firms (Henriet et al., 2012). These results suggest that modern economies, with global supply chains, limited number of suppliers and small stocks, may be more vulnerable to natural disasters than traditional, close economies. However, detailed information on real-world economic networks is not available, and the available models remain overly simplistic. The impact of disasters on supply chains are tragically illustrated by the recent Tohoku-Pacific earthquake in Japan in March 2011, and its wide consequences on industrial production and exports, especially in the auto industry. As an example, The Economic Times, an Indian newspaper, reported that “ _Japan's Toyota Motor will cut production at its Indian subsidiary by up to 70% between April 25 and June 4 due to disruption of supplies.”_ In theoretical terms, these ripple-effects across sectors can be represented by the fact that capital is non-homogeneous: capital components are not perfectly substitutable within a network of economic activities, and the relative price of different types of capital depends on the relative quantity (again, this is the argument from (Robinson, 1974; Sraffa, 1960). If the stock of capital consists of an ensemble of capital categories that have some complementarity, then the destruction of one component may reduce the productivity of other components and thus have an impact that is larger than what could be expected from the analysis of one component only. One extreme example is the case of a road that is built out of a series of segments between point A and B: if one segment is destroyed, then the road is not usable and the other segments become useless. The output loss due to the destruction of one segment cannot be estimated based on the value of one segment, but requires an analysis of the entire system (the road). The same is true – at various degrees – of the entire economic system: the loss of one component can affect the other component and lead to losses that are higher (or lower) than the value of the asset loss suggests depending on the substitutability. This problem is removed if one assumes that the capital stock is the result of an optimal process of capital accumulation, but this assumption is not valid in post-disaster contexts.

This problem can be illustrated by replacing the classical production function f(L,K) by a function with two types of capital f(L,K1,K2). If there are decreasing returns in K1 and K2, the impact of a given loss K=K1+K2 depends on how losses are distributed across the two capitals. The loss in output is larger if all losses affect only one type of capital, compared with a scenario where the two capitals are equally affected. Because the relative prices of K1 and K2 depend of their quantity, it is impossible to define a total stock of capital as K=K1+K2, and the one-commodity production function is not applicable (Cohen, 1989).

Appendix A illustrates these effects in the extreme case where the production function has no substitution (a Leontief production function). In that case, the destruction by a disaster of a (marginal) amount of one type of capital would lead to a loss of output equal to: Where the { } are parameters of the production function and describe the share of each type of capital in the total stock of capital. If is very small – i.e. if one capital is very small in value but still essential in the production process – then the impact of a minimal asset loss can be very large. Typically, it is the 12