Earn Higher Grades With Instant Assignment Help.Ask Question!

Python Programming
(5/5)

Consider the following macroeconomic model for real business cycles taken from Dejong and Dave

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Problem set 4

Linear algebra

1.     Real business cycles:

Consider the following macroeconomic model for real business cycles taken from Dejong and Dave (2011) Chapter 3:

Suppose that we have a representative household whose goal is to maximize their utility from consumption and leisure over time:

U = E0     β  u(ct, lt)

t=0

where E0 is the expected value at time 0, β is a parameter reflecting the household’s discount rate (time preferences), ct is the household’s consumption at time t, and lt is the household’s leisure time at time t.

For this problem to work, we have to introduce four constraints. The first constraint is that the household produces goods using a Cobb-Douglas production function. That is,

yt = ztkαn1−α

t   t

where yt represents the GDP at time t, zt represents and exogenous (i.e., cannot be optimized or changed) technology stock at time t, kt represents the gross capital stock at time t, and nt represents the amount of labor supplied at time t. The second constraint is that total time spent working and at leisure should add to some fixed constant. Without loss of generality we can define the total to be one (1):

1 = nt + lt

The third constraint is that GDP can be spent in two ways: consuming and investing in future capital:

yt = ct + it

where it is the amount of investment at time t.

kt = it + (1 − δ)kt

The last thing we need to define to make the problem solvable is the utility function. For this we are going to use a constant elasticity of substitution (CES) form. That is,

u(c, l) =1 − ρ

where rho and phi are parameters representing the trade off between happiness from consuming versus leisure in the model.

Your job is solve this consumer’s problem using calculus by maximizing the total utility subject to the constraints defined above. In the end, you should obtain two equations. The first equation will reveal the consumer’s inner-temporal choice between consumption and leisure. The second equation will reveal the consumer’s intertemporal choice between consuming today and consuming tomorrow. If you are struggling, the answer is in Dejong and Dave (2011) Chapter 3.

Programming

2.    Ridge regression:

Write some code which performs L2 regularization. That is, solve OLS with a constraint that the L2 norm of the betas is less than some threshold value.

Attachments:
(5/5)

Related Questions

CSI 1420 Introduction to C Programming & Unix Fall 2018, CRN 44882, Oakland University Homework Assignment 6 - Using Arrays and Functions in C

DescriptionIn this final assignment, the students will demonstrate their ability to apply two majorconstructs of the C programming language – Fu

The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is an

Path finding involves finding a path from A to B. Typically we want the path to have certain properties,such as being the shortest or to avoid going t

Develop a program to emulate a purchase transaction at a retail store. This program will have two classes, a LineItem class and a Transaction class. The LineItem class will represent an individual

Develop a program to emulate a purchase transaction at a retail store. Thisprogram will have two classes, a LineItem class and a Transaction class. Th

SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 1 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

Ask This Assignment To Be Done By Our ExpertsGet A+ Grade Solution Guaranteed

expert
joyComputer science
(4/5)
12 Answers Hire Me
expert
Robert DLaw
(4.8/5)
663 Answers Hire Me
expert
Dr Samuel BarberaStatistics
(5/5)
718 Answers Hire Me
expert
Tutor For YouEconomics
(5/5)
513 Answers Hire Me