In a discussion over the earthquake tragedy that happened in China just recently, killing more than 30,000 people, an Indian friend, Barun Mitra, asked, "In disaster relief, is it a case of market failure so government is seen as the only agency that can provide this service?"
My answer to Barun's question is NO. When Katrina hit New Orleans, I have read that private and voluntary relief work was larger than those given by FEMA + state governments + foreign governments. Here in the Philippines, when super-typhoons kill many people and knock down thousands of houses and trees, private relief is very often very fast, given by civic groups (rotary, lions, masons, etc.), religious and
church groups, media foundations, village associations, etc. This is because there is little if any, mistrust when one gives through these private and voluntary organizations. Where government entities are involved -- city or municipal or provincial or national government, public distrust is high. So government usually gives from its own "calamity fund" and attract little donation from private citizens. In addition, government relief would tend to be late because the Mayor or Governor or the President would sometimes be waiting for some media people to cover their
food and relief distribution.
In terms of weather forecasting, there's a Phil. government bureau doing this, but some people listen to CNN weather, a private news media, for additional info.
Meanwhile, The Foundation for Teaching Economics has created a curriculum addressing the role of the government and the market in dealing with natural disasters.