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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Hi, could you help me solve 1-1.3.?
Using a diagram, draw the outcome of optimal choice using an indi↵erence curve and the individual’s lifetime budget constraint.
Consider the household model that you have seen in class but now assume that the goal of the household is to consume twice as much in period 2 as in period 1. She earns $100 in the first period and $150 in the second period. The interest rate is 5%. What is her optimal saving in the first period? Note: Type in your answer approximated to two decimal points, i.e., your answer must be of the form "999.99". I will not be able to fix correct answers that were entered incorrectly, such as "999.999" or "999,99" or "999". In case the last digit in the correct answer is zero, e.g., "999.90" or "999.00", Blackboard will automatically delete it and you should not do anything about it.
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