If the derivative is presented by first discussing the intuitive motivation behind it, and then the instructor goes through an example where the

point elasticity is substantially different from the (easier to calculate) "change" elasticity, students may be encouraged to actually pursue an understanding of the derivative, so that they can have more precise and correct measures in establishing prices for their business.

Phillips (1994) provides an excellent analysis of the evolution of price elasticities since the introduction of Marshall's point elasticity.

Apart from the debate, Vazquez (1995) formulates a measure of arc elasticity that is in line with the characteristics of point elasticity and Haque (2005) shows the potential of using arithmetic means to approximate harmonic means in the computation of elasticity.

We are working on the additional technology that tests

point elasticity versus area elasticity," says Chuck Fleishman, chief marketing officer for Southwest Recreational Industries (SRI).

For the point elasticity estimates, data on passenger vehicle ownership in Japan, Republic of Korea, Taiwan, and China were regressed against international dollars per capita GDP levels.

TABLE 1 Regression Results for Point Elasticity Estimates Per Capita Income Range (1990 International Income Adjusted Dollars) Constant Coefficient [R.

Unfortunately, the concept of arc elasticity does not allow for an unambiguous ranking of the two markets: For small price intervals around the kink in the demand curves the arc elasticity ranks the elasticity of the first market lower, but for larger intervals and for intervals that do not contain that price, in particular, for intervals around either of the critical prices at which the firm may consider pricing, the ranking is in line with the results from the use of the more common

point elasticity.

The

point elasticity of S with respect to P is given in Equation 9:

The overall elasticity index and the point elasticity can be approximated from unit record household budget data without specifying the form of the concentration curves for budget shares of the commodities under consideration.

MATHEMATICAL EXPRESSION OMITTED] The point elasticity of the jth commodity evaluated at x can then be expressed in terms of p, [alpha], [beta], [[alpha].

Dalton |1920~, concerned with the practical application of the

point elasticity definition, objected that Marshall's ".

The scale elasticity measure, [Epsilon] = [Delta] ln C/[Delta] ln Q, where C is cost and Q output, is a

point elasticity associated with a particular output level and indicates the relative change in cost associated with an incremental change from this output level.