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2010 | OriginalPaper | Buchkapitel

9. The Cautious Farmer and the Local Market

Market Participation Under Uncertainty

verfasst von : John R. Miron

Erschienen in: The Geography of Competition

Verlag: Springer New York

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Abstract

In market formation, risk-averse individuals choose larger markets to reduce price or liquidity risk. In a spatial economy, larger markets mean the marginal participant incurs added shipping costs. In this sense, the scale of the market may be limited by the tradeoff between the benefits and costs of participation. Model 9A assumes shipping costs are zero—absent a cost disadvantage, the firm (a farm here) is ever better off the larger the market. In Models 9B and 9C, nonzero shipping costs may limit size of market for a marginal participant. However, what about spatial equilibrium? If some farms are close to the market and others further away, there will be an incentive for farms at greater distance to relocate nearer the market. Model 9B assumes that farms reach spatial equilibrium by forming a cooperative in which members share the aggregate cost of shipping equally. Alternatively, Model 9C assumes that farms reach spatial equilibrium by bidding up the price (rent) for land at advantageous locations. Chapter 9 is the first in this book to look at firms as both producers and consumers. As we progress toward a model of location that characterizes the regional economy, it is important to integrate demand and supply. In Chapter 7, we began to think about the nature of a firm. There is a parallel here in the contrast between Models 9B and 9C. Model 9B redefines the nature of a firm because the cooperative internalizes a market transaction (for shipping) in the same way that a firm internalizes when it does some aspect of repair production in-house. This chapter therefore looks at how another aspect of localization (market organization) and price are jointly determined.

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Vorheriges Kapitel Staking Out the Firm’s Market

Nächstes Kapitel Farming for Cash

I first considered density of customers in Chapter 7 and then again in Chapter 8 in more detail.

Economides and Siow (1988) are primarily concerned with the existence and size of financial markets. However, at the outset, that paper describes a simple locational model of trading by farmers, which is the focus of this chapter. Others who have made use of Economides and Siow (1988) to look at questions of location include Camacho and Persky (1990), Casella (2001), Gehrig (1998), Glazer, Gradstein, and Ranjan (2003), and Henkel, Stahl, and Walz (2000).

I use barter here in the economic sense of an exchange—a trade of some amount of one good in return solely for an amount of another good with no money involved—that takes place in the context of a market. This is seen here strictly as a matter of business; I exclude here any exchange (e.g., an exchange of gifts) where the motivation is, at least in part, something else.

Implicit in this description is an assertion that such a point exists and is unique. A determination of the conditions under which this assertion is valid is beyond the scope of this book.

The slope of the Walrasian exchange rate line is the negative of the exchange rate.

A market condition in which there are many buyers and sellers. From a search-theoretic perspective on markets, a seller in a thick market does not have to wait long to get a fair price for their good.

A market condition in which there are few buyers and sellers. From a search-theoretic perspective on markets, a seller in a thin market typically must wait longer to get a fair price for their goods.

A loss (or increase in cost) arising because of an unforeseen change in market conditions that causes price to change over the short term, price risk is associated with price volatility. In a search-theoretic perspective, sellers hold an asset until the price bid by a potential purchaser exceeds the vendor’s reservation price. Here, a distinction can be drawn between price risk and liquidity risk. Liquidity risk is the loss arising because of the delay in obtaining a bid at or above the reservation price. In practice, it is difficult to distinguish between price risk and liquidity risk. The approach in this book is to treat liquidity risk as simply an element of price risk.

Important work in the area of utility and decision making under uncertainty includes von Neumann and Morgenstern (1947), Marschak (1950), Hurwicz (1953), Simon (1955, 1959), Koo (1959), Bishop (1963), Harsanyi (1965, 1966), Loomes and Sugden (1982), and Sugden (1991).

For the interested reader, Sugden (1991) discusses the philosophical limitations of neoclassical perspectives on rational choice.

Bernoulli (1954) is an English translation of that paper.

For example, if we toss a fair coin twice and let X be the number of times a head obtains. X can take on the values 0, 1, and 2. From the Binomial Theorem, we know that probabilities are 1/4, 1/2, and 1/4, respectively. Therefore, \(E( X ) = 0( {{1 / 4}} ) + ( {{1 / 2}} )( 1 ) + ( {{1 / 4}} )2 = 1.0\).

In my view, Georgescu-Roegen (1954, p. 503) is correct in pointing out that mathematicians and statisticians dating back to Daniel Bernoulli and Gabriel Cramer had worked on similar ideas much before this. Harsanyi (1956) points out the similarities of game theory to earlier work by Zeuthen (1930).

That is, \(\varepsilon = \Sigma_x {U[ x ]} p[ {X = x} ]\) and \(\nu = \Sigma_x {( {U[ x ] - \varepsilon } )^2 p[ {X = x} ]}\).

Beta is the increase in mean (return) required to offset a unit increase in variance if two alternatives are to be thought to be equally preferable.

This is an approach initially suggested by Markowitz (1976). See also Levy and Markowitz (1979) and Kroll, Levy, and Markowitz (1984).

Economides and Siow (1988) also look at the case where the utility function is Constant Elasticity of Substitution (CES).

A Bernoulli trial is a statistical experiment which can result in only one of two possible realizations. An experiment consisting of a series of independent Bernoulli trials is called a Bernoulli process.

We would not have a Bernoulli process if each individual could wait until harvest time to see his endowment and that of his or her neighbors before deciding in which local market to participate.

