An agent can consume 2 goods, referred to as x and y. Her utility from consuming (x, y) is U(x, y) = xy. Assume the price of x is 1 and y is 2. She has an income of I.

(a) Write down her maximization problem and solve for the optimal values of x and y.

(b) How would the answer change if there was a ration on x so that no more than 1/3 units of x could be consumed?

(c) How would demand change if instead the consumer's utility from consuming (x,y) was U(x,y) = In(x)+ln(y).