Consider the Cobb-Douglas utility function: U(x,y) = x^a*y^(1-a) for a \in (0,1). [0 a 1] a. Suppose a = , plot the indifference curve when...

Consider the Cobb-Douglas utility function:

U(x,y) = x^a*y^(1-a)

for a in (0,1). [0 < a < 1]

a.    Suppose a = ½, plot the indifference curve when utility level is held constant at U = 1.

b.    Repeat part a, but suppose that a = ¼.

c.    Repeat part b, but suppose a = ¾.

d.    Looking at the graphs, give an economic explanation for the importance of a.

e.    Compute the Marginal Rate of Substitution, and find its derivative with respect to a. Can you relate this derivative to your plot?

f.     Which of the three indifference curves has the steepest slope. The flattest slope?

g.    Suppose these preferences represent three different individuals, all with the same income and facing the same prices. Which of the three people would you expect to buy the most x? The most y?

h.    Explain the intuition of your answer in terms of each consumers willingness to pay for good y.