Public Goods: Suppose that weather forecast systems require funding in billion-dollar chunks, and that each billion dollars invested in weather forecasting doubles your odds of getting the forecast right—that if you spend nothing your forecast, pure chance, has only a 50% chance of being right; that if you spend $1B your forecast has a 75% chance of being right, that if if you spend $2B your forecast has a 87.5% chance of being right, and so forth.

a) Suppose that for an average person the cost of getting the weather forecast consistently wrong over the life of the system is $100. If there are a million people in the area, how much should the government spend on weather forecasting?

b) Suppose that for an average person the cost of getting the weather forecast consistently wrong over the life of the system is $1000. If there are five million people in the area, how much should the government spend on weather forecasting?

c) Suppose that someone decided it would be a good idea to privatize the weather forecasting system—to have a private company broadcast the forecast over media and internet, and collect money by subjecting people to annoying ads while they listen to the forecast. Would this be sustainable equilibrium or not?