Problem 2: The Golden Rule Consider the SGM studied in class. We found an explicit expression for its steady state sA k, = k* = (1) n+8 Let & = denote consumption per capita. As shown on the slides, the steady state level of c, call it c* = y*- i*, is given by - ») A () c" = (1 (2) n+8 Find an expression for the saving rate smax that maximizes c". This is often referred to as the golden rule saving rate. Plot c as a function of s. Can you provide a brief intuition for why it is bell-shaped? Namely, why at the beginning a higher saving rate increases c", but passed a certain threshold c starts to decline?
Problem 2: The Golden Rule Consider the SGM studied in class. We found an explicit expression for its steady state sA k, = k* = (1) n+8 Let & = denote consumption per capita. As shown on the slides, the steady state level of c, call it c* = y*- i*, is given by - ») A () c" = (1 (2) n+8 Find an expression for the saving rate smax that maximizes c". This is often referred to as the golden rule saving rate. Plot c as a function of s. Can you provide a brief intuition for why it is bell-shaped? Namely, why at the beginning a higher saving rate increases c", but passed a certain threshold c starts to decline?
Chapter1: Making Economics Decisions
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Problem 2 - Macroeconomics - please help.
Transcribed Image Text:• decreasing marginal productivities for both capital K and labor N
Problem 2: The Golden Rule
Consider the SGM studied in class. We found an explicit expression for its steady state
sA
k, = k* =
n+ 8
(1)
Let = denote consumption per capita. As shown on the slides, the steady state level of c, call it
c* = y* - i*, is given by
SA
c* = (1 – s) A
(2)
n+ 8
Find an expression for the saving rate smax that maximizes c". This is often referred to as the golden rule
saving rate. Plot c as a function of s. Can you provide a brief intuition for why it is bell-shaped? Namely,
why at the beginning a higher saving rate increases c", but passed a certain threshold c* starts to decline?
Problem 3: Solow Model with Government Spending
Consider the SGM presented in class, with a little twist. Assume that a fraction 0 <h < 1 of output is
used for public spending, G; : namely, G = hY. Assume that h < s.
Summarizing, we have the following set-up:
1
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