farm size, efficiency and economies of size

14
145 FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE* P. J.&und and P. G. Hill? Ministry of Agriculture, Fisheries and Food Although the notion of economic eficiency is referred to widely, the definition and measurement of such eficiency raises many problems. This paper discusses some of these, with particular reference to the drawing of comparisons betweenfarms of direrent sizes. A discussion of conceptupl issuesprecedes an examination of some of the problems associated with the drawing of conclusionsfrom Farm Management Survey (FMS) and June Agricultural Census data. Despite the qualifications expressed, the paper includes analyses of FMS farm performance ratios. The results support .those of other studies in suggesting a threshold around the two to foztr man farm size but it is argued that the performance ratios probably overstate the curvature in the true size and eficiency relationship. 1. The concept of e5ciency and its measurement The term efficiency is often used synonymouslywith that of productivity, the most common measures of which relate output to some single input. Examples of such measures are milk yields per cow and crop yields per hectare. However,use of such measures may lead to misleading conclusions about efficiency since the various inputs into the farm production process need not be combined in fixedproportions. Moreover partial measures may not even provide reliable indicators of the differing or changing contributions of the specifically considered inputs. For example, output per head may increase as a result of developments (e.g. the substitution of capital for labour or the application of R and D) which may bear little relationship to labour’s specific contribution. It is therefore recommended that, in studies of farm performance, comparisons are made on the basis of measures which relate output to all associated inputs, even though one may then wish to examine how these measures vary between farms classified according to their use of a specific input, say land or labour. Such a procedure was used in the recent and valuable analysesof FMS data reported in Britton and Hill (1975,1978) and in the empirical analyses reported in this paper. However, before describing our own methodology we Srst consider various alternatives in order to indicate some features of the concept of efficiency. Subject to a restriction that the efficiencyconcept is to relate only to a farm’s * Paper presented at the AES Conference ‘Agricultural Land in the United Kingdom’. December 1978 (see p 226 of this Journal - Editor). t The authors are grateful to Mr D. Todd of H.M. Treasury for several helpful discussions and for the insights provided by his own papers. They also wish to acknowledge the assistance and comments of various colleagues in MAFF, particularly Mr C. W. Capstick, Mr A. M. Cowland, Mr J. A. Evans and Mr J. M. Watson. The authors are, however, solely responsible for the views expressed in the paper which do not necessarily represent those of the Ministry.

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Page 1: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

145

FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE*

P. J.&und and P. G. Hill? Ministry of Agriculture, Fisheries and Food

Although the notion of economic eficiency is referred to widely, the definition and measurement of such eficiency raises many problems. This paper discusses some of these, with particular reference to the drawing of comparisons between farms of direrent sizes. A discussion of conceptupl issues precedes an examination of some of the problems associated with the drawing of conclusions from Farm Management Survey (FMS) and June Agricultural Census data. Despite the qualifications expressed, the paper includes analyses of FMS farm performance ratios. The results support .those of other studies in suggesting a threshold around the two to foztr man farm size but it is argued that the performance ratios probably overstate the curvature in the true size and eficiency relationship.

1. The concept of e5ciency and its measurement The term efficiency is often used synonymously with that of productivity, the most common measures of which relate output to some single input. Examples of such measures are milk yields per cow and crop yields per hectare. However, use of such measures may lead to misleading conclusions about efficiency since the various inputs into the farm production process need not be combined in fixed proportions. Moreover partial measures may not even provide reliable indicators of the differing or changing contributions of the specifically considered inputs. For example, output per head may increase as a result of developments (e.g. the substitution of capital for labour or the application of R and D) which may bear little relationship to labour’s specific contribution. It is therefore recommended that, in studies of farm performance, comparisons are made on the basis of measures which relate output to all associated inputs, even though one may then wish to examine how these measures vary between farms classified according to their use of a specific input, say land or labour. Such a procedure was used in the recent and valuable analyses of FMS data reported in Britton and Hill (1975,1978) and in the empirical analyses reported in this paper. However, before describing our own methodology we Srst consider various alternatives in order to indicate some features of the concept of efficiency.

Subject to a restriction that the efficiency concept is to relate only to a farm’s

* Paper presented at the AES Conference ‘Agricultural Land in the United Kingdom’. December 1978 (see p 226 of this Journal - Editor).

t The authors are grateful to Mr D. Todd of H.M. Treasury for several helpful discussions and for the insights provided by his own papers. They also wish to acknowledge the assistance and comments of various colleagues in MAFF, particularly Mr C. W. Capstick, Mr A. M. Cowland, Mr J. A. Evans and Mr J. M. Watson. The authors are, however, solely responsible for the views expressed in the paper which do not necessarily represent those of the Ministry.

Page 2: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

146 P. J. LUND AND P. G. HILL

internal revenues and costs (whether or not they actually take monetary forms)* one might attempt to measure inter-farm variations in efficiency through the estimation of production functions. However, this approach is likely to encounter various conceptual or practical difficu1ties.t For example, systematic variations in efficiency across farm sizes would prove to be indistinguishable from scale effects and random inter-farm variations in efficiency from the variety of other factors (including measurement errors) which necessitate a stochastic formulation of the function.

