ECON 11: Problem Set 3Due October 19, 2016 before 9:30 in classPut name (Last, First), Student ID, and TA Section letter on submissionsExercise 1Suppose that an individual with income I cares about two goods, X and Y . The price of thetwo goods is pXand pY. The individual has the following utility function:U(X, Y ) = X(4 + Y ) (1)a) Find the Marshallian (uncompensated) demand for X and Y .b) Find the indirect utility function.Exercise 2Joseph likes roses (R) and tulips (T ) equally, and views them as perfect substitutes in propor-tion 1 to 1. The price of a rose is $4, the price of a tulip is $2, and Joseph has $20 to spend onflowers.a) How much of each flower will Joseph buy? (Hint: the first order conditions will not help;think about what you would do in this situation.)b) Now, suppose that the price of a tulip rises to $10. How does the consumption of Josephchange?c) What are the Josephs demands for roses and tulips as a function of prices and income{pR, pT, I}? You will have three cases depending on the relationship between pRand pT.d) How much should Josephs income increase to compensate for the rise in the price of roses?(Hint: use the indirect utility function before and after the change)Exercise 3Britney is very fashionable. When she buys a new dress (D), she also needs to buy a hat (H)to match that dress and vice-versa. So, she views the two goods as perfect complements. Theprice of a dress is $15, the price of a hat is $10, and she has $85 to spend.1a) Write down a utility function that represents Britneys preferences over dresses and hats.b) How many dresses and hats is she going to consume? (Hint: the first order conditions willnot help; draw the budget constraint and the indifference curves and look at the highest one thatintersects the budget constraint)c) What is the exact value of Britneys indirect