In a recent article in this Review, Robert Mendelsohn attempted to clarify David Bradford's misunderstanding regarding optimal fraction of capital (Sk) that is consumed and fraction of income that is (Sy). One of the criteria suggested for selecting a public projects is the present value of the future consumption income from the investment, as stated by Mendelsohn: present value of dollar of investment is worth even more if future returns from that investment are reinvested (p. 240). The social present value of dollar of private investment, V, varies considerably with the parameters, the market rate of interest, r, the social rate of time preference, i, and the rate of reinvestment, Sy. However, the impact of S on the present value, V, and its role in the selection process is not clear. The variable Sy is rather ambiguous and the optimum value, in general, for S is either zero or one. The formula mentioned at the bottom of Mendelsohn's Table 1 (p. 240) should read:

R ISK transfer and price discovery are two of the major contributions of futures markets to the organization of economic activity (Working (1962), Evans (1978, p. 80), and Silber (1981)). Risk transfer refers to hedgers using futures contracts to shift price risk to others. Price discovery refers to the use of futures prices for pricing cash market transactions (Working (1948), Wiese (1978, p. 87), and Lake (1978, p. 161)). The significance of both contributions depends upon a close relationship between the prices of futures contracts and cash commodities. This paper examines the characteristics of price movements in cash (or spot) markets and futures markets for storable commodities. Section II presents an analytical model of simultaneous price dynamics which suggests that, over short intervals of time, the correlation of price changes is a function of the elasticity of arbitrage between the physical commodity and its counterpart futures contract. Greater elasticity fosters more highly correlated price changes, and thereby facilitates the risk transfer function. The elasticity of supply of arbitrage services is constrained by, among other things, storage and transaction costs. Thus, futures contracts will not, in general, provide perfect risk transfer facilities over short time horizons. The essence of the price discovery function of futures markets hinges on whether new information is reflected first in changed futures prices or in changed cash prices (Hoffman (1932, pp. 258259)). The model in section II provides a framework for analyzing whether one market is dominant in terms of information flows and price discovery. In section III we develop a model based on section II which is appropriate for estimating the lead-lag relationship between cash prices and futures prices. Section IV presents empirical estimates of the parameters of the model for seven different storable commodities: wheat, corn, oats, frozen orange juice concentrates, copper, gold, and silver. The cost of arbitrage between cash and futures differs across these commodities. For this reason we are not surprised to find inter-commodity differences in the correlation of short-run price changes and in the substitutability of futures contracts for cash market positions. With respect to the price discovery function of futures markets, we find that while futures markets dominate cash markets, cash prices do not merely echo futures prices; there are reverse information flows from cash markets to futures markets as well.

Journal Article Estimating the Economic Model of Crime: Employment Versus Punishment Effects Get access Samuel L. Myers, Jr. Samuel L. Myers, Jr. Federal Trade Commission Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 98, Issue 1, February 1983, Pages 157–166, https://doi.org/10.2307/1885572 Published: 01 February 1983