Proceedings qf Cotferencc . G9

(CONTRIBUTED)

SOME SUGGESTIONS FOR DETERMINING THE ECONOMIC USE OF MACHINERY.

By MORAG MATHIESON.

The great progress made in agricultural engineering has led to the introduction of many new machines. Farmers, besides having to decide whether or not to use a machine, are confronted with an ever-growing range of machinery from which they can choose. In so far as the criterion of choice is anticipated profit, the solution to such problems is through an economic approach and it is with such an approach that this paper is concerned.

One important limitation, however, should be stressed at the beginning. The analysis given here is concerned with costing machines in isolation from the rest of the farm enterprise. While the costs of operation are of great importance and the principles on which they are based are of universal appli- cation, conditions peculiar to the individual farm should also be borne in mind when the choice of a machine is made.

The first step in the analysis is to study the costs of machinery operations. These can be divided into two classes, variable and fixed. The distinction between them is that while variable costs are incurred only when the machine is actually in use, fixed costs are chargeable whether the machine is working or not. Fixed costs, therefore, are independent of use and their incidence per unit worked falls in direct proportion to the volume of work done. The variation of the incidence per unit in fixed costs is reflected in the trend of total costs. The higher the fixed cost items are in relation to variable costs, the greater is the tendency of total costs per unit to vary with the volume of output.

of of

If the conception of variable costs were illustrated graphically the form the variable costs curve would be a straight line, granted the assumption constant returns to scale-that is with farm machinery equality of variable

costs per acre regardless of the acreage worked. This is a tacit assumption of Black* and in the writer’s opinion, based on the experience of costing farm machinery, this assumption is not unreasonable.

The form of the fixed cost curve is a rectangular hyperbola, whose distinctive property is the equality in area of the rectangles contained by all points on the curve and their co-ordinates ; whatever the volume of output, total fixed costs remain constant and as the volume of output increases the average fixed costs per unit fall.

Suppose there are three alternative methods of carrying out a certain operation, all of which require manual labour but two also require a machine. The first method uses labour only and needs more of it than the other two.

* Black, Clawson, Sayre and Wilcox : “ Farm Management,” Ch. xxiv.

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The second method employs a cheap machine which replaces some labour, and the third uses an expensive machine and the least labour of the three. An important problem here is t o determine the points at which it is economical to substitute one method for another.

The graph presents a geometrical solution to the problem. AA is the total cost curve per acre of Method I (the manual labour method only), BB the curve of Method I1 (the less expensive machine), and CC the curve of Method 111 (the more expensive machine).

Two points, a and a,, will be noticed on the graph. These give the acreages at which the costs per acre using Methods I and 11-point a-and Methods I1 and 111-point a,, are equal. These points also give the ranges of the economical employment of the alternative methods. Method I is the most economical for acreages less than a , Method I1 for acreages of a to a,, and Method I11 for acreages more than a,.

The position of these nodal points a and a, can be calculated algebraically. I n Method I . Let the variable costs per acre be V.

There are no fixed costs, so total costs per acre will be V. Let the variable costs per acre be V,, and the total annual fixed costs F,, so total costs per acre for x acres will be V,+F,

X Let the variable costs per acre be V,, and the total annual fixed costs F,, so total costs per acre for x acres would be V,+F,

I n Method I I .

-

In Method I I I .

- __ X

Position of point a. At point a by definition :-

= v,+I;, a

__ V

Therefore :- v-v 1 = I;, -

a

a (V-V,) = F, a =I?,

v-v,

At point a, by definition 1-

Position of point a,.

= VzS-Fz - v 1+ Fl

Therefore :-

- a1 a1

V,-V, = F, F, a , a,

a , (V,-V,) = F,F, a1 = FZ-F,

V,-V,

Proceedings of Conjeerence. 71

Where one method involves only variable costs and the other both variable and fixed costs, the nodal point is given by the figure resulting when the total annual fixed costs are divided by the difference between the two variable costs per acre.

If the two alternative methods concerned involve both fixed and variable costs, then the nodal point is given by the quotient when the difference between the two total annual fixed costs is divided by the difference between the two variable costs per acre. If the equation is insoluble then one machine is more economical for all acreages.

The rest of the paper is devoted to the application of this methodology to the problems of sugar beet harvesting. The material on which the illustration is based was collected in 1950 by Leeds University. About 50 machines were studied and most of these were of one or other of two models. The predominance of these two models is a reflection of the national position, for in the same year over 75 per cent. of the machines in use in England and Wales werc of these two makes.

Therefore, broadly speaking in 1950 three alternative methods of harvesting sugar beet were generally available. The first method involved ploughing out. hand pulling and topping, the second method required the use of separate and relatively cheap machines for mechanical topping and lifting, and in the third all the necessary operations were carried out by an expensive machine, a complete sugar beet harvester.

