3 If z% > z%a , set zi = z%a and z%u = z( 1. Otherwise, set zi = z\ 1 and zu = za.
4 Iterate until \ (zi — zU)| < c where c is arbitrarily small.
von Haefen, Phaneuf, and Parsons show that the strict concavity of the utility function implies the algorithm will find the unique solution to the consumer's problem. Plugging the optimal solutions into (3.1) allows the analyst to evaluate the consumer's utility conditional on (p1, Q1, /3t, Et) and income. Nesting this algorithm within the numerical bisection routine that iteratively solves for the income compensation that equates utility before and after the price and quality change allows the analyst to construct the individual's Hicksian compensating surplus conditional on (3t, Et).
Building on von Haefen, Phaneuf, and Parsons' numerical approach, von Haefen (2004a) has recently developed a more efficient numerical algorithm that relies on expenditure functions and the explicit definition of CSH in equation (2.5). The computational savings arising from his approach are substantial; whereas von Haefen, Phaneuf, and Parsons' numerical approach requires the analyst to solve roughly two dozen constrained maximization problems, von Haefen's approach requires that the analyst solve only one constrained minimization problem.
Under additive separability the generic Kuhn-Tucker conditions for the individual's expenditure minimization problem are equation (3.12) and
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