Economists usually say in this case that wheat is numéraire which means that other goods (corn in this case) are valued in units of wheat.

In an earlier footnote, I raised the question of whether a Walrasian outcome existed and was unique. In the case of a log-linear utility function, the answer intuitively is straightforward. Each farmer maximizes utility by allocating income so that the proportions spent on wheat and corn are α and 1 − a, respectively. At the equilibrium exchange rate, \({{( {1 - \alpha } )( {1 - k} )} / {( {ak} )}}\), a Walrasian solution exist; the market clears and farmers of each endowment are as well off as possible. The Walrasian solution is also unique; no other exchange rate clears the market.

0.36 + 0.16.

\(0.5( {0.3} ) + 0.5( {0.7} )\).

\(0.52( {0.00} ) + 0.48( {0.50} )\).

This is another place where ordinalists might well cringe. If utility is indeed ordinal, what does it mean to take a linear combination of utilities as we do when we calculated U[N].

\(0.52( {0.00 - 0.24} )^2 + 0.48( {0.5( {0.30 - 0.24} )^2 + 0.5( {0.70 - 0.24} )^2 } )\).

(3(0.7)/(5(0.3)).

0.7/1.40.

(0.3)(1.40).

(3/8)(0.43) + (5/8)(0.60).

In Economics, utility is thought to be an index (or ordering) of preference among choice. As such, utility is an ordinal measure. However, when we calculate U[N], we appear to treat utility as though it were a cardinal measure. For a discussion of the issues raised, see Ellsberg (1954).

In this regard, Economides and Siow (1988, p. 110) appear to err in arguing that equilibrium price is independent of N because aggregate supply and demand for each commodity are proportional to N. My sense is that this confuses CEER and the ratio of expected offers.

CEER is not calculable because there is no trade.

In my view, the shortcoming of risk-return analysis here is that the notion of variance loses generality when the number of realizations of a random variable (here, realizations of k) is small.

See McGuire (1972) on economic models of club formation. For other modeling of cooperation in a geographic context, see Jayet (1997) and Soubeyran and Weber (2002).

Here I implicitly assume contingent shipping rates. That is, the cost of shipping wheat a kilometer is s units of wheat, and the cost of shipping corn a kilometer is s units of corn. Similarly, the coop fee is contingent; it is f units of wheat if the farmer has a wheat endowment, and f units of corn if a corn endowment. There is no adjustment here for the exchange rate between wheat and corn that will be obtained in the market. For the storyteller, the advantage of this scheme is that it simplifies decision making for the farmer who is still in anticipation of the harvest and does not yet know his or her endowment.

Mid-radius here is the distance which divides the farm into two equal areas.

For instance, while a ring might be the most efficient shape for getting the agricultural commodity to market, it may be inefficient for the daily chores of the farmer throughout the growing season. Thünen (1966, Chapter 11 and 13 ) discusses aspects of this problem.

This might be because each farmer has a Leontief technology that requires all inputs be in fixed proportion; however, the model to this stage is silent on other inputs to production.

Economides and Siow (1988) model the case where farms are spread out along a line in one-dimensional space.

(0.40)(0.0728).

(0.40)(0.1262).

Since each farmer has an endowment of either (1, 0) or (0, 1), if I assume that each farmer carries his or her entire endowment to the market to trade (not unreasonable given that the farmer does not know the exchange rate that might be established), the shipping cost associated with each farmer is fixed whether measured per unit shipped or per farmer.

As used here, a condition of the utility function wherein, if as income is increased by a fixed proportion holding prices of commodities constant, the rational consumer purchases the same proportion more of each good. Put differently, each good has an income elasticity of +1.0. Such a utility function is also said to exhibit homotheticity.

(0.0505 + 0.0291)/2.

0.70(1−0.0398)/(0.30(1−0.0398)).

0.5(0.29) + 0.5(0.67).

0.52(0.00) + 0.48(0.480).

\(0.52( {0.00 - 0.23} )^2 + 0.48( {0.5( {0.29 - 0.23} )^2 + 0.5( {0.67 - 0.23} )^2 } )\)

In Model B, the shape of the risk-return curve is sensitive to the unit shipping rate, s. As s approaches zero, the risk-return curve approaches that for Model A in Fig. 9.6. On the other hand, as s is made larger, the risk-return curve for Model B is pulled even further back and down at larger N.

For example, Models A and B here are built on binomial probabilities that arise because we have characterized market formation as a Bernoulli Process. It is well known that the Normal Distribution (which is continuous) can approximate a Binomial distribution as the number of trials in the Bernoulli process (in this case, the size of market) becomes sufficiently large.

Wingo (1961) originated the idea that land rent offsets transportation cost savings. Later, Alonso (1964) argued that the relationship between land rent and transportation cost savings was also affected by the elasticity of substitution between land and other commodities. Since I have here assumed that the amount of land used by each farmer is fixed, I do not have to take elasticity of substitution into account.

0.5(0.27) + 0.5(0.66).

0.52(0.00) + 0.48(0.475).

\(0.52( {0.00 - 0.228} )^2 + 0.48( {0.5( {0.28 - 0.228} )^2 + 0.5( {0.66 - 0.228} )^2 } )\).

Titel: The Cautious Farmer and the Local Market
verfasst von: John R. Miron
Verlag: Springer New York
Buch: The Geography of Competition
Print ISBN: 978-1-4419-5625-5

Electronic ISBN: 978-1-4419-5626-2

Copyright-Jahr: 2010
DOI: https://doi.org/10.1007/978-1-4419-5626-2_9

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