Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Tutorial Questions (Ramsey Model)

ECON 6002/6702

NOTE: The tutorial problems are covered by the online tutor. If you have any ques- tions about the tutorial questions that are covered by the tutor, please post the ques- tions (after you have tried working on the problems) on Ed and the tutor will respond. Please use this as a learning mechanism and not just a channel to get the solutions.

1. Speed of Convergence..  Consider the Ramsey model as seen in class.  Similarly to the first tutorial, this exercise is intended at studying the speed of convergence of an economy towards its steady-state equilibrium.

= .  Show that, to a first order, = ,

where ˜(x) = x − x∗ , and stars denote steady-state variables.  Show all the steps in the calculation.

Interpret ˙˜c˜c

2.  Describe how each of the following affects the ˙(c) = 0 and k(˙) = 0 curves in Figure 2.5 (phase diagram) of Romer’s textbook, and thus how they affect the balanced-growth-path values of c and k:

(a)  A rise in θ .

(b) A downward shift of the production function.

(c)  A change in the rate of depreciation from the value of zero assumed in the text to some positive level.

3. The productivity slowdown and saving. Consider a Ramsey-Cass-Koopmans economy that is on its balanced growth path, and suppose there is a permanent fall in g.

(a) How, if at all, does this affect the k(˙) = 0 curve?

(b) How, if at all, does this affect the ˙(c) = 0 curve?

(c) What happens to c at the time of the change?

(d) Find an expression for the impact of a marginal change in g on the fraction of output that is saved (i.e.  s = ) on the balanced growth path.  Can one tell whether this expression is positive or negative?

(e) Assuming the production function is Cobb-Douglas, f(k) = kα, rewrite your answer to part (d) in terms of ρ, n, g , θ, and α.  (Hint: Use the fact that f′ (k∗ ) = ρ + θg.)