Problem 4 (Engel curve) Marianne has a utility function over hot chocolate, qi, and marshmallows, 92, of the form U(q, ma) = q q . The respective prices are p and p2, and Marianne's income is Y. a) Derive Marianne's demand curve for hot chocolate. (i.e. solve her constrained utility maximization problem and figure out how much q, she demands, given the prices and the income.) b) Derive Marianne's demand curve for marshmallows. c) Derive the equation for Marianne's Engel curve over hot chocolate. (i.e., express (a) with Y on left hand side.) d) Plot Marianne's Engel curve over hot chocolate. Remember that income goes on the vertical axis and hot chocolate goes on the horizontal axis