Optimal Storage and Marketing Over Space and Time

Abstract

Borrowing from the theory of optimal resource extraction, we develop the mechanism guiding efficient commodity storage and marketing over producing regions through the crop year. Optimal storage occurs at producing areas, and time in storage varies directly with distance to market. Prices grow with interest rates in locations where storage is efficient but more slowly elsewhere, which explains why market prices (i.e., prices at the market) grow more slowly than interest rates. The model is empirically supported by examining storage in the Corn Belt, rates of price growth at various points, and quarterly grain marketings.Many agricultural commodities are produced over wide areas, often far from markets. In addition, harvest occurs within a short period but consumption is evenly spaced throughout the year. These features mean both transportation and storage are important and are closely interrelated. In a geographically dispersed market, commodity prices decline as distance to the market increases because transport costs increase. Therefore, the opportunity cost (interest foregone) of holding stocks declines as distance to the market increases. This means storage costs at two sites identical except for location will differ. In turn, these differences suggest that there exists an optimal (least cost) marketing pattern over time.The question of interest here is the nature of the marketing pattern and the mechanism that brings it about. It turns out that the mechanism is rather simple. It is similar to the one that governs the exploitation of resource deposits with different extraction costs (Hartwick; Dasgupta and Heal, pp. reviewers for their helpful comments.The storage problem is the mining problem with a finite time horizon and with storage costs instead of extraction costs (see Benirschka).with respect to optimal location of stock holding and storage. Furthermore, the results shed light on a long-standing controversy: the perceived failure of intertemporal price relations of stored commodities to follow theoretical predictions.A central tenet of the theory of efficient commodity markets is that the rate of return from holding commodity stocks, (i.e., price appreciation net of storage costs), must equal the rate of return from holding financial assets. Departures from this are opportunities for profitable arbitrage, exploitation of which continues until the rates of return on financial and commodity assets are equalized. It follows that the difference between contemporaneous spot and futures prices should equal the cost of storage, i.e., warehousing and insurance cost plus interest foregone. However, this result is not supported by empirical evidence. Studies of commodity markets tend to find that the gap between contemporaneous spot and futures prices is smaller than the full cost of storage. For instance, Kitchen and Denbaly recently found this to be true for major grains, but failed to find similar evidence for gold and silver.As early as 1930, Keynes (p. 143) observed similar discrepancies and attributed the ...

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