An alternative and potentially more fruitful method for measuring efficiency wasoutlinedbyFarre11(1957)andfirstapplied tointer-statedataon US agriculture. This method$ is based on the concept that there is a ‘best practice’ technical efficiency frontier for firms such that whilst some firms may be operating at the frontier (i.e. at the maximum attainable technical efficiency) most firms will lie within it. On the basis of an assumption of constant returns to scale, or alternatively for iirms of given size, the method permits a firm’s overall economic efficiency to be decomposed into separate technical and allocative (price) efficiencies. However instructive consideration of the method is, its practical value is reduced by the sensitivity of its results to errors of measurement since the location and shape of the efficiency frontier are determined by the very small number of observations which appear to lie on it.

The more widely applied total factor productivity method is also best explained for the two factor case. This method measures the efficiency of the ith firm as

(1)

(2)

( W L f + rKt) vt Et =

where

Lr and Ki are the labour and capital inputs of the ith firm, wt and rt are the actual rewards to these factors paid by the ith firm and w and r may each be either their particular ith firm values (wt, rt) or some other (e.g. social opportunity cost) values (w*, r*).

One problem with this method is that if the actual rewards to labour and capital arc defined comprehensively so as to exhaust net output (i.e. w = wt and r = rr) the efficiency measure will equal unity for all firms. Non-unity values may only be obtained by using alternative prices for one or both factors. Moreover it remains to be questioned whether, say, any positive differences between the actual and the alternative (e.g. social opportunity cost) rewards to inputs reflect the distribution of a firm’s above-average efficiency or a relative understatement of the quantity and quality of its inputs.

Neither the Farrell northe total factorproductivity methods make any allowance for the dynamic nature of a firm’s behaviour - its response to changes in its operating environment and the associated adjustment costs. A useful survey by Madden (1967) of the conceptual issues and empirical evidence in a specifically agricultural context began by drawing the important distinction between long-run

Vt = ( w t h + rt&),

~ ~~~~~

* Such factors as the social consequences of having an agrarian sector, the impact of modern farming techniques on the pattern of the countryside and the externalities .arising from pollution are excluded from this analysis, except in so far as they affect farms’ internal costs and revenues. An evaluation of a fum’s private (internal) costs and revenues yl! of course be affected by price support and input subsidy arrangements and by any. addiaonal costs arising from restrictions placed on farm activities in order to reduce potentlal external costs.

t For a fuller discussion of the possibilit of measuring inter-farm variations in efficiency through the estimation of production Lnctions see Lingard (1978).

3 AlthouG capable of generalisation to the case of several factor mputs the method is best exphned in &agrarnmatic form for the two in ut case: see Farrell(1957). pp 254-256. The method has been used in non-agricultural stuies by Todd (1971, 1977).

Page 3: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE 147

and short-run average costs. Both long-run and short-run curves are normally drawn on the basis of given technology and input prices. However, whereas the long-run curve describes the costs that a farm would incur in producing at various planned levels of output if all its inputs (materials, labour, and capital, etc) could be freely adjusted, the set of short-run curves describe the costs that a farm would incur at various levels of output after having determined the levels of its more fixed inputs, at least within a certain range. There is in practice a wide range of sets of cost curves, each set relating to a different length of ‘short-run’ and hence fixity of some inputs. However, this recognition ofreality merely strengthens the point that whilst both the long-run and the short-run curves may be u-shaped the observations of individual farms in any particular period will include obser- vations on farms at various degrees of departure from the points of tangency of short-run and long-run curves and hence from the long-run cost curve. The typical farm will not be using the exact composition of inputs which would in the long- run give the minimum cost at its current level of output.

There are a number of other considerations which further complicate the issue. First the above analysis rests on an implicit assumption that cost curves remain stable through time, at least when unit costs are expressed in real (i.e. inflation- adjusted) terms. This assumption is unlikely to be valid, especially when one considers the long time horizon over which some inputs (e.g. buildings and works) remain fixed. The shape of the curves will change with varying relative input prices and their overall positions will be affected by technical progress. Thus, for example, it would not be unrealistic to postulate that if the long-run average cost curve really is u-shaped, its turning point will be moving to the right through time (i.e. occurring at ever higher levels of output) as a result of various technical developments requiring more capital equipment and human skills. However, just as it is economically inefficient for a farm continuously to adjust its more durable inputs to those optimum for its current level of output so is it economically inefficient for it to be continuously pursuing the ever shifting long-run cost curve without regard for the costs of adjustment. The second consideration is that under- lying the Farrell approach to the measurement of efficiency. Farmers, and farms, differ in their abilities to transform inputs into outputs, even though part of these differences may reflect an inadequate measurement of inputs. These differences arise both in the ex ante possibilities which farmers perceive as being open to them and in their expost day-to-day farm management capabilities given their particular committed inputs. Thus what is observed in practice is not the long-run cost curve which is (or was) applicable in the current (or any earlier) ex ante planning situation but an amalgam of observations on individual farms at different degrees of departure from their original ex ante and current ex anre optimum combinations of inputs and with differing basic levels of planning or operating efficiencies. Nevertheless it is open to question whether in assessing economies of size one should be concerned with the shape of the ex ante cost curve as opposed to the costs which farms of different size actually incur in practice. Thus it can be argued, and the authors would support this view, that the level of costs associated with short-run departures from an ex ante long-run curve and the ability of farms to incorporate embodied technical progress (provided that the associated scrapping/ replacement costs are not ignored) should both be taken into account in consider- ing the overall extent of economies of size.

