Interpretations and transformations of scale for the Pratt-Arrow absolute risk aversion coefficient: Implications for stochastic dominance

McCarl's comment to our 1986 article provides an opportunity to correct what has evidently proven to be an exercise in miscommunication. We wish to use this opportunity to address McCarl's stated concerns and to clarify our original message. McCarl claims that our statement, "the magni-tude of the risk aversion coefficient is unaffected by the use of incremental rather than absolute re-turns..., " is equivalent to r(x + c) = r(x), where x is an incremental return and c is the previous wealth level. Such an interpretation of our statement would ignore the distinction between the utility of wealth and the utility of incremental (or annual) returns. We did not mean to imply that wealth is an irrel-evant factor in utility determination. A proper interpretation of our statement, recog-nizing the wealth/incremental returns distinction, would be rw(x + c) = r,/(X), where rw is the risk aversion to wealth and ri, is the risk aversion to incremental returns given previous wealth level c. By way of an example, this means that the local willingness to deviate from a $ 10,000 wealth level is equivalent to the local willingness to deviate from a $10,000 incremental return level when wealth is already $100,000. The equivalence holds because, to the decision maker, it is only an issue of mental accounting as to whether a wealth dollar or incremental dollar (at a given wealth level) is at risk. In each case, wealth plus the increment Mark J. Cochran is currently a visiting associate professor of ag-ricultural economics at Texas A&M University, on leave from th