TABLE 7. Projected numbers and distributions of farms, with 1978 as the transition base. De- Year S S S S S S S S S S Total cline 1 2 3 4 5 6 7 8 9 10 1978 91 147 54 34 19 8 8 9 3 5 378 1982 75 114 32 34 18 12 5 6 4 3 303 75 1987 62 88 19 33 17 16 3 4 5 2 249 54 1992 51 69 11 31 16 19 2 3 5 1 208 41 1997 42 52 7 29 16 23 1 2 5 1 178 30 2002 35 40 4 27 15 26 1 1 6 0 155 23 Note. Data for 1978 and 1982 are actual census data and are included for comparative purposes. matrix. This in itself is statistically acceptable since the theory in- dicates that the outcome or form of a given distribution-that of 1982, say-is dependent only on the outcome or distribution of the immediately preceding one-that of 1978-and that the dependence is the same at all stages (see Judge and Swanson, 1961, p. 2). The transition probabilities shown in Table 5 permit certain insights into the dynamics of farm movements in the Virgin Islands. The matrix reflects many zero elements, an ob- vious indication of the lack of data on individual farms from one category to another. Row So suggests that no new farms have been entering farming, according to the assumptions above, and column So, an absorbing state, reveals that from all categories except S4, Ss, S6. and S9 farms are going out of business. The principal diagonal contains relatively large coefficients, which tend to indicate a degree of stability in farm size. The nonzero elements in row S1 signify that approximately 18% of the farms of less than three acres go out of farming in any five-year period. Of this same group, about 82% will remain in the same size category. Similarly, about 35% of the farms in S3 (10 to 19 acres) are likely to go out of business in a five-year period, about 59% are likely to stay in the same size group, and about 6% are likely to amalgamate with farms in S4 (20 to 49 acres). None of the farms in S4, Ss and S6, between 20 to 174 acres, is likely to go out of business; in fact, farms in S, show total stability. In addition, all farms between 20 and 500 acres show tendencies to expand (with the exception of those in S6). On the contrary, the largest farms exhibit the greatest inclination to founder: four out of ten farms over 1,000 acres are likely to fail in any five-year period. The elements of the fundamental matrix permit additional in- sights into the behavior patterns of farms: they give the mean number of five-year periods in each size category before going out of business, depending on the starting state. Thus, in Table 6, row S, indicates that the mean number of years for a farm of less than three acres to exist before going out of business is about 28 (5.69 x 5) years. Similarly, it is about 22 years that farms be- tween 3 and 10 acres will exist before their demise. For farms be- tween 10 and 20 acres, however, the length of time they are likely to stay in that size category is 12 years before being amalgamated with a larger farm. In its higher size classification, it is likely to stay there for about eight years before amalgamating again, and so on. Thus, the total length of time a farm operation is likely to stay in a given category is provided by the sum of elements of the fundamental matrix. These values are shown in the last column (Table 6). Thus, in the long run, farms in S6 (100 to 174 acres) and S9 (500 to 999 acres) will, on the average, exist only for five years before going out of business, while those in S4 (20 to 49 acres) have the longest life, on the average. The Projection of Farm Unit Numbers Information on the projected number and distribution of farms is not only important to present farmers, but also to younger people who may be contemplating, or training for farm- ing as a career, as well as to public administrators in the formula- tion of agricultural policy. It was pointed out previously that the transition matrix, when pre-multiplied by the base year distribu- tion of farms, produces the projection for the following time period. Continual post-multiplication of the results by the transi- tion matrix gives the projections for as many years as desired. The base year selected for projection is that of 1978, and the projected numbers and distributions are shown in Table 7. The overall pattern of decline recorded earlier is confirmed by the results of this stochastic model. Of the 303 farm units in operation in 1982, only 249 are projected to be in operation by 1987. About 54 of the current ones will probably cease farm operations. As shown, the small farms between 3 and 10 acres will continue to contain the largest absolute number of farms in any size category. However, because the base data show increases in the number of farms between 1978 and 1982 of sizes 175 to 259 acres, and of 500 to 999 acres, these are the only categories in which increases are suggested over the next 20 years. Never- theless, these increases occur at a decreasing rate over time. By about the year 2000, almost all of the largest farms would have become extinct, and those between 175 and 500 acres would almost all have gone out of existence. Farms below 175 acres in general will tend to have a much longer life and will persist in the system beyond those over 175 acres. If current trends continue, there is likely to be only about 155 farms altogether in the system by the year 2000, a decline from 754 in 1950, and from an all- time (recent) high of 828 in 1940. Explanation of the Decline in Farm Numbers The agrarian tradition in the territory of which older Virgin Islanders speak may be traced in recent times to that period around 1933 when the repeal of prohibition in the United States increased the demand for sugar, molasses and rum, and in 1934 when the Federal Government created the Virgin Islands Com- pany to stimulate the economy through the operation of sugar, rum, and hotel businesses. The initial expansion of agricultural activities led to the creation of a large number of farms in 1940, and increases in acreage under the plough reached its zenith in 1950, but the rate of growth was not sustained for long. Not even another breath of life by the Federal Government in 1949 could insure a sustained level of development based on agriculture. Thus was initiated another spiral of decline in this industry which persists to the present. The foregoing analysis addressed several quantitative dimensions of the decline, and in this section, an ef- fort will be made to provide reasonable answers to why? this decline has been taking place. In so doing, an examination will be made of the impact of the abandonment of sugar production, the development of tourism, the increase in industrial and com- mercial activities, the competition from imported foodstuffs, and the effect that policies or actions of government have had. When in 1949 VICORP was succeeded by VICO without the blessing of Congress in the continuation of rum production, it was left with the unprofitable sugar plantations, hotel and public utilities (Miller, 1979). By 1965, it was clear that the industry was feeling its death throes, since the single sugar mill in St. Croix had been sold by VICORP to a private concern, and the terms of sale required operation only until the end of the 1965-66 crop. At the close of the season, the owner announced that the factory would cease operations due to the substantial losses that were sus- tained in the previous year. This implied the elimination of the sugar industry involving over 4,000 acres of cane land, 113 farms, and a gross farm return of more than $600,000 in a single year (Blaut et al., 1965). VOL. XX-PROCEEDINGS of the CARIBBEAN FOOD CROPS SOCIETY 27