Consider that there are only two types of people in the market for pressed juices (J) and yogurt (Y): the Montagues and the Capulets. There are 1000 individuals of each type of person. Suppose that the Montagues' preferences for juice and yogurt can be expressed by the following utility function U(J, Y) = J^1/2Y^1/2. The Capulets' preferences are the following U(J, Y) = 2J + Y. Further, suppose that the price of pressed juice is Pj, the price of yogurt is Py, and income is I.

(a) (5 points) Find the utility-maximizing consumption choice of pressed juice and yogurt for a single Montague as a function of prices and income.

(b) (5 points) Find the utility-maximizing consumption choice of pressed juice and yogurt for a single Capulet as a function of prices and income.

(c) (5 points) State whether (in this problem) juice and yogurt are ordinary, normal, inferior, and/ or Giffen goods. Briefly explain.

(d) (5 points) Suppose that all Montagues' income is $10 and Capulets' income is $5. Write an equation for the market demand for juice. Now pick three or four points to sketch the demand for juice.