7. Consider the model where an individual has wealth k which they can either save or consume. If they save it, they receive a fixed and exogenous return r. The instantaneous utility function is given by: u(c, k) = c + a(k) where c is consumption, k is wealth, and a(k) is a function that defines the utility that an individual gets from holding wealth. The growth in wealth is given as the returns on wealth rk, plus income from working z(t), minus consumption c(t). a. Write out the differential equation for wealth. b. For an infinite time model, set up the optimal control problem with discounting at a rate 8. c. Write the current-valued Hamiltonian of this problem. d. Derive the steady-state level of consumption.

7. Consider the model where an individual has wealth k which they can either save or consume. If they save it, they receive a fixed and exogenous return r. The instantaneous utility function is given by: u(c, k) = c + a(k) where c is consumption, k is wealth, and a(k) is a function that defines the utility that an individual gets from holding wealth. The growth in wealth is given as the returns on wealth rk, plus income from working z(t), minus consumption c(t). a. Write out the differential equation for wealth. b. For an infinite time model, set up the optimal control problem with discounting at a rate 8. c. Write the current-valued Hamiltonian of this problem. d. Derive the steady-state level of consumption.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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