(a) Formulate the agent's dynamic problem of maximizing her life-time utility with a discounting factor p. (b) Write the Hamiltonian with a co-state variable and the maximum principle conditions. (c) Using the maximum principle conditions from part (b) above, explain the evolution of the co-state variable (i.e.,). 77

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question
I need the full answers of all parts correct and fast please
Question 4.
Suppose that an infinitely lived agent faces the following functions in each period:
Utility function:
u(c) = log(c)
Income (or, output):
y = AkªG1-a
After-tax income allocation:
(1 – t)AKªG²-a = c + k
where c denotes consumption, k denotes capital, i denotes a (constant) proportional
income tax, G denotes government expenditures, and k (= k = 1) denotes investment
in each period. The total population of agents is fixed and normalised to one.
%3D
dt
(a) Formulate the agent's dynamic problem of maximizing her life-time utility with a
discounting factor p.
(b) Write the Hamiltonian with a co-state variable 1 and the maximum principle
conditions.
(c) Using the maximum principle conditions from part (b) above, explain the
evolution of the co-state variable (i.e.,
(d) Using the current valued co-state variable, derive the growth of cons mption
((i.e., 5).
(e) If the government runs a balanced budget (i.e., G = ty), show that the growth
rate of consumption (i.e., )
is a function of t. What is the effect of change in t on
the growth rate of consumption?
(f) Rewrite the expression for the growth rate of consumption derived in part (e) as a
linear first-order autonomous differential equation and find the optimal path of
consumption.
Transcribed Image Text:Question 4. Suppose that an infinitely lived agent faces the following functions in each period: Utility function: u(c) = log(c) Income (or, output): y = AkªG1-a After-tax income allocation: (1 – t)AKªG²-a = c + k where c denotes consumption, k denotes capital, i denotes a (constant) proportional income tax, G denotes government expenditures, and k (= k = 1) denotes investment in each period. The total population of agents is fixed and normalised to one. %3D dt (a) Formulate the agent's dynamic problem of maximizing her life-time utility with a discounting factor p. (b) Write the Hamiltonian with a co-state variable 1 and the maximum principle conditions. (c) Using the maximum principle conditions from part (b) above, explain the evolution of the co-state variable (i.e., (d) Using the current valued co-state variable, derive the growth of cons mption ((i.e., 5). (e) If the government runs a balanced budget (i.e., G = ty), show that the growth rate of consumption (i.e., ) is a function of t. What is the effect of change in t on the growth rate of consumption? (f) Rewrite the expression for the growth rate of consumption derived in part (e) as a linear first-order autonomous differential equation and find the optimal path of consumption.
Expert Solution
steps

Step by step

Solved in 5 steps with 11 images

Blurred answer
Knowledge Booster
Property Damage
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education