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274 CHAPTER | 9 Price and Substitution Elasticities of Demand price is the highest; again, mid- to late afternoon on a hot summer day, for example. 3. As noted in Berndt (1991, p. 465): Since C and a i , a j appear in the elasticity expressions, computations of these estimated elasticities are based on the estimated parameters and the predicted or fitted values of C and the a i and a j , not on the observed values. It is quite easy to make computational errors when using the above equations. One useful check on elasticity calculations involves the following summation of elasticities, which must always hold: j ij = 0 for all i = 1, ..., n. (9.53) 4. As required by theory, it is necessary to make sure that the estimated cost function is monotonically increasing and strictly quasi-concave in input prices 1 ; that is, one must verify that fitted values for all inputoutput equations are positive and that the n × n matrix of substitution elasticities is negative semidefinite at every observation. 5. Finally, it is important to keep in mind that computed elasticities are based on estimated parameters, which implies that they are stochastic and, as such,