Imagine that you have been asked to buy the food for a cookout, where your friend will be cooking hot dogs (x) and hamburgers (y). Let your preferences over these two products be represented by u(x, y) = xy. Suppose that we do not yet know the price of the goods, and so we can write the prices as pr and py. Finally, let M represent the amount of money you have. (a) Derive your demand for x and for y. Be sure to show all of the work involved in this derivation. (b) (2 points) Is your demand elastic, inelastic, or unit elastic? How would you explain what this means to someone who has not studied managerial economics? (c) (4 points) What is the income elasticity of x? Show your work. (d) (2 points) What is the cross-price elasticity of x? Show your work. (e) (2 points) What does the cross-price elasticity of x tell us about the income and substitution effects for x and y in this case?