Consider a society with N = 2 people, Anne and Bob. There are two goods in the economy, a market good (x) and an environmental good (e). The environmental good can be thought of as environmental quality and it is a pure public good, so everyone consumes the same quantity of it. The market good is a private good, and it is split between Anne and Bob so that: x = xA + xB. Assume that x = 16 and e = 4. Anne and Bob have different preferences over these two goods, and their utility functions are given by: (,) = 1 2 and (,) = 1 2 a) (10 points) Calculate the utility of Anne and Bob for the following allocations. Note that the allocations are given in the format (xA, xB, e). i. A = (16, 0, 4) - everything to Anne. ii. B = (0, 16, 4) - everything to Bob. ECON 491/591 Dr. Gabrielle Vasey 2 iii. C = (12, 4, 4). iv. D = (8, 8, 4). v. E = (4, 12, 4). b) (4 points) Note that each of the above allocations uses all of the goods available in the market, and therefore