Consider the utility function U(C'1, 02) = 1n(Cl) + ln(02). (a) Using a program of your choice (say excel or matlab) plot indifference curves in the space (01,02) for I7 = -0.5, 1, and 1.5. Consider values of 01 in the interval (0,1]. Set the range of the vertical axis to [0, 2]. (b) Find an analytical expression for the slope of the indifference curve and show that it is equal to the (negative) of the marginal rate of substitution. (c) Show analytically that the indifference curves are convex. (d) For the 3 indifference curves plotted above, nd the slope of the indifference curve at the point 01 = 1 and the corresponding value of 02. Explain why the indifference curves at 01 = 1 become atter as the level of welfare declines