However, the problem of the inherent variability inefficiency betweenindividual farms still remains and it is easily demonstrated that differing variations in efficiency between farms of differing size will affect one’s judgment about the existence of economies of size. Suppose that observations on individual farms’ unit costs of production and levels of output are as indicated by the crosses in Figure 1. This figure, which is hypothetical, has been drawn so that the variation in unit costs decreases with increasing output. In the absence of measurement

Page 4: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

148 P. J. LUND AND P. G. HILL

errors, the lower continuous line indicates the unit costs of the most efficient farms at each size, whilst the higher broken line indicates the ‘size-efficiency’ relationship that would be inferred from grouped-data averages or standard regression techniques. Whether or not the dispersion in efficiency between farms having the same output varies with output in the way suggested, it is a pattern corresponding to the broken line rather than the continuous line which is reflected in the results of Britton and Hill and similar analyses. Figure 1 An illustration of a hypothetical relationship between average costs and output

Kev * x

Average 1 I ObSeNatiOnS for individual farms.

economies of size curve for most efficient farms.

economies of size curve for farms of average efficiency within each size group.

n

I output

The importance of this distinction between efficiency variations and economies of size lies in the fact that in considering the consequences of changes in a farm’s size one needs to consider both the movement along the economies of size curve and the farm’s likely departure from it. The factors which make a farm less than technically efficient at its current level of output may well prevail at other levels of output but possibly to differing extents. Thus, for example, to the extent that the skill of the farm management (i.e. of the individual farmer) on a small farm may not be suf6cient to manage a much larger farm, one would expect an increase in the farm size to be accompanied by a decrease in relative efficiency. If this were indeed the case, the line that an individual farm would follow would differ from both of those shown in Figure 1 and could fall less steeply than either. To change a small farmer into a large farmer may require more than a change in farm size.*

11. The use of the FMS : Some measurement problems The measure of farm efficiency used in the studies by Britton and Hill was gross outputt per €100 total inputs, where the latter are defined to include an imputed

~

* This point was noted by Britton and Hill (1975), see p 55-57. t The gross output measure used in the Britton and Hifanalyses was replaced in 1973/74 by the

new and slightly different measure ‘total farm enterprise output’ which is used in our analysis. The precise definitions of the two measures of farm output are provided in the sections on Definitions of Terms in the relevant annu! reports. It should be noted that analyses of farm size and efficiency based on FMS and sirmlar data sources relate to farms and not to each of their possibly several enterprises, though some definitions of farm types may approximately equate the two in the case of highly specialist farms.

Page 5: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

FARM SIZE, EFFICIENCY A N D ECONOMIES OF SIZE 149

cost for the labour input of the farmer and his wife. This is the most general of the various performance measures shown in the annual Farm Management Survey report Farm Incomes in England and Wales and broadly corresponds to the inverse of unit costs. If the hypothetical relationship between unit costs and output portrayed in Figure 1 did in fact exist one would observe a positive relationship between the performance measure and output across the lower range of output, little relationship around some best performance output level, and a less marked negative relationship across the higher range of output.

However, thereare a number of reasons why comparisons of the ‘total outputs/ total inputs’ performance measure across farm types and sizes as shown in the annual FMS reports and examined by Britton and Hill do not correspond exactly to comparisons of outputltotal costs with output. First the numerator is not a quantity of output but a sum of values of output (for crops) or of output adjusted for stock changes* (livestock) and of miscellaneous revenues and grants. Thus it reflects both the volume of a farm’s output and the average prices received. To some extent any inter-farm variations in average prices will reflect quality dif- ferentials or other real differences in such features as packaging and delivery, timing of sales or lower unit costs associated with larger volume trading but there may be some small additional differential, reflecting market power, which should not appear within an efficiency (as opposed to aperformance) measure. Any differences in the market power of farms is likely to result in an overstatement of the efficiency of larger farms vis-h-vis smaller ones and any similar dif- ferential in market power on the input side will have the same effect.

