Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all aspects of life in the city. There are only two residents willing to live within citylimits, Abe and Betty. Abe earns an income of 4313, and Bettyr earns an income of 4-40. A traveling salesnian is 1'3 visiting the town, offering odor oonversion units which conveniently inputs garlic odor and outputs clean air. Preferences over clean air ([3] and all private consumption goods {a} for individual 15 are given by: U:- = 5 - Infz + 311(3) The total provision of clear air is given as the sum of individual purchases: C = CA + Ca (+051 when the local government purchases clean air in parts (IQ(5)]. The price of clean air is 2 while the price of all other consumption goods is 1. 1. For both Abe and Betty, calculate each individual's private provision of clean air, taking the other's provision as given. That is, solve for 8,4 as a. furwtion of CE in Abe's optimizatim problem [and solve for Cg as a. function of CA in Betty's optimization problem]. Can you explain the sign on the contribution of the other resident in these response functions? 2. If the government does not intervene, what level of clean air will be provided? How many units are provided by Abe? How many by Betty?11 11 11 3. What is the socially optimal level of clean air provision? (You may assume a utilitarian social welfare function) Does this value differ from that found in (2)? Explain in the context of externalities.4. Suppose the local government is dissatisfied with the level of private provision. The govern- ment taxes both Abe and Betty 30 each in lump-sum fashion (net-of-tax incomes are effectively reduced to 440 and 410 respectively) to provide 30 units of clean air. Both Abe and Betty are free to purchase additional units of clean air if they find it privately optimal to do so. What is the total level of clean air provided? Clearly explain the impact of the taxation/provision by the local government on the private provision by each resident. How does this answer compare to (2)?Vermont Hardwood crafts solid wood furniture using a combination of time-tested hand construction and modern finishing techniques. Residual wood finishing chemicals are washed away as run-off and deposited in the nearby lake, a favorite fishing site for locals. A variety of technologies, including high volume, low pressure sprayers and on-site solvent recovery sills are available for implementation. These technologies allow the manufacturer to reduce chemical emissions at a cost: Ci(a) = 20 - a2 where a is the level of pollution abatement. A city planner determines that the benefit to the residents of pollution abatement is 10 per unit. 1. Sketch a graph depicting the private marginal costs and benefits of abatement, and label the private market equilibrium. On the same set of axis, sketch the social marginal costs and benefits of abatement, and label the efficient outcome. Indicate the DWL if the city takes no action.\f3. If the city institutes a per-unit tax on chemical emissions, what specific tax (7*) will reach the socially optimal amount of abatement?4. Suppose that the planner institutes the per-unit tax calculated in (b). Assume that the true costs of abatement are revealed as Co(a) = 20.a2 - a. Illustrate the problem graphically and indicate the DWL relative to the social optimum. What level of abatement will be undertaken by the firm? Calculate the DWL.5. Suppose instead that the planner institutes a mandatory minimum abatement at the socially optimal level found in (2). Again, assume that the true costs of abatement are revealed as 9 C2(a) = 20 . a2 - a. Illustrate the problem graphically and indicate the DWL relative to the social optimum. What level of abatement will be undertaken by the firm? Calculate the DWL