. Consider the following utility function over goods 1 and 2, u (x1,x2)=√√√In A + alnæı + (1 − a) Inx2 where A 0 and a € (0, 1). (a) [15 points] Derive the Marshallian demand functions and the indirect utility function. (b) [15 points] Show two different ways to derive the Hicksian demand function for good 2. (c) [10 points] Using the functions you have derived in the above, show that the Hicksian demand function for goods 2 is homogeneous of degree zero in prices.

Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?