The discrepancies between desired and actual measures having the greatest impact on the observed relationship between performance and farm size are, however, likely to arise within the denominator of the performance measure. First, one may note that a substantial general understatement of farm costs arises through the use of estimates of machinery depreciation based on original (historic) cost. The notes in recent FMS reports have suggested that, on the basis of aggregate data, depreciation at replacement cost might be some three times higher than the historic cost estimates shown in the report. It is difficult to assess the effect this has on comparisons of performance measures across farm types and sizest but the results of the current switch to replacement costs will be awaited withinterest.1

However, the greatest problems in deriving meaningful measures of efficiency for individual farms seem less likely to be overcome by potential data improve- ments. They arise on the labour side and essentially from the quantitative import- ance of the inputs of the individual farmer and other family members in the total *The FMS analyses reported in Farm Incomes in England and Wales, 1976177 (Ministry

of Agriculture, Fisheries and Food, 1978) were the first to identify separately the stock appreciation of breeding livestock and exclude it from total farm enterprise output. This factor was therefore included in the numerator of the performance measures examined by Britton and Hill.

t The switch to replacement costing may perhaps be expected to have a greater proportionate effect on the total costs of small farms than on those of large farms in so far as small farms have older machinery, but a lesser one in so far as they are less capital intensive and use machinery which was bought second-hand or is already fully depreciated.

2 The depreciation of farm buildings is implicitly included withm the item Land and Building Costs which covers ‘the rent paid by tenants including the imputed rent on tenant’s improve- ments, the rental value of owner-occupied farms (and) the farm share of rates and tenant- type repairs to land and buildings’. The im licit valuation of buildings depreciation is thus that in the determination of existing rents Lhether or not imputed). One should, however, acknowledge that the FMS treatment of rent does not correspond exactly with that required for efficiency comparisons since the pure economic rent of land is treated as a cost and the rent or rental value of farm cottages and that part of the rental of the farmhouse, not associated with the farm business’ as a revenue item instead of a deduction from costs. However, the authors suspect that the quantitative importance of the errors arising from these imperfections may be small. The quotations arc from page 9 of the report Farm Incomes in Englandand Wales, 1976177 (Ministry of Agriculture, Fisheries and Food, 1978).

Page 6: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

150 P. J. LUND AND P. 0. HILL

labour input. In the case of, say, a manufacturing company the opportunity cost of the inputs of the managers can be reasonably estimated by their salaries and other rewards and although the ‘profits’ of a large unincorporated business may include the rewards to the entrepreneur’s labour and management inputs these may be fairly small relative to total employee remuneration. The situation is obviously different when one is examining farms mainly reliant on family labour and management and perhaps then comparing these with larger farms run by companies. The treatment of farmer and family inputs is of crucial importance in the measurement of farm performance and inevitably affects any conclusions drawn about economies of size and differential farm efficiency.

The appropriate valuation of the contribution of the inputs of a farmer and his family is that which they would receive if exactly comparable inputs were bought in from outside. Theoretically even this treatment would be less than adequate since if applied to all farmers and family workers the implied additions to aggregate labour supply and demand would alter the price and/or quantity of services supplied by the current employees and have further repercussions through associated labour markets on the prices and quantities of other inputs and all outputs. However, the practical problems involved in applying the more limited treatment are likely to be considerable even if these general equilibrium conse- quences are ignored. The limited treatment would require correct measurement of the various labour and management inputs supplied by the farmer, his wife and other family members and the earnings that each of these persons would receive were their services to be bought-in by the farm. The extent to which the FMS performance measures properly indicate economies of size and variations in farm efficiency is dependent upon the extent to which this limited ideal is achieved. The current practice is to value unpaid family labour, excluding that of the farmer and his wife, at the appropriate rate for comparable paid labour and to adjust the payments to other family labour for any obvious difference between its actual and comparable earnings. In deriving the ‘total outputsltotal inputs’ performance measure an allowance is also made for the input of farmer and wife manual labour by valuing the estimated time worked by the farmer and his wife at the appropriate paid labour rates.

These allowances clearly go some way towards the appropriate limited treat- ment suggested above but at least three problems remain. First the estimates of the quantity of manual labour services supplied by the farmer, his wife and unpaid family labour seems likely to be subject to considerable errors. Farmers not unnaturally find it difficult to quantify the duration of their total working time and to allocate it between different activities. Britton and Hill considered this problem and noted both the relatively greater importance of farmer and wife labour on small farms and some evidence* suggesting a general understatement of this input. This would cause the performance measure to overstate the ef- ficiency of smaller farms vis-d-vis larger ones. On the other hand these authors also presented a figuret suggesting that the understatement may not exist on smaller farms and that thereafter its extent may vary with farm size. Such a pattern could reverse the direction of the bias noted above. Any tendency for the manual labour skills and hence potential manual labour earnings of farmers and their wives to vary with farm size would also bias comparisons of the measure across farm sizes.

The most significant departure of practice from the ideal probably lies in the treatment of the managerial, secretarial or clerical inputs of the farmer and his * See Brittonand Hill (1975), pp 97-105. This evidence mainly consisted of a comparison of the

FMS estimates of the value of farmer and wife manual labour and the results of a survey conducted by NED0 in 1970 which asked about average numbers of hours worked on a holding.

t See Britton and Hill (1975), Fig. 5.18, p.98.

