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)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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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