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However, our results are not limited to this specification and should hold for any quasi-concave consumer surplus function.
The solutions are unique because the consumer surplus function is quasi concave and the corresponding cost function (5) is linear (see Hausmann 1985, p. 1257).
Notice that the consumer surplus function is quasi-concave and thus it implies that optimal consumption is bound, even at zero marginal costs (Hausmann 1985).
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Corresponding to consumers' surplus functions, as long as the consumer's willingness to pay is more than the cost of the purchase of products and the operation of organizations, we generally assume that there always exist organizations which can satisfy the cost constraints they have established under the condition of ignoring interest rates.
Second, the expected consumer's surplus (also derived from the calibrated consumer's surplus function) is used as a predictor for the reported tariff rating.
} end{aligned} (5)Like Iyengar et al. (2008), Lambrecht et al. (2007) and Schlereth and Skiera (2012), we assume a quadratic functional form for the consumer's surplus function as follows u_t(n) = beta_1 n - beta_2 n^2 - k_t(n), (6 where (beta_2>0betare>0) are the individual preference parameters that express the consumer's gross surplus of consumption relative to the monetary units (k).
end{aligned} (40)This completes the individual estimation of a consumer's surplus function.
An exemplary estimation of an individual consumer's surplus function can be found in the Appendix 2. We then evaluate our model in two different ways.
First, given the expected usage under a given tariff (derived from the calibrated consumer's surplus function) is compared to the reported average usage under each given tariff.
The individually calibrated consumer's surplus function can then be used to predict (1) the respondent's stated average usage, (n_{rm avg},) under a given tariff and (2) the respondent's tariff rating.
Open image in new window Fig. 6 Changes in aggregate consumer surplus as a function of changes in the size of the buyer group, s.
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