Assume a comsume with the utility funciton
U = U(x,y) = X2Y2
and the typcial budget constraint
M = PxX + PyY
a. Set up the constrained maximization problem and derive the first-order conditions.
b. Derive the consumer's demand for X and Y in terms of parameters.
c. Derive the own-prices of elasticiites of demand. Do the demands obey the law of demand?