Question 2 (26 points): Suppose an individual's utility function for two goods X and Y is given by U(X,Y) = X(1/2)y(1/2). Denote the price of good X by P., price of good Y by Py, and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency condition for the utility maximization problem of the individual. (Very Important: In the questions below you must show the steps. In particular, you must clearly write the equations from which you get your answers. Otherwise, you are not going to get any credit.} d) (6 points) Suppose P, 2, P, 1, and /= 100. Find out the utility maximizing amounts of X and Y consumed by the consumer. e) (5 points) Now suppose the price of X, P, increases to 4 while Py=1, and /= 100. What are the new levels of demand for X and Y? f) (6 points) Decompose the total change in demand for X resulting from a price increase from 2 to 4 into the income and substitution effects.