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FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE 151

wife. No allowance for these is made in the FMS even though they are inputs which when supplied by other persons are treated as costs. Imputation for these inputs would raise even greater problems than those affecting manual inputs since the unit value of managerial inputs is less easily assessed. However, it seems likely that the total value of these inputs will tend to increase with farm size, partly because their required volumes are likely to be related to farm size and partly because farmers with larger farms may have higher alternative (i.e. oppor- tunity cost) earnings as managers.* One likely effect of ignoring these inputs is that the performance measure for medium sized farms will be increased vis-d-vis that of smaller farmers. However, the effect as between medium and large farms is likely to be rather different because of the greater incidence of paid managers on larger farms. On farms with paid managers the understatement of the value of these types of inputs is likely to be less. Thus even if real unit costs were on average equal across farm sizes the current FMS treatment of these inputs would generate the familiar pattern of performance increasing with farm size up to some point and then possibly declining somewhat. Moreover, it should be noted that the problem cannot be overcome by excluding payments to salaried managers: one wants to know what the pattern would be if all managerial-type inputs were included as economic costs and not what it would be if they were all ignored. One should not exclude the possibility that persistent differences in performance measures between individual farms simply reflect differences in the opportunity cost earnings of their entrepreneurs. The idea that observed efficiencies would tend towards equality if perfect measurement could be attained is not easily discredited.

Given the obvious difficulties involved in the valuation of managerial, sec- retarial, and clerical inputs by the farmer and his wife one may have to be content with observing variations in the best available performance measure across farm sizes, remembering of course that these variations reflect economies of size, differences in efficiency at given size and the necessarily inadequate measurement of some inputs. This procedure is followed in the remainder of this section which considers the FMS ‘total outputs/total inputs’ performance measures for various farm types and sizes and for years up to 1976/77.t However,onemust alsoobserve that the FMS provides performance measures for farms classified by hypothetical labour inputs (Standard Man Days: SMDs) and not by actual output while Britton and Hill have considered classifications by both SMDs and farm area. The use of an actual input as a measure of farm size will in general tend to indicate a decline in performance with increasing output where none exists. If, for example, ‘total outputsltotal inputs’ ratio was constant across all output, an apparent decline in performance with farm size would result from observations above the average line (i.e. those for high performance farms) being shifted to the left while those below the average line would be shifted to the right. The use of a measure based on hypothetical inputs for a given output avoids this particular problem but, for a single input, ignores the differing normal input requirements of different types or combinations of output. A corresponding bias in the other direction would occur if farm size was measured by output or SMDs when the prime interest lay in farm size as measured by area. Despite these qualifications comparisons of performance measures across farms with differing SMDs or areas may be required for policy purposes and are now presented. * The exclusion of the cost of freely provided fann advisory services, e.g. those of ADAS! from

the measured inputs may have the opposite effect but is likely to be of less quantitative importance.

t An anonymous referee has suggested the possibility of estimating cost functions using all the individual Fh4S observations. This approach, which would appear to include the specifi- cation and comparison of alternative fUnCtiOM1 forms, has not been followed in this study but would appear to be a possible direction for future research.

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152 P. J. LUND AND P. G. HILL

Tables 50-56 of the 1976-77 FMS report Farm Incomes in England and Wales show averages of various performance measures, including the preferred ‘total outputs/total inputs’ one, for various types and (SMD) sizes of farms providing data for both 1975176 and 1976177. For the top six of the seven SMD size-groups the tables also show the average ratios for ‘High Performance Farms’ and ‘Low Performance Farms’, these being the farms lying in the top and bottom quarters of farms in each typelsize group when ranked according to their indi- vidual ‘total outputsltotal inputs’ performance ratios. Figure 2 shows the per- formance ratios in 1976177, by SMD size-group, for farms classified as ‘Dairy’ and ‘Cropping’. These are the two broad farm types having a relatively high total number of farms and a reasonable spread across SMD sizes.

The main feature displayed by these figures is the wide dispersion in the performance ratios within the upper six size-groups over which the High and Low Performance Farm analysis is reported. This dispersion is such that for both farm types all six ratios for High Performance Farms lie above all six for All Farms, all of which in turn lie above those for Low Performance Farms. The dispersion in performance ratios between farms within each size-group is clearly far greater than that which exists between farms in different size-groups, both on average and at the ‘High Performance Farm’ frontier.* However, the figures also indicate a marked increase in the performance ratios up to the 600-1 199 SMD size group (equivalent to about 50 hectares for Dairy farms and 100 hectares for Cropping farms) with some slight increase thereafter in the case of Dairy farms.

