1. Consider the following utility function over goods 1 and 2,
u(x1,x2) = 21n x1 + ln x2.
(a) Derive the Marshallian demand functions and the indirect utility function.
(b) Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1.
(c) Using the functions you have derived in the above, show that
i. the indirect utility function is homogeneous of degree zero in prices and income;
ii. the Hicksian demand function for goods 1 is homogeneous of degree zero in prices.
2. Consider the following utility function,
u (x1, x2) = √x1 + 2√x2
(a) Derive the Hicksian demand functions and the expenditure function.
(b) Derive the indirect utility functions.
3. Consider the following utility function,
u(x1, x2) = min [ 3√x1, a3√x2], a > 0
(a) Derive the Arlarshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? Are the two consumption goods normal goods?
(b) Derive the Hidcsian demand functions. Does the Hicksian demand increase with price?