169

THE PROBLEM OF IMPUTING A CHARGE FOR FARMERS MANAGEMENT: A MODEL SOLUTION

D. S. Simon University of Hull

In the literature concerned with defining the returns available to farmers there has been considerable discussion of the value of the farmer’s input in terms of management. It is argued by many that the value of the farmer’s management should, in the same way as the value of the farmer’s labour, be charged against farm income before stating a return on capital.

At present the main method used to circumvent the problem is to use the Management and Investment Income as a guide, having deducted a charge for the farmer’s labour. Where the charge for maitaging the farm is required, an additional arbitrary imputation is made.

This article seeks to develop a model in order to enable this imputation to be made on a basis which, although to some extent arbitrary, is at least justified in that it is based on past data.

The model The model is based on the assumption that there are two distinct classes of farm work - farm manual labour and farm management. The amount of labour is measured by the size of the farm in standard man days.

The management element of farming is assumed to be carried out by the farmer-operator at least up to the size of farm where this element will constitute a full-time occupation. Thereafter the farmer will act as full-time manager and will employ other expertise (e.g. farm workers or farm managers) to the re- quired extent. These costs will be included in the labour cost of the farm as recorded in the Farm Management Survey.

For a small farm where the farmer provides a large proportion or all of the labour himself (say up to 500 smd), the management will be carried out at the same time as the farmer is carrying out manual labour (e.g. making plans whilst driving a tractor). As the farm size increases the farmer will devote more time to management and so will hire more labour to fill the gap in labour requirement created by his reduced own labour input.

The assumption is further made that the amount of management required varies proportionately with the size of the farm measured in terms of standard man days. This assumption explicitly excludes from the model the fixed time element of management which is required for all sizes of farm.

We can postulate the model in two parts. Firstly, where management of the farm is less than a full-time occupation. In

this case in determining the net farm income as defined in the Farm Manage- ment Survey, the labour cost charged will be the total labour requirement, less

170 D. S. SIMON

the amount of the farmer's own time available after carrying out the required management.

Secondly, where management of the farm is more than a full-time occupation for the farmer, the labour cost charged will be the whole of the labour input required for the farm and also the management input provided by others which the farmer is not himself able to provide.

This model may be expressed symbolically using the following definitions : S = size of farm in standard man days of manual labour (as measured in

the Farm Management Survey) D = number of standard man days of work done by the farmer in one year.

(Both manual and management input are subsumed into this variable) p = the proportion of the size of the farm measured in standard man days

which must be worked in a management capacity in order to run the farm. (This represents an additional time requirement over and above that measured by 5')

w = labour rate per standard man day m = management rate per standard man day L = total annual labour cost of running the farm. (This figure includes

both manual and management labour actually paid for by the farm.) Thus the labour input required each year = S smds and the management input required each year = p S smds.

Therefore, total input of manual and management time = (1 + p ) S smd but the farmers own input of time = D smd Therefore, input which must be paid for = S (1 + p ) - D smd At this stage we must deal with the two parts of the model separately. Firstly, where management of the farm is less than a full-time occupation.

In this case the farmer does all the management and devotes the time he has remaining to manual labour.

The time he requires for management = p S Therefore for th is part of the xriodel p S < D

Now the total charge for management and labour on such a farm would be given by the charge for labour WS plus the charge for management mpS, i.e. Total Charge = wS + mpS.

But this will not all be paid for because the farmer will undertake all (i.e. p S days) management and spend the rest of his time (i.e. D - p S days) on manual labour.

Therefore the Labour Cost L = w(S - ( D - pS) ) + mpS - mpS = w(S- D + p S ) = w(S(1 + p ) - D)

Secondly, where management of the farm is more than a full-time occupation, the farmer will spend all his time on management and will have to hire additional management and all the labour.

Again, the time required for management will be p S smds but the farmer is unable to supply all this time.

For this part of the model p S > D. Now the total charge for labour on such a farm is again wS and for manage-

ment mpS, i.e. Total Charge = wS + mpS.