We have subjected these patterns to more thorough examination by applying formal statistical tests to the performance ratios for 1975/76and 1976/77forfarms in two important and more homogenous sub-types, Specialist Dairy and General Cropping, classified by SMD size-group and to the more broadly defined Dairy and Cropping Farms classified by area.? Two different types of statistical tests were conducted on the differences between the mean performance ratios for farms classified by these variables. First, an analysis of variance was conducted in order to test the hypothesis that the mean Performance ratio was the same in each of the several size-groups. Second, a series of t tests was conducted to test the hypothesis that mean performance was the same in adjacent size-groups. In addition tests were conducted on the differences between the variances of the ratios for farms in adjacent size-groups. The results of these various statistical tests are detailed in Table 1. For Specialist Dairy (by SMD) and Dairy (by area) farms they indicate significant overall differences in performance ratios between farms in different size-groups though the differences become insignificant when the smaller size-groups are excluded from the analysis. There was no obvious relationship between the variance in the ratios and area size-group for these fqrms. The results for the General Cropping farms were more clear-cut, consisting of no significant difference between mean ratios classified by SMD or area but a general decline in the variance of the ratios with area size. The broad conclusions of the results of this detailed analysis for two farm

types in the last two years are supported by an examination of the ratios for the three main broad farm types over a number of years. Table 2 shows ratios for these sets of farms for each of the last nine years over which the same SMD size-group classification has been used. For each of 27 sets of data there is a marked increase in the mean performance ratio up to the 600-1199 SMD size-group, followed by an increase or no change in 22 instances over the next step (1200-

Given measurement errors which will obviously increase the observed variation in the ratios between farms of the same size, the pattern of the ratios for ‘High Performance Farms’ 6.e. the top quarter) may be taken as a rough indication of the location of the efficient farms’ frontier.

t Performance ratios for farms in the more homogeneous sub-types classified by area were not readily available.

Page 9: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE 153

Performance 2007 Ratio

180-

160-

Figure 2 Performance measures for cropping and dairy farms by SMMD size group, 1976/77 all farms, high performance farms and low performance farms

(a) Cropping

8 e 0 a , "

180-

160-

140-

120-

140-

120-

X

100-

High 0 0 Performance

0 0 0 Farms 0

X X X x All Farms

X

X

@

X

@

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8

High Performance

e Farms

X All Farms

@I Low Performance Farms

Less Farmsize than 275- 600- 1200-- 1800 - 2400- 4200 (SMD) 275 599 1199 1799 2399 4199 or more

1 Performance 200 Ratio

(b) Dairy

Less , Farmsize than 275- 600- 1200 - 1800 - 2400- 4200 (SMD) 275 599 1199 1799 2399 4199 or more

Note : Performance measure is total farm enterprise output (excluding breeding livestock stock appreciation) per flOO total inputs (including farmer and spouse manual labour). Source: Farm Incomes in England and Wales, 1976177 (HMSO), tables 50, 51,53,56.

1799 SMDs). The increase or lack of change continues through to the next size (1800-2399 SMDs) in 15 instances. This increase in performance ratios* is most

* It will be noted that these comparisons of several years' data have not been subjected to formal statistical analysis. Such a formal analysis would be possible though more complex than that described above. However. it should be noted that whereas the difference between the mean ratios for adjacent size-groups in any one year may not be statistically significant the obser- vation of similar differences over a number of years may be. It is the regularity of the pattern, rather than its ability to account for inter-farm variations in performance ratios, which is of note.

Page 10: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

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ns, o

ver a

ll gr

oups

F

Hig

hly s

igni

lican

t.

and

1976

177

Upp

er 5

M

eans

, ove

r all

grou

ps

F

Not

sign

ifica

nt at

10%

leve

l.

1976

/77

Upp

er 4

M

eans

, ove

r all

grou

ps

F N

ot s

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fican

t at 1

0% le

vel.

- tw

o 5

Mea

ns, 4

pairs

t O

nly

diff

eren

ce be

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n fir

st tw

o Y

W

sign

ifica

nt (a

t 10%

leve

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aver

age

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aria

nces

, 4 p

airs

F

E

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ic p

atte

rn: t

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at 5

% bu

t in

oppo

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di

rect

ions

.

Gen

eral

Fo

r bot

h C

ropp

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1975

176

and

1976

177

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and

1975

176

Gen

eral

19

7617

7 C

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- tw

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F F

t F

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?

? 8

Not

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ant a

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l. N

one

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vel.

Page 11: FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE

FARM SIZE, EFTXCIENCY AND ECONOMIES OF SIZE

Table 2 Mean performance ratios, 1968/69-1976/77 for dairy, livestock and cropping farms

155

YEARS SMDSIZEGROLJPS 1968169 69/70 70171 71/72 72/73 73/74 74/75 75/76 76/77

Dairy Farms under 275 275-599 600-1.199

1,200-1;799 1,800-2,399 2,4004,199 4,200 and over

Livestock Farms under 275 275-599 -1,199

1,200-1,799 1.800-2.399 2;400-4; 199 4,200 and over

Cropping Farms under 275 275-599 600-1,igq

1,200-1,799 1,800-2.399 2;4004;199 4,200 and over

96 110 116 116 119 117 NA

88 109 122 120 121 NA NA

102 104 116 119 119 118 111

92 110 113 117 119 115 NA

85 109 120 121 123 NA NA

99 112 122 124 123 125 118

92 109 117 120 1 20 122 116

86 111 123 131 124 133 NA

99 1 1 1 125 126 119 124 1 20

105 126 134 137 134 131 131

106 126 141 147 149 148 NA

99 119 128 129 128 131 121

113 133 140 143 141 137 143

116 144 156 170 163 167 NA

104 125 138 137 134 134 123

98 115 126 128 129 132 131

105 130 147 152 164 152 NA

121 149 159 151 153 150 138

84 98 112 116 120 120 1 20

77 99 117 133 139 128 NA

116 132 144 146 146 142 136

89 112 125 127 129 126 129

99 116 129 135 135 132 NA

109 127 144 140 145 147 124

91 106 114 117 118 116 1 20

96 111 122 130 131 117 NA

107 129 135 134 140 138 137

Source: Successive issues of Farm Incomes in England and Wales (HMSO): each year's figures

