Modified version of problem 6.14 from Nechyba text

Suppose Victor consumes gasoline (Good X) and "all other goods" (Good Y). Assume that hispreferences over these two goods are summarized by the utility function U(x, y) = 200x12+ y.Finally, assume that victors annual income is $50,000, Px= $2.50 and Py= $1.

a. Find victors utility-maximizing bundle of X and Y by first computing his MRS(x, y) function and then setting up a system of two equations and two unknowns that the utility-maximizing bundle (x*, y*) must satisfy.Call it bundle A.

b. Now assume that the government imposes a gasoline tax of $2.50 per gallon, effectively raising the price of a gallon of gasoline to $5 per gallon. Using the same method as in part (a), find victors new utility-maximizing bundle.Call it bundle B.

c. How much gasoline tax ($T) does victor pay per year? Briefly explain your answer.

d. Suppose that the government does not need the tax revenue. They were only trying to reduce gasoline consumption for environmental reasons. Therefore, they cheerfully give victor back the gasoline tax revenue he pays in part (c) ($T) as a lump-sum cash transfer, which he is free to spend on more gasoline or all other goods or both. The cash transfer effectively raises his annual income to $50,000 + $T. But he still must pay $5 per gallon of gasoline. e. Using the same method as in parts (a) and (b), find victors newest utility maximizing bundle.Call it bundle C.Does thetax and rebate program succeed in reducing victor's gasoline consumption from part(a)? Does the tax and no rebate program in (b) and have better job of reducing his gasoline consumption?

f. Use U(x, y) = 200x12+ y to determine if victor is just as well off under the tax and rebate program as he is with no tax and no rebate. Show that his utility is lowest with the tax and no rebate.