A concept of optimal quality and an application

Abstract

This paper develops a concept (and a model) of optimal quality so as to determine the level of quality that maximizes both customer's satisfaction and firm's profit. The concept, as developed in the paper, is meant to represent a benchmark for policies aiming to help achieve the optimum for both customers and firms. The paper presents an application of this concept in a private sector-dominated subset of the Turkish healthcare sector and explores the actual and optimal quality-differences in the sector in question. It turns out that actual and optimal levels of quality (as well as those of quantity) in the sector are fairly close to one another, and, to achieve the optimal levels, the sector should increase quality and reduce quantity of the service by a small determinable margin.

Keywords:

• Optimal quality
• optimal quality-quantity frontier

Notes

1. For a summary of the alternative conceptions of quality, see Rao et al. (1996).

2. Juran has made use of some notion of optimality in his concept of quality, but his notion is confined to a limited producer's optimization in the form of cost minimization, excluding customer's optimization.

3. For analytical convenience, we will consider the case of ‘a representative customer’ to analyse the behaviour of the customers of the service x. Similarly firms providing the service x are to be represented by ‘a representative firm’.

4. Customers might, of course, face a case of multiple quantities and multiple qualities. Extending the framework here to the case of multiple-quantity multiple-quality dimensions is not difficult to undertake. For analytical convenience and simplicity, however, we focus, in this paper, on the case with one service with varying quantities and qualities. Here q ₁ and q ₂ could also be conceived to be aggregated proxies for multiple disaggregated quantity and quality dimensions.

5. The second-order conditions are satisfied if the determinant of the bordered Hessian matrix associated with this optimization problem is positive.

6. The second-order conditions are satisfied if the Hessian matrix associated with this case is negative definite.

7. The second-order conditions are satisfied if the determinant of the bordered Hessian matrix associated with this optimization problem is positive. The second-order conditions for an explicitly formulated optimization problem of this kind are worked out in Appendix 3.

8. A proper wording of the overall efficiency condition would be as follows: the marginal utility ratio (i.e. the marginal rate of substitution of q ₁ for q ₂) should be equal to the marginal rate of product transformation of q ₁ for q ₂ along the quality–quantity frontier, which is also equal to the marginal cost ratios.

9. The reason for choosing a log-linear form for the utility function is as follows: the log-linear utility function, which is among the most widely used utility function forms in economics, fits almost perfectly into the set of data we have used. Needless to say, the particular functional form chosen affects the empirical results. As shown in the utility-relevant regression results, R ² is quite high, t-ratios are good, and the coefficients have the theoretically expected signs. Hence, we can reasonably argue that the ‘goodness’ of the empirical results vindicate the appropriateness of the particular utility function form we have chosen.

10. Juran's notion of optimal conformance', which is somewhat close to, but narrower than, the notion of optimal quality defined here, is only cost-based. It does not take into account the demand-based (satisfaction-based) factors. Nor does it take into consideration the resource-based constraints.

11. For technical derivation of these relationships, captured by comparative static derivatives, see Appendix 3.

12. In the measurement of the cost of quality, we also made use of the data on the ratio of quality costs to total revenue.

13. Note that, for a greater amount of resources, maximum quantity would be obtained in combination with a level of quality higher than the minimally accepted level, in which case c would attain a higher value. That is to say, the value of c is based on the amount of available resources.