NA: Not available. taken from the first issue in which figures for that year appear.

marked for Dairy farms and least evident for Cropping farms. Beyond 2400 SMDs there is no pattern in the ratios for Dairy farms but a tendency for them to fall for Cropping farms. Thus for Dairy farms these long period comparisons indicate a steady increase in performance ratios to about 2000 SMDs with little change thereafter and for Cropping farms little difference between the size groups in the 600-4199 SMD range. The general pattern for Livestock farms lies somewhere between these two.

These empirical findings must, however, be viewed in the light of the factors discussed earlier. Considered together these factors (market power and the measurement of labour quantity and price and managerial inputs) suggest that the above-noted relationships between performance ratios and farm size overstate the strength of the relationship between efficiency and farm size. Moreover, any general tendency for the dispersion in efficiency to decrease with farm size would also lead one to overstate the extent of economies of size and hence the potential efficiency gains from increasing farm size.

III. The relevance of changes in the farm size distribution An indirect method of analysing the existence or otherwise of economies and diseconomies of size, and of any optimum farm size, lies in the examination of changes in the farm size distribution. The underlying theory is that if there exists some optimum farm size the force of competitive pressures will gradually lead to an increase in the proportion of farms of that size and of the proportion of total industry output produced by them. Certainly there is a long established

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156 P. 1. LUND AND P. G. HILL

trend towards larger farms in the United Kingdom, and it might be questioned whether, for example, the census data for England and Wales for 1969-75 do not indicate the existence of economies of size right through to the ‘4200 and over’ SMD size-group, which increased its overall percentage of total SMDs from 17 to 21 per cent in the six-year period?

Our suggested answer to this question is that the Census evidence is consistent with, but does not by itself prove, the existence of economies of size throughout the entire size range. Part of the change in the size distribution can be explained by the apparently substantial economies of size at lower sizes suggested by the evidence presented in the preceding section and perhaps by a gradual increase in the farm size at which they can be attained. However there are a number of other reasons why farm sizes may increase and hence why one should not attribute the observed change to one particular possible cause. One lies in the difference between efficiency and profitability. Efficiency, defined as total outputs/total in uts, is an average concept whereas profit maximisation is dependent on pursuit

produce at a level of output at which its (rising) marginal costs equal price and this level of output will be above that at which its average costs will be lowest and its ‘efficiency’ highest :,paradoxically a more profitable farm may be less ‘efficient’ than a less profitable one. Moreover the benefits expected from an increase in farm size may, or may not, be realised. Indeed given the lumpiness of many farming assets, particularly land and buildings, it would be unlikely that any actual increase in farm size would correspond exactly to that required to maximise either actual or expected profitability. Even if the normal optimum farm size was found to be one of exactly 150 hectares the complex geography of our landscape would inevitably result in a wide distribution of actual farm sizes. Finally, and perhaps of greatest overall importance, it should be recognised that there are a vast number of personal and social reasons why farm sizes may increase which are entirely unconnected with economies of size.

IV. Conclusions In this paper we have considered some of the conceptual and practical problems affecting the measurement of farm efficiency and comparisons across farm sizes. We have drawn attention to the point that measured efficiency necessarily includes the contributions to a firm’s output of inputs which may have been ignored or inadequately measured. We have also suggested that some alternative quantifi- cation and pricing of inputs, more in accord with social opportunity costs, might considerably reduce apparent differences in measured efficiency. More funda- mentally we have questioned whether efficiency maximisation is an appropriate farm objective.

Despite these considerations we have analysed FMS data in some detail, reaching conclusions about farm performance ratios which are broadly in line with those of Britton and Hill.* These are: (i) that there is certainly a kind of threshold around the two to four man farm size with farms smaller than this having significantly lower performance ratios; (ii) that there is some evidence of a continuing increase through to about the 1800 SMD size; (iii) that, while there is a hint of a decline at the very top end of the size range, it seems safer to conclude that performance ratios are constant beyond this size; and (iv) that the above statement is a summary over patterns which differ in detail between farm types and also between years. We have however indicated that, for a variety of reasons, this summary of observed performance ratios probably overstates the curvature in the true size and efficiency relationship which may in reality be much flatter.

o P marginalist principles. Assuming given prices, a profit-maximising farm will

* Similar conclusions were also reached by Dellaquaglia (1978) in respect of data for Scottish agriculture for the years 1973/74-1975/76.

