 1. The vegetable area has reported a spike from 2.7 lakh ha to 3.7 lakh ha, with an annual growth rate of 1.8 per cent. However, the growth is not positive for all the vegetables, viz., potato, leafy vegetables, and other vegetables have recorded a negative growth rate. Among vegetables, onion had the highest area under production followed by tomato and potato. But, Percent share of onion to the total vegetable area in the state has raised from 33 per cent to 51 per cent, the same has fallen for potato (from 14% to 9%). As hypothesized, area under total vegetable production has increased over the period. Thus, the research hypothesis was accepted on the basis of evidences provided above.

Total production of vegetables in Karnataka has increased from 42 lakh tonnes in 1998-99 to 68 lakh tonnes in 2018-19, with an annual growth rate of 3.9 per cent (Table 2).

The highest growth in production was observed in onion (7.5% per annum) followed by tomato, cole crops and gourds. Similar to the area trend, production share of potato and other vegetables group has fallen significantly, which could majorly attribute to the low profitability of such crops.

Yield per hectare of vegetables grown for three periods is presented in table 3. Overall, productivity of vegetables has increased at 2.2 per cent annually, yet, other vegetables group has witnessed fall in its productivity with annual rate of−1 per cent. Among all vegetables tomato has highest productivity (32 MT/ha) and leafy vegetables has least productivity (11 MT/ha). This implies that efforts to increase productivity is highest in tomato and least in leafy vegetables.

Relative contribution of components to aggregate growth of vegetable in Karnataka output was decomposed into yield effect, area effect and the interaction effect and it is presented in table 4. It demonstrates the per cent contribution of area, yield and their interaction for increasing production of vegetables over the period of 20 years. It is evident from the results that the area effect was most responsible factor for increasing production of tomato, onion, guards, cole crops and other vegetables group. Thus, in effect for overall vegetables, it is 66 per cent. On the contrary area effect is negative for potato and leafy vegetables to the extent of−230 per cent and−17 per cent. These results are contrary to the findings of Anonymous (2008), which stated agriculture growth at national level was attributed to the yield effects.

Yield effect was found responsible for an increase in production of potato and leafy vegetables (362 % and 119 %, respectively). In neither of the vegetable’s interaction effect of area and yield has a major share in total production effect, representing a lack of synergies between them. After normalizing the components of total production effect to 100 per cent, individual effects are presented in Fig. 2.