Ivy is a typical student and she spends her $200 allowance on booze (X) and books (Y). Her utility function is given by:
U = 15 XY
and PX = $10 and PY = $5.
(a) Solve for Ivy's optimal purchases of X and Y.
(b) The government believes that the sum of the intelligence on the planet is a constant and the population keeps growing. A tax is imposed on books and the price doubles, i.e. PY = $10. How many books will Ivy purchase now?
(c) Using your answers from (a) and (b) above, calculate Ivy's price elasticity of demand for books and her cross price elasticity of demand for booze with respect to the price of books.
(d) Sketch Ivy's demand curve for books.
(e) If the government had asked Ivy how much of her income, at most she would be willing to give up (say in the form of a lump-sum income tax) to prevent the increase in the price of books, what would her answer be, assuming of course, she does not lie?