Problem (Demand - Demand functions, necessities and luxuries) Consider a consumer with preferences for x and y captured by the utility function U(x,y) = x(y+100). 1. Let px be the unit price of X, py the unit price of Y and M the consumer's budget and write the expression for the consumer's budget constraint. 2. What is the expression for this consumer's marginal rate of substitution? Given your finding, does the consumer have convex preferences over X and Y? 3. By using the budget constraint and the tangency condition leaving px, py and M indicated as parameters, find the consumer's demand for X and his demand for Y. Keep in mind that these are functions of the prices and the budget M. 4. Does the consumer consider product Y a normal or an inferior good? Does the consumer consider product Y a necessity or a luxury? Now, assume that px = 1 and py = 1. 5. In an X/Y diagram, draw the consumer's income consumption curve