This paper analyzes the effects of contracts for exhaustible resources. The conclusions are as follows: (1) for a single mine, with increased risk production for the spot market falls, long-term contracting increases, total output falls, contract length generally decreases, equilibrium spot prices increase, and contract prices may rise or fall; (2) with changing economies because of past production, output (spot prices) rises (fall) and then falls (rise), and this scalloped pattern remains with entry and storage included; and (3) contracting permits pairwise gains, may create losses for others, and prices are “fuzzy” signals as they may change for several different reasons.

An argument by Buchanan that the criterion of Pareto optimality is of little value when used solely with traditional economic variables is expanded and developed formally in an axiomatic framework of individual choice. Individual decisions are first aggregated to group decisions, and then group decisions are aggregated to give social decisions. Social decisions are compared with the Pareto-optimal conditions for social choice. Finally, there is a short discussion of the implications for the study of social choice and institutional change.

G. S. Maddala, R. Blaine Roberts; Statistical Cost Analysis Re-Revisited, The Quarterly Journal of Economics, Volume 96, Issue 1, 1 February 1981, Pages 177–181

7 The F-statistic for the first test is F(4,107) = 0.50 while for the second test it is F(4,11 1) = 0.81. Both of these values are well below the critical-F at conventional levels of significance. 8 Further experimentation showed that one additional parameter could be eliminated by, for example, disposing of the last join point (setting d2 = 0.). However, since the purpose here was simply to show that fewer than 12 parameters are required, the equation has been left in the present form.