THE PROBLEM OF IMPUTING A CHARGE FOR FARMER’S MANAGEMENT 171

However, since the farmer spends all his time on management, the amount of management time that must be paid for is pS - D and which will cost m(pS - 0). Thus, the labour cost L = wS + m@S - 0). We have therefore derived a model to estimate labour cost incurred in running

WherepS < D, i.e. management is less than a full-time occupation for the a farm.

farmer Labour Cost L = w(S(1 + p ) - D)

Where p S > D, i.e. management is more than a full-time occupation for the farmer

Labour Cost L = w S + m(pS - D)

The implications of the model Within the model it is assumed that the time available to the farmer in any year is constant, that the proportionate time (i.e. smd of management per smd of manual labour) required for management is constant, and that the daily rates for labour and management are constant. Thus, the only variables within the model are the Labour Cost L which is in turn a function of the remaining input variable, the size of the farm S in standard man days. Thus the relationship between the farm size and labour cost can be anticipated.

Now forpS < D L = w(S(1 + p) - D )

i.e. L = S.w(l + p) - W D The labour cost varies directly with the farm size, the factor by which the farm

size is to be multiplied being w(l + p) , and the intercept of the line if plotted will be -wD (on the L axis) showing the value of the farmer’s input if all his input were manual labour only.

However, we have already suggested that for small farms, most management will be done whilst the farmer is carrying out manual labour, therefore for small farms p, the proportionate time required for management will appear to be zero and the equation will become

L = Sw - W D showing that the farm cost will vary only as the labour element of cost varies.

Thus we can hypothesise that, for farms requiring less than full-time manage- ment, the labour costs will initially increase at the rate at which labour is paid and then when management commitments require the farmer to reduce his manual labour contribution to the farm work they will increase at a higher rate because labour has to be paid to cover the additional management time spent by the farmer.

Now forpS > D L = WS + m(pS - D )

i.e. L = S.(w + mp) - mD The labour cost again varies directly with the size of the farm, but this time the

factor is increased: (w + mp) compared with (w + wp), since management skills must be paid for at a higher rate than labour. Thus we can hypothesise the curve which would be shown by plotting Labour Cost against farm size as in Figure 1.

Now if we can derive D andp we can derive w and m. Thus we can state what should be the proper charge for the farmer’s input.

172

costs f

D. S. SIMON

Gdt.=(w+m.p) /

..YL.- .. / I

I I I I I *

S=D/p Standard Man Days

/

I L

man uays

/

/

/

/

-mD ! Le. ifpS c D charge for farmer's input = mpS + w( D - pS) or for a small farm where management is carried out by the farmer at the same time as undertaking manual labour, charge for farmer's input = mpS + wD and ifpS > D charge for farmer's input = mD.

Testing the model In order to test the model, data from the Farm Management Survey, as reported in Farm Incomes in England and Wales for the years 1973174 and 1974175 (Ministry of Agriculture, Fisheries and Food, 1976), were used. To ensure generality of conclusions the data for all farms, both tenanted and owner occupied, were combined to plot the curve of labour cost against standard man days.

Then in order to estimate the intercept a regression analysis was carried out using data from farm sizes 299 smd to 1,799 smd. This intercept was used to represent -wD.

THE PROBLEM OF IMPUTING A CHARGE FOR FARMER’S MANAGEMENT 173

The gradient of the line between the mean for the 275-399 smd and the 60&1,199 smd groups of farms was used as a proxy for w (the labour rate per smd) enabling an estimate of D to be made. Next, using the first part of the model

i.e.pS < D L = w(S(1 + p ) - D) for a farm of 1,250 smds, estimated from the line between the means of the groups of farm sizes 600-1,199 smds and 1,200-1,799 smds an estimate for p , the proportionate time required for management was assessed.

p S > D L = wS + mCpS - 0) for a farm of 3,000 smds, estimated from the line between the means of the groups of farm sizes 1,800-2,399 smds and 2,400- 4,199 smds, an estimate for m, the management charge per smd of manage- ment time, was made. Thus, the model led to an assessment of the appropriate charge to be made for

farmers managerial effort - fm per smd of management carried out, where the number of smds of management required are given by pS for a farm of S smds.

The calculations The data were assembled from the table (in MAFF (1976)) entitled ‘Comparison of certain physical and financial data on wholly tenanted and owner occupied farms’. The data for both types of farms were aggregated to give the basic information set out in Table 1 .

Finally, using the second part of the model

Table 1 Farm labour cost data

1973174 1974175

FARM SIZE MEAN MEAN LABOUR MEAN MEAN LABOUR SMDS SMD COST f SMD COST f

275-599 453 68 1 452 147 600-1.199 880 1,827 876 2,118

1,800-2.399 2,087 5,853 2,073 7,687 2,400-4.199 3,011 9,261 3,032 11,888

1,200-1,799 1,448 3,696 1,476 4,553

Thus these figures can be plotted as is shown in Figure 2, which shows the graph follows the shape expected from the model.

