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The set-up remains deterministic (i.e., no uncertainty) and has two periods. c is period 1 consumption and c' is period 2 consumption. S is savings, w is wealth, and r is the return on saving. max [w.r.t c, S] {U(c) + W (c') subject to - c + S <= w c' <= (1 + r)S Inada conditions hold max [ w.r.t S] {U(w - S) + W (S(1 + r))} (a) Solve for optimal savings as a function of r and w. (b) Assuming W =  W (c) = U(c) = c^1-γ / (1-γ), γ >= 0, solve for ∂S/∂r and show that if γ f γ > 1, ∂S/∂r < 0; if γ = 1, ∂S/∂r = 0 (c)Try to explain intuitively what these results in (b)

The set-up remains deterministic (i.e., no uncertainty) and has two periods. c is period 1 consumption and c' is period 2 consumption. S is savings, w is wealth, and r is the return on saving. max [w.r.t c, S] {U(c) + W (c') subject to - c + S <= w c' <= (1 + r)S Inada conditions hold max [ w.r.t S] {U(w - S) + W (S(1 + r))} (a) Solve for optimal savings as a function of r and w. (b) Assuming W =  W (c) = U(c) = c^1-γ / (1-γ), γ >= 0, solve for ∂S/∂r and show that if γ f γ > 1, ∂S/∂r < 0; if γ = 1, ∂S/∂r = 0 (c)Try to explain intuitively what these results in (b)

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter5: Business And Economic Forecasting
Section: Chapter Questions
Problem 2E
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The set-up remains deterministic (i.e., no uncertainty) and has two periods. c is period 1 consumption and c' is period 2 consumption. S is savings, w is wealth, and r is the return on saving. max [w.r.t c, S]

{U(c) + W (c') subject to -

c + S <= w

c' <= (1 + r)S

Inada conditions hold

max [ w.r.t S] {U(w - S) + W (S(1 + r))}

(a) Solve for optimal savings as a function of r and w.

(b) Assuming W =  W (c) = U(c) = c^1-γ / (1-γ), γ >= 0, solve for ∂S/∂r and show that if γ f γ > 1, ∂S/∂r < 0; if γ = 1, ∂S/∂r = 0

(c)Try to explain intuitively what these results in (b) 

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