Assume a world in which only two goods, X and Y, are available for consumption. Consider an individual for whom u = xy, where u is the level of utility, while x and y are the consumption levels of goods X and Y. A. Use this utility function to derive the (ordinary) demand for good X as a function of its price (PX ) and the individual's income (M). B. Suppose that the individual has an income of $160 per period, and that the price of good Y is $4 per unit. Illustrate and calculate the income and substitution effects on the consumption of good X, assuming that the price per unit of good X rises from $4 to $16. C. If it is possible to avoid this price increase by joining a co-operative for a fixed fee per period, illustrate and calculate the highest fee that the individual would be willing to pay.