The Farm Economist, Vol. VIII., No. 2, p 24-26.
THERE seems to be some confusion in objectives in two recent articles in this journal.1 The following note sets out purely to appraise certain aspects of the theoretical models inferred in these articles and concludes with an alternative explanation of variations of total farm output in New Zealand.
(1) Mr. Allen seems to feel that Mr. Bellerby has underestimated the ‘flexible factor’ argument as one explanation of the level of output during a depression. Mr. Bellerby states the position clearly enough on page 330: 'The entire cost level may be affected by an associated fall in wages and the rate of interest, or in the price of fertilizers, feeding stuffs, and other principal inputs of farming.2 Such changes lower the cost curve throughout its length and diminish the farmers' incentive to reduce output to any degree.'
Now, in the theory of production as usually presented, every factor of production is used according to its marginal contribution, and, if certain other conditions are met, the payment of all the factors according to the value of that contribution should just exhaust the total product.3 A change in product prices should, in theory, be reflected in a new pricing for each factor and use of that factor. The depression situation in farming is characterized by the lack of opportunitites of alternative employment in the economy, the general attachment to the land, and a hope that things will come right in the long run. If, under these conditions, farmers are prepared to accept whatever reward is left over after paying current prices for market-priced inputs, then it is a decline in the price at which they supply their labour and brains to the firm which is responsible for the lowering of the cost-curve. If the owner has full equity in the farm itself, there is possibly a decline in the subjective price at which he supplies the' land' to the firm as well.
The differences between Mr. Bellerby and Mr. Allen can be resolved, partly at any rate, by observing that in the U.S.A. and in New Zealand the majority of farms are family farms in which the labour share of the total product is far higher than in the United Kingdom. In general there seems to have been a decline in
1 The Farm Economist, vol. vii, no. 8, pp. 325-35 ; nos. 9-J 0, pp. 383-92.
2 My italics.
3 This assumes that a linear homogeneous function of the first order applies to the agricultural firm with reasonable exactitude.
AGRICULTURAL SUPPLY FUNCTIONS: A NOTE 25
factor prices in most countries in the depression and a relatively greater decline in those factors which in agriculture never had a very clear ‘market price’, such as the owner's labour and management reward.
(2) The concept of a backward-sloping supply curve seems to rest on a mistaken view of the theory of supply and demand. A supply curve is supposed to represent the alternative quantities of goods which would come forward on to the market at different demand prices other things remaining equal. For the many reasons which have been variously stressed by Mr. Allen and Mr. Bellerby, it has become generally accepted that there is little variation in output possible over quite a wide range of prices in the short run and therefore that the aggregate supply of agricultural products is inelastic, i.e. it has an almost vertical supply price relationship.
On this interpretation anyone yearly estimate of output represents one point on such a supply curve. It represents that output which was in fact produced owing to the various circumstances we know govern a given output, such as the influence of the weather, variations in inputs, &c. In the aggregate, that particular output position is far more likely to be determined by these considerations than by the price set by the demand schedule. It is also more ljkely that there shall be a price adjustment to clear the market, especially of perishables.
To say that a series of such yearly observations may be visualized in terms of a ‘supply curve’ clearly does an injustice to the pure theory of supply and demand. What they represent is a series of equilibrium points where a predetermined level of output was presumably cleared by an adjustment in prices. If that output is to be related to any system of prices, then it should surely be to some complex of farm prices over the previous five years or so. We may then properly speak of the ‘one-year lagged response in wheat acreage to a change in wheat prices’, and so on.
Now a further general property of agricultural output seems to be that it always moves in the same direction, i.e. towards a greater output. We need not enter into a discussion about the relative merits of population increase and income elasticity of demand at this point. This movement is not always continuous. Indeed, it fluctuates considerably according to the vagaries of the weather, &c., but in general, successive yearly observations of farm output when plotted usually move across the page to the right. On this interpretation, each observation represents a position where the various market forces and weather conditions finally equilibriated sllpply and demand. These positions have been very neatly graphed for the United States by W. W. Cochrane when at the University of Pennsylvarua.1 Rather fortuitously, the data from 1912 to 1949 fall into several groups, from which Mr. Cochrane is able to build a complete picture of agricultural supply and demand in the United States. He explains shifts from one group to another across hjs graph in terms of rapid periods of technological advance, the vertical supply functions thus taking up new positions each time.
(3) Mr. Allen's data for New Zealand do not show such a tendency to clump together in groups of years but appear to show a continuous shift of the supply function from 1929 to 1941. As Mr. Allen points out (p. 391) there is a very strong trend factor, complicated by a fluctuating yield factor (p. 388), in the volume of production series. This is worth further investigation. As is well known, the New Zealand agricultural economy is mainly a livestock one, dependent on grassland production. The winter period when the grass ceases to grow is usually tided
1 An analysis of farm price behaviour, Pennsylvania State College Progress Report, no. 50, May 1951.
26 AGRICULTURAL SUPPLY FUNCTIONS: A NOTE
over by saving adequate reserves of hay and grass silage from the previous growing season.
Any model, then, which explains the shifts in the yearly observations of New Zealand gross agricultural production must clearly take into account weather influences, feed reserves, and average trend in output. In connexion with some other work1 on the nature of aggregate supply in New Zealand agriculture the author has been able to produce such a descriptive model of New Zealand gross output without direct reference to the price system at all. In the following equation the dependent variable (Y) is the volume of production series quoted by Mr. Allen. The independent variables are an index of summer rainfall at Hamilton, North Island (X1), the total acreage of pasture taken as hay or silage in the preceding year (X2), and a linear time trend (X3).
Y = 51.30 + 0.0444X1 + O.2594X2 + 5.0014X3
This equation ‘explains’ 94 per cent of the year-to-year variation in New Zealand gross output from 1929 to 1950. Such a close relationship may be regarded as fortuitous in the extreme, but the equation demonstrates that farm output is wellnigh predetermined in New Zealand, and that the presumable relation of prices to output must be connected in a long-term sense with the evident faith that New Zealand farmers have in the future.
University of Oxford,
Agricultural Economics Research Institute.
1. Economic Record, May 1955. For reasons stated at the time, this analysis was carried out in first differences of the original logarithms. The equation presented here was calculated from coded logarithms of the original time series and remains in the coded form. The value of the Von Neuman ratio is 1:76, which is not significantly different from the expected value of 2.09.