20 points) Katie, a consumer with a fixed income (m), only consumes burgers and pickled cucumbers (x1 and x2) and firmly believes that they should be consumed in fixed proportions: two burgers with three pickled cucumbers.
(a) Find the utility function that represent Katie’s preferences. Are they homothetic? Explain. 5 points
(b) Write and solve the consumers utility-maximization problem to find her demand functions, x1(p1, p2, m) and x2(p1, p2, m).
(c) Using your previous results, try replacing the x1 and x2 in the Utility function by the demand functions x1(p1, p2, m) and x2(p1, p2, m). This creates a new ”indirect utility function” that is a function of only prices and income, v(p1, p2, m).