The variable costs in sugar beet harvesting include charges for labour, traction power and repairs. The speed of work and the composition of the working team decide the costs of labour and traction power. In the sample both models of the machine attained the same standard speed of work-four hours an acre.*

Another point revealed by the investigation was the composition of standard working teams. The team for the complete harvester consisted of two men and a tractor. The cheaper machines, however, required a larger team. One man and a horse worked the topper, another man and a horse used a side delivery rake to push the tops out of the way of the oncoming lifter which was worked by two men and a tractort. Altogether this method required one tractor, two horses and four men.

Repairs have been charged as a constant variable cost per acre. The figures used were obtained by dividing the estimated total repair bill incurred during the machine’s life, by the estimated length of the machine’s life expressed in acres.

In this investigation fixed costs include depreciation and an interest charge on capital. Use or variable cost depreciation has been ignored and depreciation is treated entirely as a fixed cost. Obsolescence is probably the most important source of depreciation with sugar beet harvesters since these machines are comparatively new inventions and their design is constantly changing. A working life of five years has been taken as the basis of the depreciation charge which has been calculated in the following manner :-The assumed scrap price of the machine at the end of its working life (10 per cent. of the new price) has been deducted from the new price and the balance divided by the assumed

* The National Institute of Agricultural Engineering have tested these models and give similar average rates of work for them.

t The alternative to using a side delivery rake is to push the tops aside by hand. Few farmers in the sample used this hand method, probably because of the extra expense- 151- per acre-involved.

72 Agricultural Economics Society.

length of the working life. Interest on capital is charged by allowing 4 per cent. interest per year on the estimated average sum invested in the machine during its working life.

Fixed and variable costs are given below for the three alternative methods of sugar beet harvesting. These costs are for the lifting and topping of beet but do not cover the costs of carting the tops and the roots from the field.

Method I . Ploughing out, hand pulling and topping. Variable and total costs per acre = L7 Is. Od. (50 man hours and 4 tractor hours.)

Method I I . Separate topper and lifter. Total annual fixed costs = L30. Variable costs per acre (16 man hours, 8 horse hours, 4 tractor hours and ;I/- an acre

= L3 10s. Od.

for repairs.)

Method I I I . Complete sugar beet harvester. Total annual fixed costs = &IlO. Variable costs per acre (S man hours, 4 tractor hours and 151- per acre for repairs.)

= L2 11s. Od.

Man labour charged at 216 an hour. Tractor labour a t 41- an hour. Horse labour at 113 an hour.

The graph shows the total cost per acre curves for the three methods. Cost per acre is measured on the vertical axis and acreage harvested on the horizontal axis. AA, BB, CC are the curves for Methods I , I1 and I11 respectively. Point a is the acreage where costs per acre are equal for Methods I and 11, and point a , where costs per acre are equal for Methods I1 and 111.

The dgebraical solution to the position of points a and a , is given below :-

Position of point u.

Poistion. of point a,.

a = F, v-v,

a = 30 -- 7.05-3.5

a = 5.45

a, = 110-30 3 ‘5-2 a55

a, = 84.21

Proceedings of Conference. 73

If the smaller and cheaper machine was not available, the comparison would be between the large machine and the pure117 manual method. There- fore :-

a, = F, v-v 2

110 7.05-W5S

- -

From this it will be seen that while the graph gives an approximation of the answer, the formula gives an exact solution and eliminates the laborious work of calculating out costs per acre and then the plotting of the figures obtained on a graph.

The practical use of this methodology is illustrated by the specific example of sugar beet harvesting. From the aspect of costing the operation in isolation from the rest of the farm business, the formula described here indicates the most economical method to use with a given acreage. This is, of course, not the complete solution to the problem, the effects of the choice of method on the whole farm enterprise has also to be considered. In particular, account should be taken of each farm’s regular workers and their productivity if they were not harvesting sugar beet. Consideration should also be given to possible variations in the rate at which beet is harvested by mechanical and manual methods respectively. The timeliness which is usually afforded by the use of a machine may be partly offset by delays which result when a machine is used in unfavourable conditions. All delays, whether mechanical or manual, increase the costs and may lead to considerable losses through the deterioration of the unharvested crop. Granted then these limitations which are part and parcel of work in farm management, the apparatus of thought contained in this paper should prove of value to those studying the economics of machine use.

The writer wishes to thank Mr. D. W. McInnes, who carried out the field work for the investigation into sugar beet harvester costs.

~~~

* Compare with the figure of 20 acres which is said to justify the use of a mechanical sugar beet harvester in Colorado in 1947/48. The choice there appears to have been limited to either a complete harvester or to purely manual methods. Sitler & Burdick : I ‘ The Economics of Sugar Beet Mechanisation,” Colorado A. & M. College--Bulletin 411-A.1950, page 5.

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THREE METHODS OF HARVESTING SUGAR BEET