Q1. Joan's utility depends on two commodities: her view of the sea and wine. Her utility function is:
U = 24x - 6x2+ 4y
where x = hours of view "consumed" per day
y = wine.
The view is free, i.e. Px = 0. The price of wine Py = 5. Her available income is 10. Assume that Joan does not look at the view beyond the point where it bores her, i.e. when the marginal utility of the view is negative.
(a) Sketch the budget constraint and indifference curves.
(b) What would be her utility maximizing choice of view and wine?
(c) If the view were blocked and she were fully compensated with wine so that she felt no better or worse than at the position chosen in
(b), how much additional wine would she have to be given as compensation?
Q2. Tom's income is $480and he spends it on two goods, X and Y. His utility function is U = XY. Both X and Y sells for $8 per unit.
Calculate Tom's utility-maximizing purchases of X and Y.
(b) How will his utility change if his income decreases by $2.00?
(c) If the price of Y increased to $11.52, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility as in part (a) above?