9. (40 points) Three homeowners (Brienne of Tarth, Sansa Stark, and Rhaegar Targaryen) reside on the banks of a contaminated lake. The quality of the lake improves as the level of contaminant in parts per million (ppm) decreases. The table below provides information on the homeowners' willingness-to-pay (in discrete form) for improved quality of the lake and on the cost (in discrete form) of cleanup of the lake. a. (20 points) What are the net benefits to Brienne of Tarth, Sansa Stark, and Rhaegar Targaryen if: i. Brienne of Tarth privately cleans up the lake till the equilibrium level? ii. Sansa Stark privately cleans up the lake till the equilibrium level? iii. Rhaegar Targaryen privately cleans up the lake till the equilibrium level? b. (15 points) Suppose the lake is cleaned up till the socially efficient level and the total cost of cleanup is divided equiproportionately amongst the three homeowners. Which homeowners will be better off? c. (5 points) What does your answer tell you about sharing the costs of public goods? Brienne of Tarth Level of Contaminant Marginal Willingness-to-Pay (Rupees per ppm) Sansa Stark Rhaegar Targaryen Marginal Cost of Cleanup (ppm) (Rs per ppm) 4 11000 6000 3000 5000 3 8500 3500 2000 6500 2 7000 1000 1500 8600 1 5500 0 1000 15000 0 4500 0 500 24000 5