Thus it may be seen that the gradients of the first parts of the curve (from 275 smd to 1,199 smd), which we shall take as a proxy for w, the labour rate per smd are

for 1973174 f2.68Ismd 1974175 E3.23Ismd.

Next, using data for tenanted and owner occupied farms of the specialist types the regression analysis for farms 275-1,799 smd was carried out to estimate the intercept -wD.* The results are stated here:

Intercept for 1973174 = -€762

Correlation coefficients were both 0.91. 1974175 = -€1,028

These data and their analyses can be obtained from the author on request.

174

Figure 2 Labour costs plotted against Standard Man Days: 1973/74 and 1974/75

Labour cost f '000s

12 - 11 - 10-

9 -

8 -

7 -

6 -

5 -

4 -

3 -

2-

1 -

- 1973174

- - - - - - 1974175

D. S. SIMON

-0 ' 1 I I

500 1,000 1,500 2,000 2,500 3,000 Standard Man Days

Therefore, dividing by the relevant rates w (as set out above), we can derive

Farmers smds of input 1973/74 = - = 284

the number of smds of input by the farmer. 762 2-68

lso28 - 318 1974/75 = - - 3.23 This difference may well be due to spurious differences in the data, therefore

For p S < D L = w(S(1 + p ) - D)

Therefore p = (5 + D) jS - 1

Thus we can calculate the proportion of management time required for a farm of given size. We will interpolate from Figure 2 the labour cost for a farm of 1,250 smd which will satisfy the conditionpS < D.

Therefore we have D = 300, S = 1,250, w = €2.68 for 1973/74, and €3.23 for 1974/75, L = f3,000 for 1973/74 and €3,600 for 1974/75.

we will assume that the farmer's input, D, is 300 smd per year.

THE PROBLEM OF IMPUTING A CHARGE FOR FARMER’S MANAGEMENT 175

= 0.136

For 1974175 P=(m 3’600 + 300) / 1,250 - 1

= 0.132 Thus we can approximate the management time required to 13.5 per cent of

the smds required on the farm. Now having estimated p it only remains to estimate m, the management

charge per smd. To do this we need to examine a large farm on which manage- ment skills are hired - i s . pS > D which is explained by the second part of the model.

Labour cost L = wS + m(pS - D )

polate from Figure 2 and substitute into the equation, Now th is will be fulfilled by a farm of 3,000 smd and therefore we will inter-

L - w s p S - D m = - derived from the equation above

Therefore we have D = 300, S = 3,000, w = 2.68 for 1973/74 and 3.23 for 1974/75, L = f9,200 for 1973/74 and f11,700 for 1974/75.

For 1973/74 m = 9,200 - 2.68 x 3,000 0.135 x 3,000 - 300

= 11.05 11,700 - 3.23 x 3,000 0.135 x 3,000 - 300 For 1974/75 m =

= 19-14 Therefore the payment for 1 smd of management in the year 1973/74 was f 11 -05 and in 1974/75 was f 19-14, representing full-time management salaries of f3,300 and €5,750 approximately (for 300 smds). These salaries are comparable with those of managers in industry at that time.

Using the model to calculate the return on capital employed These derived rates for farmers’ manual labour and management input may be used to calculate the return on capital for investment in farming enterprises. This will be illustrated only for the year 1973/74 for the sake of brevity.

From Farm Incomes in England and Wales 1973/74 (MAFF, 1976) using the table, ‘The comparison of certain physical and financial data on wholly tenanted and wholly owner occupied farms’ which is reproduced in Table 2, the analysis continues for all farms in the survey.

Thus it is possible to apply the results of the model to the analysis of returns to investment in farming enterprises. This example has dealt with all farms in aggregate, but it would be feasible to deal with specific types and sizes of farms using Farm Management Survey data.

