ECON5068 Assessment Brief 2023/24
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Assessment Brief 2023/24
Please make sure you carefully read and understand the question or task. If you have
unanswered questions, please post these on the course Moodle Discussion Forum, and we’ll respond.
1. Question
Questions are available at the end of this document. Students should answer all questions.
2. Further Details
A. Each group will have three members at the most. The expected duration to solve the questions not accounting for the computational time is 3 hours. Some
questions will involve computation which can take anywhere between few
minutes to a few hours depending on the system used and the algorithm written.
B. Students are free to form their own groups.
C. There is no peer evaluation.
D. Students are advised to meet atleast three minutes. Students are expected to keep record of these meetings.
4. Feedback
For this assignment, group level feedback will be provided via Moodle. Generic (class-level) feedback and grade profiles will be posted on Moodle.
Students can use academic staff office hours for additional feedback on your work.
5. Submitting
Submit your coursework using the named submission link in the Assessment Section of your Course Moodle page. Take care to submit by the deadline or you may face
lateness penalties.
Document creation
1. Please name files in the following way: StudentID_CourseCode_QuestionNo. e.g.
7299019_ACCFIN4029_1. If there is no question choice, use 1 as the default. 2. The file type must be saved as .doc, .doxc, .xls, .xlsx or .pdf.
3. Include your student ID in your document, ideally in the header on each page with
the course code and title, e.g. 2489545_ACCFIN1003_Finance1.
4. The maximum file size limit on Moodle is 230MB
5. The maximum file size limit on Moodle is 230MB.
Referencing and bibliography
For information, please go to theUniversity Library webpage.
If you make use of AI at any point in your research or writing process, no matter at what
stage, you must acknowledge the use of that source/platform as you would any other piece of evidence/material in your submission.
Turnitin
Your coursework will be processed through Turnitin for similarity checking. You can submit a draft of your coursework to Turnitin before submitting your final copy. You will find
information about using Turnitin in the Student Information Point Moodle [USIP/PSIP]
6. Generative AI
Generative AI offers many new opportunities for learning and the development of academic skill although, like any technology, it must be used judiciously. Students should consider the data protection and privacy issues that can be caused by using AI. Consider how your
personal information will be used before signing up to AI tools and ensure you read any data protection policies before interacting with AI. You should not feel pressured into using AI
tools if you are uncomfortable with the data protection or privacy issues. Bear in mind that responses to AI queries can be biased due to the inherent biases present in their training data. This can lead to unfair and discriminatory responses.
Copying (including paraphrasing) AI responses to queries would be considered as plagiarism, as it would for copying the response from any internet search.
Further information can be foundhere.
7. Extensions and non-submission with good cause
Good cause for non-submission, late submission and extension of more than 5 days
We understand that during your studies, events that you cannot control (e.g., death of a family member, personal circumstances, physical and mental ill health, etc.) may impact your ability to perform well in or complete assessments.
If you are experiencing such circumstances, you can submit a good cause claim in MyCampus.
You have five working days from the assessment deadline date to submit your good cause claim. If you are prevented from submitting your claim within five days for good reason, you must detail this in your claim. You will receive an acknowledgement on MyCampus when
you submit. After you have submitted your claim, you have five working days to retract it.
If you have any questions, please contact your subject team:
business-accounting-finance@glasgow.ac.uk
Guidelines
1. You should include your Matlab code in the Appendix. The code should be commented (do not overdo this).
2. Figures should be suitably labeled and titled. You can have them either in the main body or in the appendix.
3. Follow standard guidelines for referencing, there should be a bibliography section listing all the references used.
4. Mathematical equations should be properly formatted. Microsoft Word supports inserting math symbols and equations. If you are familiar with Latex or Scientific Word, you can use these instead.
5. Some questions have word limits, you should strictly adhere to these limits.
Read the group coursework briefing for further information.
There are two questions. You must answer both questions.
1. Consider the problem of a value maximizing firm whose profit function at time t is given by
Π(Kt ) = eA(¯)Kt(θ)
where e is the natural exponent, A(¯) denotes fixed the productivity level, Kt denotes capital and
θ is a parameter representing the elasticity of output with respect to capital. Assume that there is no depreciation of capital, so the law of motion of capital is given as
Kt+1 = Kt + It
where It is investments in capital at time t. The price of a unit of capital good isp and investment is subject to a smooth convex installation cost given by
C(It , Kt ) = 
It(2) ,
where γ is a constant denoting the adjustment cost parameter. Time is discrete and runs to infinity, t = 0, 1 ... ∞ . Firm manager discounts future values with the factor β .
Based on the above information, answer the following two questions:
1.1 Write down the Bellman equation and derive the optimal investment decision condition. Define marginal Q and provide an economic interpretation. How is average Q related to marginal Q for this firm? [20%]
1.2 Solve the Bellman equation using dynamic programming. You can calibrate model param- eters as follows
. β = 0.95, θ = 0.7, γ = 0.2 and p = 1.2. Discretize capital grid with 301 uniformly spaced points in the interval [30, 80]. Constant Productivity Level is A(¯) = 1.5.
Plot value function and investment policy functions. Interpret these graphs. Explain how optimal investment responds to
. changes in the adjustment cost parameter.
. changes in how the firm manager values time.
Answer in not more than 500 words. [40%]
2. Consider a two period firm model similar to the one you studied in Unit 1 modified to include uncertain productivity. In period 1, the firm starts with some capital Kt = K1 that it owns. Within each period, the firm chooses labor Lt at fixed wage rate w and produces output using the production function
f(Kt , Lt ) = θtKt(α)Lt(1) −α t = 1, 2.
where the productivity level θt evolves randomly across periods. In each period, productivity can be one of three possible states:
θ ∈ {θL ,θM ,θH }
representing low, medium and high states respectively. The firm starts period 1 with low pro- ductivity θL . The evolution of productivity is independent through time. The probability of occurrence of each productivity state (in every period) is given by
P(θL ) = 1/5, P(θM ) = 3/5 and P(θH ) = 1/5
The firm decides on investments It in each period which becomes productive capital with one period delay. Capital depreciates every period at the rate of δ . The firm discounts future values with the discount factor β. The firm is liquidated at the end of period 2 and the revenues from liquidation is distributed as dividends. Assume that all prices are constant and normalized to unity.
Based on this information, answer the following two questions:
2.1 What are the state and choice variables in this model? What is the value of the firm? Write down the sequential constrained optimization problem of the firm and derive first order conditions that characterize optimal investment policy. Interpret these equations. [20%]
2.2 Numerically solve for investments using Newton’s method if K1 = 30,β = 0.96,α = 0.33,δ = 0.025, w = 0.25; and θ ∈ {1/2, 1, 3/2} are the low, medium and high state productivity values, respectively. Plot and interpret investment policy function for different values of initial capital K1 . Answer in not more than 250 words. [20%]
2023-11-23