1.1 Introduction
In this assignment you will take the role of a professional economist, assessing the likely impacts of the proposal detailed in section 2. You will analyse the proposal using techniques developed throughout this course, and prepare a research report detailing your ndings and their implications.
1.2 Formatting requirements
Your assignment must be typed using Microsoft Word, or a similar word processor. The document should have a professional appearance, appropriate to a corporate workplace. Format your assignment as follows:
Use A4 sized paper with all margins at least 2.5cm.
Include a title page as the rst page of your report.
Body text to be 12pt and black. (There is no minimum line spacing.) Include a word count at the end of every section except the analysis section.
All pages, except the title page, to be numbered.
Use headings to indicate sections, and subheadings to provide organisation and structure within a section. (Do not use subheadings in the introduction or conclusion.)
Optional: Save your assignment as a PDF to ensure that your document and equations appear as you intend.
1.3 Grading
There are a total of 100 marks available in this assignment, and the assignment contributes 50% of your grade for Managerial and Business Economics. The marks allocated to each step of the report’s analysis section are detailed in section 3. The marking criteria for the remainder of the assignment can be found in the rubric.
1.4 Scenario
Our client, MirageCorp, is an insurance company considering launching an ‘income insurance’ product in the nation of Aqualand. Income insurance is a product that fully insures a household against changes in income caused by a major injury or illness.
At present, no businesses are selling income insurance products in Aqualand. Initial market research suggests that there are a total of 3,600 households in Aqualand and all of them are interested in purchasing income insurance.
Your client expects that the xed cost of launching the income insurance product will be $2,700,000 per year, and that each policy issued to a customer will cost the company an additional $500 in sales commissions.
1.5 Your task
Your client wants you to analyse the potential market for income insurance and report on the following:
What is the maximum price the company can charge a household for an income insurance policy?
What is the expected pro t (or loss) for the company if it becomes a monopoly provider of income insurance?
Is there a risk that rival insurance companies will also enter the market, selling identical income insurance products? If so, what would be the expected pro t of your client? (You should assume that any competitors would face the same costs as your client.)
1.6 Household preferences
A typical household in Aqualand has an income of $30,000 per year, which they spend on food (good x) and clothing (good y). Their preferences over consumption baskets are represented by the utility function,
U = x1=4y1=4:
The associated marginal utilities are,
y1=4 x1=4
MUx = 4 3=4 and MUy = 4
y3=4:
x
Each household has a 20% probability of experiencing a major injury or illness in any given year. If a household experiences a major injury or illness, its income will be reduced to $4,800 per year.
1.7 Production of goods
In the market for food (good x), there are currently four rms competing in prices, i.e., Bertrand competition. While there is no xed cost of production, each rm’s marginal cost of producing good x is $3.
On the other hand, for good y, there are two rms (Firm A and Firm B) competing in quantities, i.e., Cournot competition. The cost structure is identical for these rms such that each rm has the marginal cost of $6 and xed cost of $5,500,000. As a result, each rm ends up making a pro t of $8,000,000.
2 Report
Your report should be prepared with the following structure:
- Introduction
- Analysis
- Discussion
- Conclusion
The requirements for each section of the report are detailed below.
2.1 Introduction
You need to have a title that makes it clear what this report is about and whom it is prepared for. Your introduction should succinctly and accurately summarises the purpose of your report. You should also outline the methodology employed in your analysis, and your key ndings. The introduction has a 200 word limit.
2.2 Analysis
In the analysis section you must complete each of the steps detailed below. When completing the steps you must:
Type all equations using the ‘Insert Equation’ function (or equivalent).
Show all of your working and include su cient written description for the reader to follow your process.
Note that hand draw gures and equations are not acceptable. There is no word/page limit for the analysis section.
Step 1: Write down the formula for the optimality condition for a typical household (1 mark). (Hint: At the optimum the slope of the indi erence curve is equal to the slope of the budget line, i.e., tangency condition.)
Step 2: Derive an expression for the typical household’s marginal rate of substitution. (1 mark)
Step 3: Find the price of good x and the price of good y in equilibrium. In nding the price of good y, assume that each household’s income is $30,000 with probability 1. (You must explain your reasoning, otherwise you will not obtain any marks.)(4 marks) (Hint: To nd the price of good y, rst use your answers in Step 1 and Step 2 to gure out how much of your income will be spent on each good when your income is $30,000. Then combine this information with either rm’s pro t to determine the price of good y.)
Step 4: Plug in the values you obtained in Step 2 and Step 3 into the formula for the optimality condition (Step 1) to determine the relationship between the quantities of good x and good y. (1 mark)
Step 5: Find the typical household’s optimal consumption basket when its income is $30,000. What is the household’s associated level of utility? (7 marks)
Step 6: Find the typical household’s optimal consumption basket when its income is $4,800. What is the household’s associated level of utility? (7 marks)
Step 7: What is the typical household’s expected utility if it does not purchase insurance? (2 marks)
Step 8: What is the expected payout to the typical household if it does purchase insurance? (2 marks)
Step 9: Calculate the typical household’s risk premium for the income insurance. (9 marks)
(Hint: Express both goods as a function of income, I, in the utility function.)
Step 10: What is a household’s maximum willingness to pay for insurance? (2 marks)
Step 11: Complete any additional calculations that you require to support your recommendation. (4 marks)
2.3 Discussion
Use subheadings to organise the discussion section. Your discussion should address all the issues raised in the scenario. This includes explaining the signi cance of the ndings of your analysis in the context of the scenario, and providing arguments in support of the conclusions of your report. Be sure to base your discussion on the results in your analysis section and avoid assertions or speculation. Use economic terminology as appropriate.
The discussion has a 500 word limit.
2.4 Conclusion
Your conclusion should succinctly and accurately summarises the ndings of your analysis and the implications of these ndings for the scenario. The conclusion has a 200 word limit.