MATH1003 QUANTITATIVE METHODS WITH ECONOMICS S2 2022
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MATH1003 QUANTITATIVE METHODS WITH ECONOMICS
S2 2022
Background information + Task Description
A mobile food van is known for its takeaway menu featuring local produce. The amount of produce harvested varies each year. There can be good years, average years and bad years. In average years, the mobile food van operator is able to source a reliable and stable amount of produce. In good years, the operator obtains an above average amount of produce. This excess produce must be cleared as quickly as possible due to a lack of refrigeration space inside the van. In bad years, the van operator receives less produce than they normally do in average years. The van operator wants to maintain revenue to ensure ongoing employment of staff. To do so:
In bad years, the van operator increases the price of meals.
In good years, the van operator is contemplating the temporary removal of the GST component
from the price of meals to encourage clearance of excess produce.
Your task is to write a report which outlines the mobile food van’s revenue:
During average years with no price changes
During bad years with a $15 price increase per meal; and
During good years with temporary removal of 10% GST
The mobile food van’s supply and demand functions are represented by the following equations:
Demand equation: p = 245 − 12aq
Supply equation: p = 0.000022q2 + 5.5bq + 44
q is the number of customers (in hundreds per year)
p is the price of a meal in dollars.
a and b are coefficients to be chosen as per Step 1 below.
Your report is to be presented in 7 sections using the following structure:
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Title Page (50 words) |
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The title should make it clear what the report is all about. Follow with your name, student number and date of submission. |
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Abstract |
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Write this section last (after you have completed all other sections) |
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(100 words) |
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State the main points of the report. Use simple declarative sentences to state procedures followed, what was achieved and what were the notable results. |
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Introduction (250 words) |
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State the problem or issue being addressed. State the reasons for this report (from the van operator’s point of view). Provide general background information State the goals or intended outcomes of the report. |
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Analysis |
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Briefly describe (in your own words) the mathematical procedures used. Through this |
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(300 words + |
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description, demonstrate you understand how the procedures used led to your |
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calculations) |
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results. Present your algebraic calculations for the three revenue situations. |
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Results |
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Present two Excel graphs. Each graph should feature three lines: |
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(50 words |
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Graph 1 - Original Supply Equation, Original Demand Equation + Adjusted Demand |
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for graph |
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Equation (for Price Increase) |
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and table headings) |
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Graph 2 - Original Supply Equation, Adjusted Supply Equation + Original Demand Equation (for GST removal) After the graphs, present a completed version of the blank table given on the next page. |
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Discussion (400 words) |
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Give your interpretation of the results and in doing so answer the two prescribed discussion points (which are at the bottom of the next page) . |
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Conclusion (100 words) |
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Explain in one paragraph how your report meets the goals or intended outcomes first written in the Introduction. Do not present any new information here. |
Steps required to complete the Analysis
You must describe the steps below in your own words and then present your calculations in the same order as these steps :
1. Obtain two random numbers for a and b between 0.1 and 0.9 inclusive (to two decimal places). Use the Excel random function =Rand() or the RANDOM key on your calculator.
2. Find the equilibrium price and quantity algebraically for an average year (with no price change).
3. Adjust the demand equation for a $15 price increase.
4. Use algebra to find the new equilibrium price and quantity.
5. Adjust the supply equation for the removal of GST.
6. Use algebra to find the new equilibrium price and quantity.
Steps required to complete the Results
1. Use Excel to construct two graphs, each featuring 3 lines:
Graph 1 - Original Supply Equation, Original Demand Equation + Adjusted Demand Equation
for $15 Price Increase (from Steps 2, 3 and 4).
Graph 2 - Original Supply Equation, Adjusted Supply Line for GST Removal + Original Demand
Equation (from Steps 5 and 6).
2. Use your results to complete the following summary tables. Round answers to two decimal places.
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COMPARING AVERAGE + BELOW AVERAGE YEARS |
Average Years |
Below Average Years ($15 price increase) |
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Equilibrium quantity |
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Equilibrium price van would charge without any price change |
LEAVE BLANK |
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Equilibrium price consumer pays |
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Revenue van receives without any price change |
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Revenue van receives with the price change |
LEAVE BLANK |
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2022-07-20