Tyrion consumes food (F) and wine (W). His utility function is U (F, W) = ln (F) + 2W. Let Pdenote the price of food, and throughout the question the price of wine is set at 1. Tyrion's income is Y.

(a) Find Tyrion's optimal choices of food and wine as a function of Y and P . [7 marks]

(b) Tyrion's wife tells him he'd better lay off the wine. Assuming his utility function is still asabove, for what values of income Y will Tyrion not buy any wine? [3 marks]