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FARM SIZE, EFFICIENCY AND ECONOMIES OF SIZE 157

Our conclusions concerning the size and efficiency relationship are therefore somewhat cautious. Moreover we would stress that whether or not such a relationship does exist one cannot assume that an increase in a farm’s size will lead to an increase in its efficiency. The drawing of a distinction between average economies of size and efficiency variations at given size would lead us to expect that a change in farm size, and certainly any involuntary one, would tend to shift a farm further away from the efficiency frontier and hence result in a smaller improvement in efficiency than the average relationship would suggest. This is partly because of the importance of the aptitudes and capabilities of theindividual farmer and his ability to cope with alternative farm sizes and partly because any change in size seems likely to lead to above-average adjustment costs over a number of years. To some extent these factors may only apply in the short-run though one should also note the recent work of Edwards (1978) which, on the basis of a case study offarms in central Somerset, indicates that farm size increases may only be achieved at the expense of increased farm fragmentation. If this pattern of increasing fragmentation is general, one should expect increases in farm size to result in below average ‘economies of size’ efficiency gains. On the other hand there may remain scope for efficient farm amalgamations and increases in size at the lower end of the size range.

References Britton, D. K. and Hill, N. B. (1975). Size and€ficiency in Farmiryr. Farnborough. Saxon House. Britton, D. K. and Hill, N. B. (1978). Differences in Eficiency by Farm Size and Tenure. Paper

Dellaquaglia, A. P. (1978). Size and Efficiency in Scottish Agriculture, &or. agric. €con. 28,

Edwards, C. J. W. (1978). The Effects of Changing Farm Size Upon Levels of Farm Fragment-

Farrell, M. J. (1957). The Measurement of Productive Efficiency, J. R. Statist. SOC. 120,253-281. Lingard, J. (1978). Size and Eficiency in Farming: Can Production Functions Help? A Paper

Ministry of Agriculture, Fisheries & Food 1978. Farm Incomes in England and Woles, 1976177.

presented to AES Conference, December 1978.

149-158.

tation: A Somerset Case Study, f. agric. Econ., 29,143-153.

presented to AES Conference, December 1978.

London: HMSO. Todd, D. (1971). The Relative Eficiency of Small and Large Firms, Committee of Inquiry on

Todd, D. (1977). Efficiency and Size: Comments and Extensions, €con. SOC. Rev. 8, 305-312. Small Firms. Research Report NO. 18. London HMSO.

RBsum6 TAILLE DES EXPLOITATIONS, EFFICACITI? ET ECONOMIES D WHELLE

Bien que le terme eflcacitk kcorzomique soit une notion trPs largement invoquke, il est nkanmoins tres dificile de la saisir et la mesurer. Cet article se propose d’examiner certaines des dificultks rencontries dans la difinition de cette expression, en se plagant particuliirement sous l’angle de comparaisons entre exploitations de tnilles diffirentes. L’examen de certaines des dificultis qu’il y a ci tirer des conclusions de l’enqugte sur la gestion des exploitations agricoles (Farm Management Survey) et des statistiques agricoles de juin est prPc&dP d’une analyse critique des probli?mes conceptuels. En dbpit des rkserves exprimies, cet article renferme aussi des prisentations succinctes des donnies les plus rPcentes provenant de ces deux sources, parmi lesquelles des analyses statistiques des ratios de performance des exploitations tirkes de la Farm Management Survey. Les rksultats de ce travail concordent avec les conclusions d’autres etudes qui dkgagent la prksence d’un seuil aux environs de

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158 P. J. LUND AND P. G. HILL

l’exploitation occupant de deux h trois hommes, mais en estimant toutefois que les ratios de performance accentuent avec exageration la courbe dam le rapport exact entre la taille et I’eficacitd.

Zusammenfassung

FARMGROSSE, EFFIZIENZ UND WIRTSCHAFTLICHKEIT DER GROSSE

Obwohl der Beg@ der wirtschcifllichen Efizienz allgemein gebraucht wird, werfen die Definition und die Messung einer solchen Efizienz viele Probleme auf. Dieser Artikel beschiftigt sich mit einigen von ihnen, wobei insbesondere Vergleiche zwischen Farmen unterschiedlicher Grosse angestellt werden. Eine Diskussion begrflicher Ergebnisse geht einer Untersuchung yon einigen Problemen voraus, die mit den Folgerungen verbunden sind, die aus der Priifung des Farmmanagements (FMS) und dem landwirtschaft- lichen ZensusmateriaI vom Juni gezogen worden sind. Trotz der zum Ausdruck gebracliten Einschrrinkmgen beinhaltet der Artikel eine kurze Darstellung der neuesten verfigbaren Information aus diesen zwei Quellen einschliesslich einiger statist ischer Analysen von FMS Farmleistungsverhiltnissen. Die Ergebnisse unters tiitzen die anderer Studien und deuten darauf hin, dass eine SchweIIe bei der Farm- grosse von zwei bis drei Mann besteht, aber es wird argumentiert, dass die Leistmgsverhiiltnisse wahrscheinlich die wahre Grosse der Kriimmung und das Efizienzverhaltnis iibertreiben.