2. Suppose the solution to a consumer's utility maximization problem is the following indirect utility function: V (p1, p2, M) = (PIP2)-1/2 a. State in words what the indirect utility function measures. b. Derive the Marshallian (uncompensated) demand functions for r, and 12. Explain your method. c. Derive the expenditure function. d. Derive the Hicksian (compensated) demands for a, and x2. Explain your method. e. Suppose p1 = 1, p2 = 1, M = 100, and there is a per unit tax of $1 on good 1. Caluclate the CV, EV, and change in consumer surplus. f. Calculate the tax revenue generated from the per unit tax. g. How much over and above the tax revenue raised would the consumer be willing to pay to have the tax removed? h. How much worse off is the consumer in utilities by raising the revenue via a per-unit tax on good 1 as opposed to a lump-sum tax on income? i. How much over and above the tax revenue raised must the consumer be paid to leave her as well off as before? (Equivalently, what would be the deficit a government would run if it compensated consumer enough to leave her welfare under the per-unit tax equal to her pretax welfare?)