Problem 1:
Like we did in lecture, think about ds/dr.
a) Plot s(r) and ds/dr as a function of theta. (You don't have to be perfectly to scale, just try to give the general shape.) Explain why this is consistent with what we talked about in class.
b) Do p and r play a role in whether the substitution effect or income effect is larger? Why or why not? (Try to explain conceptually rather than just mathematically.)
Problem 2:
(This problem follows problem 2.13 in the second edition of Romer.) Consider the Diamond model with logarithmic utility and Cobb-Douglas production. Describe how each of the following affects kt+1 as a function of kt:
a) A rise in n.
b) A downward shift of the production function.
c) A rise in alpha.
Problem 3:
(This problem follows problem 2.15 in the second edition of Romer.) Suppose that in the Diamond model capital depreciates at rate delta, so that rt = f'(kt) - delta.
a) How, if at all, does this change in the model affect kt+1 as a function of kt?
b) In the case of logarithmic utility, Cobb-Douglas production, and delta=1, what is the equation for kt+1 as a function of kt? Comment on whether you find this surprising.
c) Consider again values of theta other than 1 (i.e. cases other than log utility). Specifically, consider cases where theta is greater than 1.
Describe graphically and/or in words how the case where delta = 1 differs from the case where delta = 0. Be as specific as possible.