3. Consider someone who gets utility from consumption in two periods 1 and 2. Her utility function is U = (c1)^(1/2) + (?c2)^(1/2) = ?c1 + ??c2 (a) Suppose ? = 1.

What is the marginal rate of substitution when c1 = 2 and c2 = 8? What is the level of utility? (b) What is the MRS when c1 = 1/2 and c2 = 8? (c) Solve for c2 as a

function of c1 and utility U. This gives the level of c2 which generates utility U for a given c1. (d) Set ? = 1. Plot out two indifference curves. Put c1 on the

horizontal axis and put c2 on the vertical axis. Consider the indifference curve for U = 10 and U = 12. Find the levels of c2 which give this utility when c1 = 1,

4, 9, 16 and 25. Plot the two indifference curves.