(a) A consumer's utility function is given by u(x1, x2) = x1x2 for two goods x1 and x2. Suppose that the consumer has $100 of income, and that the prices p1 and p2 of x1 and x2 are p1=$4, p2=$3. If the price of x1 increases to p1=$5, what is the effect on optimal consumption of x1 and x2 for this consumer? Explain your answer with a diagram.
(b) Suppose that utility is now given by u(x1, x2) = min{x1, x2}, and that prices and income are given as in part (a) of this problem. What is the effect of the price increase on optimal consumption? Explain your answer with a diagram.