JOURNAL OF THE SCIENTIFIC AGRICULTURAL SOCIETY OF FINLAND 454 Maataloustieteellinen Aikakauskirja Voi. 47: 454—461, 1975 On the dynamics of farm size distribution in Finland Devendra Sahal Abstract. This study attempts to explain why farm structure in Finland is what it is. The static aspects of size distribution are summarised by means of log-normal distribution and tested with respect to data on more than 500 communes for years 1959 and 1969. As to the dynamic aspects, despite some correlation between percentage growth and size at the beginning of the time period and which is believed to be partly spurious, the observed phenomena do not seem to be incompatible with the proposed version of law of proportionate effect. The latter need not be observed at every point in time. 1. Introduction Studies of farm size distribution seem to be few presumably because it does not make sense to study »business concentration» in an industry char- acterized by many entrepreneurs operating under a relatively competitive market structure. However, it is unlikely that farm entrepreneurs fail to account the (expected) scales of utilization in decisions related to investment in capital inputs and classifying the latter into durable and indivisible categories does not enhance our understanding of the former. Of course, cost curves yield no prediction about the distribution of firm size. In any event, a basic under- standing of the process of farm growth is necessary if we do not want to formulate production functions on a purely ad hoc basis. This is a sufficient justification of the present study which attempts to explain why the farm structure in Finland is what it is but even more important, why it changes the way it does. The theoretical framework of the study presents no difficulty because »much of the discussion pertaining to the size of the firm is equally applicable to the size of the plant» (Shen 1965, p. 420), especially in agriculture. In fact, by concentrating on farm size rather than the firm size we are able to bypass most of the taxonomic difficulties associated with the question as to what is a firm. Our sample is, in fact, more closely related to technology since the basic unit is the plant rather than the firm (Shen 1965, p. 422). https://www.c-info.fi/en/info/?token=9i4vs7mLWu4j6jdY.Gxk5RWIsqm_QRoQcZ8JHeQ.5XNzJCNgpGoGmdF_t-MDUIStFYeWqjUvkvamnBZd06xVyJvoPeqrI-87iG-PIHUq9WbwaUMW5gSsXtQE-hahEq9dtL0nl2a4oFtUi5NAd60ZNmxSi3X0-79um6_31kXJj9V-MgU7O0YiOgT9EGzs76N5VkIMOj1HjDBBrw 455 2. The model Underlying the basic model is the view that entrepreneurs’ decisions concern- ing scale of utilization are governed by the desire to realize the economics of scale subject to organizational constraint. Imperfections in capital market are ignored. Variations in elasticity of demand with regard to farm size are assumed, not too unreasonably, to be nonexistent and it is tested1 whether »there is a limit to the rate at which any firm can grow, a limit provided by the capacity of its existing management .. . Economics of growth exist for all sizes of firm . . . but they disappear once an expansion based on them has been completed» (Penrose 1968, p. 262 263). 2,3 Granted that the Penrose effect is a force to be reckoned with, it would tend to nullify the desire to improve the economics of scale so that we are likely to observe over a ’sufficiently’ long period of time that the probability of a given proportionate change in size during this time interval is the same for all farms regardless of their size at the beginning of the period. Thus a simple explanation of the process of firm growth is provided by the law of proportionate effect. 4,5 In the present context, if such a law indeed holds, the farm size distributionis likely to be log-normal since the law states that6,7 1 We shall presently see that the test is only indirect which is because of the empirical necessity, of course, a direct test seems to be all but impossible anyhow. As Mrs Penrose herself puts it: »The patterns sketched need fit no individual firm; firms of the same size will not necessarily grow at the same rate, and the point at which the rate of growth starts its real decline will be different for different firms. Furthermore, this point may be extremely hard to locate statistically, for in practice growth takes place in spurts, and periods of relative decline may well be followed by periods of accelerated growth» (Penrose 1968, p. 213). 