On the assumption a public authority provides a service to the public, that has a value to that public, then there should be an acceptance by that public that that value should be adequately compensated for. Efficiency will be some function of the investment in people and technology and the distribution of power-politics that facilitate its operation. Investment will be a function of the public at large, their access to technology, and the power-politic distribution of their society.

Public policy design is certainly something to look forward for finding a more efficient public service. One of the main values a design process generates is a shared responsability that promotes the citizen participation in the whole policy design process. This shifts the public from being value reviewer to a value generator. This method has been a good start for some countries for having a more transparent and open process, but it has a long way to go before it can be applied in countries with complex and corrupt political environments. If you want to look for a few examples I would recommend a lab that has done incredible public policies based on a Design approach called LIP (laboratorio de innovación publica). This lab is based in the Universidad Católica de Chile and has some great examples.