Consider two individuals. Antoine and Belinda, with marginal benefit functions respectively given by: MBA = 10  Q and MBB = 5  Q, where Q represents the amount of a (pure) public good. Suppose the good is supplied at marginal cost of MC = 2Q. 

1. Obtain the aggregate demand function for the public good. Draw a diagram that includes Antoine and Belinda's individual MB functions and the aggregate demand curve. Calculate efficient amount of Q and add it to your diagram with the MC curve. Be sure to label the diagram fully. 

2. Suppose the government wishes to subsidies the provision of the public good. What subsidy should they set per unit of the good supplied? 

3. Now suppose that the marginal damage to Antoine is uncertain. With probability 0.6, he has MBL A = 5  Q, and with probability 0.4 he has MBH A = 17.5  Q. What is the expected aggregate demand for the public good? 

4. If the government sets the subsidy you proposed in part 2, will the supply of the public good be optimal after the uncertainty is resolved? Explain why or why not.