By Michael Pohst
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Extra info for Algorithmic Methods in Algebra and Number Theory
2. A few foods probably have negative income elasticities at the average level of incomes in the United States and other highincome countries, but whether a particular commodity has a positive or negative income elasticity is a question that must be answered empirically. For individual foods, at least those with relatively few built-in services, income elasticities are thought to decline as incomes increase. Households with high incomes will generally have smaller income elasticities for foods than households with low incomes.
In empirical analyses, a common point to use is the arithmetic means of Pi and Qi. An alternative equation for defining price elasticity is the arc or average formula E = [(Q0 − Q1 ) / (Q0 + Q1 )]/[( P0 − P1 ) / ( P0 + P1 ] = [(Q0 − Q1 ) / (Q0 + Q1 )][( P0 + P1 ) /(P0 − P1 )]. The subscripts now represent two different points on a demand curve. The arc equation is mainly a device for computing an elasticity at an average between two points—not the average of the elasticities on the arc between the points.
2 The derived demands for most, if not all, farm commodities are thought to be price inelastic. Thus, price and total revenue are expected to be directly related or, put another way, an increase in output, with other factors held constant, will reduce prices and the total revenue obtained by farmers. This was recognized at least as early as 1915 when Henry A. Wallace wrote, “The Demand Laws . . indicate to me that the farming class as a whole is penalized by over-production and rewarded for under-production” (as cited in Stigler 1962: 17).