Feder, G., Just, R. E., & Schmitz, A. (1980). Futures markets and the theory of the firm under price uncertainty. The Quarterly Journal of Economics, 94(2), 317-328.*******
==Notes by yinung==
related to Sandmo (1971);
The theory of the firm under price uncertainty has been the subject of a considerable number of studies. While the papers by Sandmo , Leland , Batra and Ullah , and others have undoubtedly advanced the understanding of the decision making of firms under uncertainty, the theory is not complete unless forward delivery contracts are considered. Such contracts, referred to as “futures," are playing an increasingly important role in a number of commodity markets.
This paper examines the behavior of a competitive firm under price uncertainty where a futures market exists for the commodity produced by the firm. Working with the Sandmo approach, we found that production decisions depend only on the futures market price and input costs; the subjective distribution of future spot price affects only the firm’s involvement in futures trading. Conditions are then determined under which a firm will either hedge, speculate by buying futures contracts, or speculate by selling futures contracts. The results indicate that an important social benefit derived from the existence of a futures market is to eliminate output fluctuations due to variation in producers’ subjective distributions of future spot price.
Shankar, S. (2012). Production economics in the presence of risk*. Australian Journal of Agricultural and Resource Economics, 56(4), 597-620. Wiley;
This paper provides an overview of the literature on production under the influence of risk. Various specifications of stochastic production function such as models with additive and multiplicative uncertainty, Just and Pope model, output-cubical, state-allocable and state-general models are discussed. Further, criteria determining optimal producer behaviour are derived for deterministic production technology and for various kinds of state-contingent technologies such as output-cubical, state-specific, state-allocable and state-general technologies. Finally, a brief discussion is presented about the drawbacks of each of these specifications of technology.
- Arrow, K.J. (1953). Le des valeurs boursiers pour la repartition la meillure des risques. Technical report, Cahiers du Seminair d’Economie, Centre Nationale de la Recherche Scientifique (CNRS), Paris.
- Briec, W. and Cavaignac, L. (2009). An extension of the multi-output statecontingent production model, Journal of Economic Theory 39, 43–64.
- Chambers, R.G. and Quiggin, J. (1998). Cost functions and duality for stochastic technologies, American Journal of Agricultural Economics 80(2), 288–295.
- Chambers, R.G. and Quiggin, J. (2000). Uncertainty, Production, Choice and Agency: The State-Contingent Approach. Cambridge University Press, Cambridge, UK.
- Chambers, R.G. and Quiggin, J. (2002). The state-contingent properties of stochastic production functions, American Journal of Agricultural Economics 84(2), 513–526.
- Chambers, R.G. and Quiggin, J. (2003). Price stabilization and the risk-averse firm, American Journal of Agricultural Economics 85(2), 336–347.
- Chavas, J.-P. (2008). A cost approach to economic analysis under state-contingent production uncertainty, American Journal of Agricultural Economics 90(2), 435–446.
- Debreu, G. (1952). A social equilibrium existence theorem, Proceedings of the National Academy of Sciences of the United States of America (38), 886–893.
- Hirshleifer, J. and Riley, J.G. (1992). The Analytics of Uncertainty and Information. Cambridge University Press, Cambridge.
- Jaramillo, P.E., Useche, P., Barham, B.L. and Foltz, J.D. (2010). The state contingent approach to farmers’ valuation and adoption of new biotech crops: Nitrogen-fertilizer and drought tolerance traits. July 2010 Annual Meeting. Agricultural and Applied Economics Association, Denver, CO.
- Just, R.E. (2003). Risk research in agricultural economics: opportunities and challenges for the next twenty-five years, Agricultural Systems 75, 123–159.
- Just, R.E. and Pope, R.D. (1978). Stochastic specification of production functions and economic implications, Journal of Econometrics 7(1), 67–86.
- Kumbhakar, S.C. (2002). Specification and estimation of production risk, risk preferences and technical efficiency, American Journal of Agricultural Economics 84(1), 8–22.
- Love, H.A. and Buccola, S.T. (1991). Joint risk preference-technology estimation with a primal system, American Journal of Agricultural Economics 73(3), 765–774.
- Love, H.A. and Buccola, S.T. (1999). Joint risk preference-technology estimation with a primal system: reply. American Journal of Agricultural Economics, 81(1), 245–247.
- Nauges, C., O’Donnell, C. and Quiggin, J. (2009). Uncertainty and technical efficiency in finnish agriculture. Number (53rd) Conference, Cairns, Australia. Australian Agricultural and Resource Economics Society.
- O’Donnell, C.J. and Griffiths, W.E. (2006). Estimating state-contingent production frontiers, American Journal of Agricultural Economics 88(1), 249–266.
- O’Donnell, C.J., Chambers, R.G. and Quiggin, J. (2010). Efficiency analysis in the presence of uncertainty, Journal of Productivity Analysis 33, 1–17.
- Quiggin, J. and Chambers, R.G. (1998). Risk premiums and benefit measures for generalized-expected-utility theories, Journal of Risk and Uncertainty 17(2), 121–137.
- Rasmussen, S. (2003). Criteria for optimal production under uncertainty. the state-contingent approach, The Australian Journal of Agricultural and Resource Economics 47(4), 447–476.
- Rasmussen, S. (2004). Optimizing production under uncertainty: generalisation of the state-contingent approach and comparison of methods for empirical application. Unit of Economics Working papers 24184, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
- Sandmo, A. (1971). On the theory of the competitive firm under price uncertainty, The American Economic Review 61(1), 65–73.
- Shephard, R.W. (1953). Cost and Production Functions. Princeton University Press, Princeton, NJ.
- Shephard, R.W. (1970). Theory of Cost and Production Functions. Princeton University Press, Princeton, NJ.
- Yaari, M.E. (1969). Some remarks on measures of risk aversion and on their uses, Journal of Economic Theory 1(3), 315–329.
Agnar Sandmo (1971) “On the Theory of the Competitive Firm Under Price Uncertainty." The American Economic Review, Vol. 61, No. 1 (Mar., 1971), pp. 65-73. URL: http://www.jstor.org/stable/1910541; lse.ac.uk 提供的 [PDF];****
==note by yinung==
這篇利用 risk-averse 的 utility function 假設, 證明完全競爭廠商, 在有 price uncertainty 下, 最佳決策是
where c'(x),邊際成本, is increasing in x