2. Suppose that Rachel's utility function is U($, y) = 53:0'5y'5. Her income is $50, the price of good :1: is pa,- = $5, and the price of good y is pg = $2.5. (a) Looking at Rachel's utility function only, does she have a general preference for either good? Explain. (b) Using calculus, what is M RS = %:? (c) What is the slope of Rachel's budget constraint? (d) Given your answer to (a) and the relative prices of the goods, can you predict which good she will have more of in her optimal bundle? (e) Suppose she decides to consume a bundle with 6 units of good a: and 8 units of good y. Does the bundle lie on her budget constraint? Explain. (f) Compute the slope of Rachel's indifference curve that passes through this bundle, i.e. compute Rachel's M R3 at this bundle by substituting in for the values of I and 3; into M RS : %:. Is this bundle optimal? How do you know? (g) Using a simple example, explain how Rachel could obtain the same level of utility and save money by modifying her consumption bundle? (h) Solve for Rachel's optimal consumption bundle using the steps from class. (i) Graph Rachel's budget constraint and two indifference curves. One should pass through the su opti un e om part B . e ot er s o e tangent to t e opt1m un e you so v b 'malbdl' Th h huldb h 'alb d1 led for in (h). As always, make sure your graph is superwell labeled