I. Car-owners value gasoline because it allows them to produce travel services according to s = I + g, where s denotes travel services produced , g denotes liters of gasoline. The can always choose to produce travel services by walking (which costs nothing), in which case, g = s = I. Car-owners derive utility from travel servicxs via the utility function s) = 310g(s) + (I J) log(r) We can think of zr as expenditures on goods other than travel services, so that the price of zr is I _ The car-owner has income equal to y, and gasoline costs p Yuan/liter. (I) Solve the car-owner's Marshallian demand function for gasoline. IGpt] (2) Suppose .3 = 0.01, and p = 6 Yuan/ liter, below what level of income will the car-owners choose to walk? 12ptJ (3) Suppose there are 200 million in China and assume they are identical with the same utility function given above (with = 0.01) and an annual income of Yuan. For the car-owners, ive realize we can approximate their relation betwcxn s and g simply as s = g. Using this approximation, what would be the aggregate market gasoline demand function (measured in billions of liters, i.e., 109 liters)? [2pt] (4) InstCQd of assuming all car-owners have the same income, we assume their incomes are distributed normally as N(60000, i.e., with mean 60,000 Yuan and standard deviation 1000 Yuan. What then would be the market demand function for gmsoline? 12pt] The following questions build on the assumptions and approximations made in (2) and (31. (5) Now suppeN' the government imposes a gasoline tax of 3 Yuan/lit,er. As a result, the net price faced by car-owners increases by 2 Yuan/liter (i.e., from G to 8 Yuan/liter). Assume that the supply of gasohne is a linear function of its price. Solve for the market supply function. [2ptl (G) How much revenue docs the government realize from the tax? What are the tax incidences for consumers and producers? [2pt] (7) How much profits are lost by the gas industry as a consequence of the tax? [2ptl (8) Calculate the loss in consumer surplus (as defined in our textbook) due to the tax. [2pt] (9) Calculate the total government expenditure that is needed to compensate the car-owners that their utility stay unchangexl after the tax (i.e., the compensating variation). 14ptl [Hint: try to simplify the equation as much as possible before you use a calculator!] (10) Compensating variation is the more accurate measure of the impact on consumer's welfare than the change in consumer surpltus. Compare the two and discuss why, in applied work, we sometimes use the change in consumer surplus instead of the compensating variation for welfare analysis? The sum of the compensating variation and profits lost provide one measure of the welfare associated with the gasoline tax. Compare this total to the revenue produced by the tax. Which one is larger? What does it imply? [2pt] [Hint: you may still answer this question with good reasoning and get partial/full credit even if you didn't manage to get the coriu:t numbers for