Pankti consumes two goods, x and y. Her utility function is given by
U(x, y) = ln(xy).
(a) Are Pankti’s preferences homothetic? Explain.
(b) Suppose when Pankti’s income is 12, her optimal bundle consists of 2 units of x and 6
units of good y. Without solving for Pankti’s Marshallian demands for x and y,
determine how her consumption of x and y would change if her income doubled
(holding constant the prices of the goods). Justify your answer as well as you are able.
(c) Find an expression for Pankti’s indirect utility function, V (px, py, m), using the
method of Lagrange multipliers. Confirm your answer to part (b) using the
Marshallian demands you derive in the process of solving the optimization process.
(d) Suppose the price of good x is 2 and the price of good y is 2. Find Pankti’s utility
when her income is 24. Now suppose the price of good x doubles to 4. How much extra
income does Pankti need to obtain the same level of utility she had prior to the price
increase?
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