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The structure of the new fund appears to be a highly promising model. As the first fund of its size to use this model, close monitoring is important to ascertain whether the extremely positive predictions will materialise on a timely basis. If it operates according to plan, the model might be a blueprint for other regions facing similar issues. Having succeded in launching a pilot project in the International Year of Microcredit, that achieves a lasting improvement of living conditions for large numbers of households quickly, cost-efficiently and in a sustainable fashion where there is a great gap between human capital and investment capital gives this year an additional highlight. Against the backdrop of the Millennium Development Goals this effort might be among the desperately sought solutions for poverty reduction.

Returning to our initial question, the quality of MFIs’ assets tends to reinforce the view that there is no “micro-bubble” in the sector. The capacity of Latin American MFIs to maintain good portfolio quality in times of crisis should reassure investors seeking confidence in the risk-return profile of microfinance investments. The main risk, as shown by the Argentinean case, is liability management. Currency mismatches and liquidity issues are progressively being addressed and should remain at the centre of our attention. The heavy concentration of investments in a few MFIs is becoming a risk that will probably continue to grow and that requires further public-private coordination. The best way to move forward is to adopt innovations such as currency hedging, emergency liquidity funding and credit bureaus without undermining the distinct methodologies and structures MFIs have created, which contrast to those of typical commercial banks.

In summary, microfinance entered a critical phase of consolidation in 2005. It will no longer be sufficient for the majority of MFIFs to continue simply as fundraising and investment institutions. A more pioneering role is in order. The “frontier of microfinance” has not yet reached a point at which it is widely regarded by private investors as a credible and efficient financial product. It has not yet sufficiently penetrated the poorest and most difficult countries, and the agricultural sector. The private sector is not in a position to take the lead in deepening microfinance so that it can address these challenges. This means that the role and fundamental duty of KfW Entwicklungsbank remains that of the promotional investor, stimulating the private sector in close co-operation with our like-minded friends. We face interesting challenges at the new frontier of microfinance.

In this book, we will be concerned primarily with the analysis of the relationship between two or more variables. For example, we will be interested in the relationship between economic entities or variables such as — and , — and in an analysis of demand and supply, — and such as and . If one variable, say , changes in an entirely predictable way in terms of another variable, say , then, under certain conditions (to be defined precisely in Chapter 4), we say that is a function of . A function provides a rule for providing values of given values of . The simplest function that relates two or more variables is a linear function. In the case of two variables, the linear function takes the form of the linear equation = + for ≠ 0. For example, = 3 + 5 is an example of a linear function. Given a value of , one can determine the corresponding value of y using this functional relationship. For instance, when = 2, = 3 × 2 + 5 = 11 and when = −3, = 3 × (−3) + 5 = −4. We will say more about functions in Chapter 4. Linear equations or functions may be portrayed by a straight line on a graph. In this chapter, we introduce graphs and give a number of examples showing how linear equations can be used to model situations in economics and how to interpret properties of their graphs.

In summary, microfinance entered a critical phase of consolidation in 2005. It will no longer be sufficient for the majority of MFIFs to continue simply as fundraising and investment institutions. A more pioneering role is in order. The “frontier of microfinance” has not yet reached a point at which it is widely regarded by private investors as a credible and efficient financial product. It has not yet sufficiently penetrated the poorest and most difficult countries, and the agricultural sector. The private sector is not in a position to take the lead in deepening microfinance so that it can address these challenges. This means that the role and fundamental duty of KfW Entwicklungsbank remains that of the promotional investor, stimulating the private sector in close co-operation with our like-minded friends. We face interesting challenges at the new frontier of microfinance.