Conclusion We have therefore shown that it is possible to impute a management charge for the farmer’s input to a farm by using a model of the type defined. In this analysis

176 D. S. SIMON

Table 2 All fanning types 1973174

TENANTED OWNEROCCUPIED

Average size of farm, smds 93 1 885 Average valuation €17,499 €17.063 Net Farm Income before deducting Land and

Building costs or farmer’s labour f 7,896 €7,722 Land and Building costs €1,568 f 1,726

Thus it is possible to calculate (a) Net farm income after deducting Land and

Building costs €6,328 f 5,996 (b) Management Input required (13.5% of farm size) smd I26 119 (c) Fanners’ time available for manual work

(300 - (b)) smd 174 181 (d) Value of fanners management input (f I 1 -05 x (b)) 21,392 €1,315 (e) Value of farmers manual labour input (f2.68 x (c)) €466 €485 ( f ) Value of farmers input ((d) + (e)) €1,858 f1,800 (g) Net income after land and labour charges ((a) - ( f)) €4,470 f4,196 (h) % Return on Tenant Type Capital ((g)/valuation) 25.54 % 24-59 %

all types of farm have been averaged but the model can equally be applied to different farming types in different areas in order to ensure that the specific model required is derived.

This analysis further enables the return on capital employed by the farmer to be calculated by deducting the relevant manual labour and management charge from the net farm income before expressing it as a percentage of the capital employed. Thus it increases the ability to measure the efficiency of capital investment in the farming sector.

Therefore although this model requires certain generalisations to be made, it does present a method of resolving the controversy of the determination of the value of the farmer’s management input to the farm.

References Britton, D. K. (1970). Analysis of Net Farm Income: An Examination of Farm Management

Ministry of Agriculture, Fisheries and Food (1976). Farm Incomes in England and Wdes, survey Data, J. agric. Econ. 21,351-371.

1974175 London: HMSO.

Rkurnd

L‘EXPLOITANT AGRICOLE DANS LA GESTION DE SON ENTREPRISE - UN MODeLE DE SOLUTION AU PROBLeME

Dans la littdrature konomique consacrde d la definition de la rdmunkration que retire I’exploitant agricole de son entreprise, extrhement nombreuses sont les analyses qui tentent de cerner la valeur d imputer au facteur de travail ddversd par l’exploitant lui- meme dans la gestion de son entreprise. Nombreuses sont les conclusions qui prdconisent que la rdmndration du capital soit calculke apris deduction sur le revenu de l’exploitation d’un coat imputable d ce facteur de gestion, au m@me titre que le cotit du travail manuel accompli par l’exploitant.

A l’heure actuelle, la principale mbthode utilisde pour surmonter le problime consiste h se guider sur les chiffres etablissant le revenu

COOT A IMPUTER AU FACTEUR DE TRAVAIL DEVERSE PAR

THE PROBLEM OF IMPUTING A CHARGE FOR FARMER’S MANAGEMENT 177

de la gestion et des investissements, apr2s ddduction d’un colit reprisentant le travail manuel de I’exploitant. Lorsque l’on veut imputer un coiit au facteur de travail dkversk dans la gestion de I’exploitation, I’on a recours h une estimation arbitraire.

Cet article cherche ri ddfnir un modde qui permette de procdder h cette imputation du colit de gestion sur des bases qui, bien qu’arbi- traires dans une certaine mesure, se justijient nkanmoins en ce sens qu’elles reposent sur des chi‘res antirieurs.

Zusammenfassung DAS PROBLEM DER BERECHNUNG EINES PREISES FUR DAS MANAGEMENT DURCH FARMER: EINE MODELLOSUNG

In der Literatur, die sich mit der Definition von Ertriigen beschiiftigt, die Farmern zuJiessen, l h s t sich eine betriichtliche Diskussion iiber den Wert des Inputs durch den Farmer in Form von Management finden. Viele sind der Ansicht, dass der Wert des Managements durch den Farmer genau wie der Wert der Arbeit des Farmers gegen das Farmeinkommen vor der FestIegung eines Ertrages fiir das Kapital aufgerechnet werden sollte. Im Augenblick besteht die meist gebrauchte Methode zur

Umgehung des Problems darin, dass das Management-und Investitionseinkommen a h Richtstab beniitzt werden, wobei ein Preis fur die Arbeit des Farmers abgezogen wird. Fur den Fall, dass der Preis fk das Management der Farm benotigt wird, wird ein zusiitzlicher willkurlich festgelegter Betrag beriicksichtigt.

Dieser Artikel strebt die Entwicklung eines Modells an, mit dem diese Berechnung ermoglicht werden soll, und zwar auf einer Basis, die wohl in gewissem Umfang willkiirlich, aber andererseits wenig- stens gerechtfertigt ist, da sie auf friiherem Datenmaterial beruht.