John consumes good X and Y. His preferences are represented by the utility function (X, Y) =
Ln X + 2Y. The price of good Y is 1 and the price of good X is PX. His income, M is greater
than 1.
(a) Derive John’s demand for X and Y.
(b) Derive the price elasticity of demand for X.
(c) What will happen to John’s total spending on X when the price of X decreases by 10%?
(d) Suppose the government levys a unit tax on Y, what would be the substitution effect on X
for John?
(e) Suppose John’s income increases by 5%, will his demand for Y rise by more than 5%?
Does John treats Y as a normal good or inferior good?
(f) Suppose the government gives a full remission of the tax on Y to poor consumers and John
qualifies. Will John be as well off as he will before the tax?