2 4. A person's utility function is U =5(In X)+2(InY) (a) Find the marginal utilities of goods X and Y. (b) Find the direct second derivatives and the cross partial derivatives. What do these four derivatives tell us about how: (i) the marginal utility of X changes when consumption of X increases with Y constant; (ii) how the marginal utility of X changes when consumption of Y increases with X constant; (iii) how the marginal utility of Y changes when consumption of Y increases with X constant; and (iv) how the marginal utility of Y changes when consumption of X increases with Y constant? (c) Find the equation of a typical indifference curve, with either Y or X as the dependent variable. Do the indifference curves cut either or both axes? (d) By differentiation, determine the slope and convexity or concavity of the indifference curve. Sketch some indifference curves