ECON6002 Tutorial 2 (Ramsey Model)
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ECON6002
Tutorial 2 (Ramsey Model)
1. 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.
2. 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 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) = ka, rewrite your answer to part (d) in terms of ρ , n, g , θ, and α . (Hint: Use the fact that f\ (k* ) = ρ + θg .)
2022-11-09