[SOLVED] Assignment 3 Individual Report R

Assignment 3: Individual Report

Assignment 3 is assessed on an INDIVIDUAL basis. Your solutions should be uploaded to Moodle as a single written document, which may contain graphics and mathematics (but which does not just list your code), and which makes clear links to well-labelled MATLAB files which should be uploaded to Moodle (as .m files) at the same time. Your solutions may be in PDF (e.g. generated via LaTeX), Word, or any other appropriate format, but they must  NOT depend on the marker having access to any additional software beyond a PDF reader, Microsoft Word, and a copy of MATLAB. Credit will be given for providing working code, and for providing suitable comments within the code to allow it to be used accurately.

Simply submitting a collection of MATLAB files is not enough.

There are 5 questions in this assignment, with the marks for each question indicated at the end of the question.

Your report needs to be submitted to the VLE submission point by 4pm on Friday 10th January.

Late submission.

Late submissions without penalty are only allowed for participants who have been granted an extension. To request an extension please see the relevant form. on the moodle.

Otherwise, the project is subject to the standard University policy: “Work which is up to one hour late will have five percent of marks deducted. After one hour, ten percent of the available marks will be deducted for each day (or part of each day) that the work is late, up to a total of five days, including weekends andbank holidays e.g. if work is awarded a mark of 30 out of 50, and the work is up to one day late, the final mark is 25. After five days, the work is marked at zero.” For more details, see Guide to Assessment, Standards, Marking and Feedback.

Academic misconduct.

Any collaboration with your fellow students should be avoided. The work submitted for assessment must be yours and yours alone. Remember that there are severe penalties for academic misconduct offences such as plagiarism and collusion. For more details, see

Guide to Assessment, Standards, Marking and Feedback .

Supply and Demand Model

The assessment is based around a supply and demand model introduced in the paper

“ Landscape and flux theory of non-equilibrium open economy” by Zhang & Wang (link – also available at the VLE submission point).  The model is described in section 2.2 of the paper and models the balance of price P and quantity Q in a single market.  It should be noted that these values are the deviation from equilibrium values, so a negative price refers to a price below the equilibrium value. The relevant equations are equation 6 in the paper;

As in the paper, we are assuming that the speeds of adjustment (labelled α,  β   in the paper) are both equal to 1.  The remaining parameters ab, c and d are related to the demand function and supply curve as defined in the paper.  You can refer to the paper in your report, but if you wish to use any of the figures to aid in your answers to the questions then you should produce your version of the figure.  For example, it may be useful to include your own version of figure 1 from the paper.

Question 1

First, we consider the case where supply is linear (i.e. b  =  0).  Find & classify all fixed points using the parameter values a  = −  1,  b  =  0,  c  =  1 & d  = −  1.   Sketch a phase portrait, indicating any interesting features.  Discuss your results in the context of the model.

[20 marks]

Question 2

Considering the full model with (b  ≠   0), produce phase plots of the system for parameter combinations

i)  a  = − 0. 5,  b  =  0. 3,  c  =  0,  d  = − 1.

ii) a  = − 0. 1,  b  =  0. 3,  C  =  0,  d  = − 1.

iii) a  =  0. 5,  b  =  0. 3,  C  =  0,  d  = − 1.

Annotate any relevant features and discuss your results and the main features of the system’s behaviour in the context of the model.  Repeat your analysis of parameter set i) and iii) with C  = −  0. 3, again discussing any interesting behaviour.

[25 marks]

Question 3

Using an appropriate modification, add the effect of seasonality to the model.  Use the parameters from Question 2. iii). Justify and discuss your choice of seasonality, including your choice of parameter values and/or ranges, and explain the consequences of these changes using example trajectories and/or phase plots.

[20 marks]

Question 4

Use an appropriate modification to include noise into the system so that it can be represented as a system of stochastic differential equations (SDEs).  Provide a careful justification for your choice of noise term(s). Use the parameters from Question 2. i)

Discuss the results using example trajectories, including interesting behaviours induced by the noise.

[20 marks]

Question 5

Summarise how your findings could be used by governmental regulators, or by businesses, to guide their actions and ensure stable market behaviours. Your answer should be a maximum of 250 words and should be accessible to a non-specialist audience.

[15 marks]