2 Elsewhere Mrs Penrose is even more explicit: »Since the services from ’inherited’ mana- gerial resources control the amount of new managerial resources that can be absorbed, they create a fundamental and inescapable limit to the amount of expansion a firm can undertake at any time . . . There are thus two aspects of the nature of the managerial limit on the rate of expansion of a firm: First, the services available from the existing managerial group limit the amount of expansion that can be planned at any time because all plans for expansion absorb some of the services available from this group and the larger and more complex the plans themore services will be required to digest and approve them on behalf of the firm. .. . Secondly the amount of activity that can be planned at a given time limits the amount of new personnel that can profitably be absorbed in the ’next period’ (Penrose 1968, p. 48 49). 3 Williamson (1966, p. 1) readily agrees: »One of the most discredited concepts in the theory of the firm is that of an 'optimum size’ firm . . . there is no more reason to expect pro- fitability to decline with size than there is evidence to suggest that it does. This raises the question as to what does limit the size of a firm. The answer ... is that there are important costs entailed in expanding the size of a firm, and that these expansion costs tend to increase with firm’s growth rate,» Jorgenson (1967), Lucas (1967) and Treadway (1970) also assume that there are rising internal adjustment costs in the expansion of firms. 4 With the previously noted qualification concerning the length of the time period. 6 Reader familiar with the paper of Shen (1965) will recognize its influence here and subsequently. 6 »A variate subject to a process of change is said to obey the law of proportionate effect if change in the variate at any stage in the process is a random proportion of the previous value of the variate» (Aitchison and Brown 1957, p. 22). 7 Indeed, a number of studies attempt to fit skewed distributions to microeconomic data (Hart and Prais 1956, Simon and Bonini 1958), but the underlying theory has not been made clear. 456 X; J X; Xi _ i rj = J 1 j = 1 n (l) xj- where {ij} is a set of mutually independent random variables, independent of the set {xj}. By successive substitution Xj = (rj + x) Xj _ J = (r j + 1) ( r j - 1 + 1) Xj _ 2 (2) = (r j +!) (r j -l+!) • • • ( rl +1) xo Therefore, when |rj| is small compared to 1 and n is large, a random variable is lognormally distributed so that [(log e it)H t] 2 “ * F (x ) \ eay 2n t) o (3) A priori it seems necessary to add some further qualifications to this simple model. Thus exit occurs most frequently for farms of small size8 so the probability that a farm will die is unlikely to be independent of its size. Con- sequently we suppose that the law is valid for the size distribution of all the farms excepting those that leave the industry. With this qualification in mind, the dynamic aspects of the model are easily represented by 9 V(x t + 1)= p*V(x t) + (Tt 2 (4) where V(x t +t ) and V(x t ) are the variance of the logarithms of the farm size at time t + 1 and time t; the test for the model is whether f}2 is unity because if small farms grow more rapidly than big, it will be less than unity, there will be regression towards the mean, and vice versa. The residual variance a\, of course, simply measures the deviation in growth about the average rate of growth. Of course, it may turn out that the model is applicable only to the farms exceeding a certain minimum efficient size. But that remains to be seen. 3. Results Log-normal distribution was fitted to the average size data at the regional level of aggregation. Given the scarcity of the degrees of freedom available, farm size data were combined with the forest size data. The goodness of fit of the theoretical distribution was tested using a x 2 test with n-3 degrees of freedom where n is the number of groups. The results are presented in Table 1. While the normal distribution is decisively rejected, the fit of log-normal is 8 especially in view of the governmental intervention in Finnish agriculture. 9 See Hart and Prais (1956, p. 172) for the algebra involved. Equation (4) represents the law of proportionate effect in its strong form. 457 Table 1. Farm size and forest size distribution in Finland at regional level of aggregation^ P> x 2 under the theoretical assumption ofcensus year 1 log-normal distribution normal distribution 1. 1959 0.02